Learning Task 1: Write and answer the following in your answer sheet
1. Evaluate the following polynomials in your answer sheet.
f(x) = x4 – 7x2 + 2x - 6
x=1
b. f(x) = 10x3 + 4x2 - 5
x = -3
f(x) = x4 + 5x3 - 2x + 3
a.
at
at
C.
find (2))2
2. Factor each polynomial completely using any method
(x + 1)(x2 – 5x + 6)
b. (x2 - * - 6)(x2 + 6x + 9)
x3 + 3x2 - 4x - 12
a.
C.
LABAR
Answers
Answer:
Evaluating Polynomials:
a. f(1) = -10
b. f(-3) = -239
c. f(2)² = 3125
Factoring Polynomials:
a. (x + 1)(x² - 5x + 6) = (x + 1)(x - 3)(x - 2)
b. (x² - x - 6)(x² + 6x + 9) = (x - 3)(x + 2)(x + 3)(x + 3)
c. x³ + 3x² - 4x - 12 = (x + 3)(x - 2)(x + 2)(x - 2)(x + 2)
A polynomial can be evaluated and factored by long division, factoring and synthetic division methods.
1. Evaluate polynomials
[tex]\mathbf{f(x) = x^4 - 7x^2 + 2x - 6}[/tex]
Substitute 1 for x
[tex]\mathbf{f(1) = 1^4 - 7(1)^2 + 2(1) - 6}[/tex]
[tex]\mathbf{f(1) = 1 - 7 + 2 - 6}[/tex]
[tex]\mathbf{f(1) = -10}[/tex]
[tex]\mathbf{f(x) = 10x^3 + 4x^2 - 5}[/tex]
Substitute -3 for x
[tex]\mathbf{f(-3) = 10(-3)^3 + 4(-3)^2 - 5}[/tex]
[tex]\mathbf{f(-3) = -270 + 36 - 5}[/tex]
[tex]\mathbf{f(-3) = -239}[/tex]
[tex]\mathbf{f(x) =x^4 + 5x^3 - 2x + 3}[/tex]
Substitute 2 for x
[tex]\mathbf{f(2) =2^4 + 5(2)^3 - 2(2) + 3}[/tex]
[tex]\mathbf{f(2) =16 + 40 - 4 + 3}[/tex]
[tex]\mathbf{f(2) =55}[/tex]
Square both sides
[tex]\mathbf{f(2)^2 =3025}[/tex]
Hence, the results of evaluating the polynomials are [tex]\mathbf{f(1) = -10}[/tex], [tex]\mathbf{f(-3) = -239}[/tex] and [tex]\mathbf{f(2)^2 =3025}[/tex]
2. Factor the polynomials
[tex]\mathbf{(x + 1)(x^2 - 5x + 6)}[/tex]
Expand
[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x^2 - 2x - 3x + 6) }[/tex]
Factorize
[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x(x - 2) - 3(x - 2) )}[/tex]
Factor out x - 2
[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x - 3)(x - 2) }[/tex]
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9)}[/tex]
Expand
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x^2 +2x - 3x - 6)(x^2 + 3x +3x + 9)}[/tex]
Factorize
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = [x(x +2) - 3(x + 2)][x(x + 3) +3(x + 3)]}[/tex]
Factor out x + 2 and x + 3
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = [(x - 3) (x + 2)][(x + 3)(x + 3)]}[/tex]
Remove square brackets
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x - 3) (x + 2)(x + 3)(x + 3)}[/tex]
[tex]\mathbf{x^3 + 3x^2 - 4x - 12}[/tex]
Factorize
[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = x^2(x + 3) - 4(x + 3)}[/tex]
Factor out x + 3
[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x^2 -4) (x + 3)}[/tex]
Apply the difference of two squares
[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x -2)(x+2) (x + 3)}[/tex]
Hence, the results of factoring the polynomials are [tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x - 3)(x - 2) }[/tex], [tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x - 3) (x + 2)(x + 3)(x + 3)}[/tex] and [tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x -2)(x+2) (x + 3)}[/tex]
Read more about polynomials at:
https://brainly.com/question/11536910
Related Questions
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Answer:
-3
Step-by-step explanation:
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It is easy all you have to do is 15-3 because 1+2=3
Calculate the correlation coefficient, r, for the data below.
Answers
This question is incomplete, the complete question is;
Calculate the correlation coefficient, r, for the data below.
X = -10 -8 -1 -4 -6 -7 -5 -3 -2 -9
Y = -15 -13 4 -4 -7 -11 -6 -2 1 -13
Answer: the correlation coefficient, r, for the data is 0.9896
Step-by-step explanation:
Given the data in the question;
correlation coefficient r = ?
we know that, C_Coeff is;
r = [ (Zn(∑xy) - (∑x)(∑y) ] / [ √[( n∑x² - (∑x)²) ( n∑y² - (∑y)²)] ]
so ;
X Y X² Y² XY
-10 -15 100 225 150
-8 -13 64 169 104
-1 4 1 16 -4
-4 -4 16 16 16
-6 -7 36 49 42
-7 -11 49 121 77
-5 -6 25 36 30
-3 -2 9 4 6
-2 1 4 1 -2
-9 -13 81 169 117
∑ -55 -66 385 806 536
now we substitute our values into the formula
r = [ (10×536 - (-55)(-66) ] / [ √[( 10×385 - (-55)²) ( 10×806 - (-66)²)] ]
r = 1730 / √( 825 × 3704 )
r = 1730 / √3055800
r = 1730 / 1748.0846
r = 0.9896
Therefore the correlation coefficient, r, for the data is 0.9896
What is the image of (−8,−8) after a dilation by a scale factor of 1/2 centered at the origin?
Answers
Answer:
(-4,-4)
Step-by-step explanation:
Since this is centered at (0,0), we have to multiply the x and the y coordinates by the scale factor.
-8 × 1/2 = -4
Solve.
-|-10|+ (-3) + |5|=
A. -18
B-8
C. 8
D. 12
E18
Answers
Answer:
The answer is for-|-10|+(-3)+|5|=-8 which is B
The triangle is rotated 90 degrees clockwise around the pount (0,0)
Answers
Answer:
(2,6)
Step-by-step explanation:
Option:B
The triangle is rotated 90 degree clockwise around the point (0,0). The point is (-6,2) is made to rotate. The image so formed is at the point (2,6).
What is the Distance between 6+3i, 6-3i
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2-8..........
ITS UR ANSWER!,✌✌
please answer asap no trolls!
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Answer:
Yes.
Step-by-step explanation:
3.5 + 5.5 > 7.8
Can y’all help me solve this.
Please!!!!!!!
Answers
9514 1404 393
Answer:
all statements are true
Step-by-step explanation:
The line 4y=-16 can be rewritten to standard form as ...
y = -4 . . . . a horizontal line with all points having y-coordinate = -4
__
The line 3x = 27 can be rewritten to standard form as ...
x = 9 . . . . a vertical line with all points having x-coordinate = 9.
__
All of the statements about these lines are true.
Convert the mixed number below to an improper fraction.
523
Answers
Answer:
17/3
Step-by-step explanation:
if you meant 5 2/3
Multiply the denominator by the whole number
3 x 5= 15
Add the answer above to the numerator
15 + 2= 17
Write the answer from above over the denominator
17/3
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Antoine is drawing a scale map of the park he uses a scale of 1cm : 15 paces. A pond is 75 paces from the front gate of the park how far is the pond from the gate on the map
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Answer:
5
Step-by-step explanation:
i just did it
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Answers
3x3=9
4x4=16
14 is between 9 and 16.
Find the slope intercept equation of the line
PLEASE HELP ME!!!!!
Answers
Answer:
y = -x + 6Step-by-step explanation:
Slope-intercept form:
y = mx + b, where m is slope and b is y-interceptWe see on the graph y-intercept is b = 6, point (0.6)
To find the slope we need a second point, choosing point (5, 1)
Using slope formula:
m = (1- 6)/(5 - 0) = -5/5 = -1So the line is:
y = -x + 6Answer:
y = -4/5x + 5
Step-by-step explanation:
the formula for slope intercept is y=mx+b.
m represents the slope of the line and b is the y intercept. all you have to do is replace those variables.
the y intercept is the point where the line crosses the y-axis (the line going up and down on the graph). (0,5) is the y intercept and so 5 would replace b in y=mx+b
so far we have y=mx+5
The slope is the vertical change between two points is called the rise, and the horizontal change is called the run. Starting from a point on the line you would move vertically until you're in line with another point. In this case, let's just use (0,5) from before. You would go up four to line up with a point. Then, move horizontally to meet up with the point and count the units, which is five here. And so, the slope would be 4/5.
And then you get the equation:
y=4/5x+b
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Answer:
no
Step-by-step explanation:
no
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X=22
14 plus 8 gives you x
[tex]\frac{x}{20} =\frac{14}{8} \\x=\frac{14}{8} \times 20=35[/tex]Answer:
35
Step-by-step explanation:
Name the factors in each of the following problems
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What is 42= -7 × (z - 3)?
Answers
Answer:
z=-3
Step-by-step explanation:
Answer:
z=3
Step-by-step explanation:
42=−7(z−3)
Simplify both sides of the equation.
42=−7(z−3)
42=(−7)(z)+(−7)(−3)(Distribute)
42=−7z+21
Flip the equation.
−7z+21=42
Subtract 21 from both sides.
−7z+21−21=42−21
−7z=21
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-7z/-7=21/7
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Between what two multiples of ten is 328
Answers
Answer:
It's between 32 (which is 320) and 33 (which is 330).
Step-by-step explanation:
328 / 10 = 32.8
Multiply The polynomials. (3x^2+4x+4)(2x-4)
Answers
Answer:
6x^3 - 4x^2 - 8x - 16
Step-by-step explanation:
6x^3 + 8x^2 + 8x - 12x^2 - 16x - 16
combine
6x^3 - 4x^2 - 8x - 16
A florist sells 3 roses for a total of $10. Each rose costs the same amount. What is the cost of 12 roses?
A. $9.60
В. $10.40
C. $14.00
D. $15.00
Answers
Answer:
C
Step-by-step explanation:
Answer:
Step-by-step explanation:
if 3 roses costs 10 dollars
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The ______ of a function consists of set of all output values
Answers
Consider a binomial experiment with n = 5 trials where the probability of success on a single trial is p = 0.30. (a) Find P(r = 0). (b) Find P(r ≥ 1) by using the complement rule.
Answers
Answer:
0.16807 ; 0.83193
Step-by-step explanation:
Given that:
Number of trials, n = 5
Probability of success, p = 0.30
P(r = 0)
Using the binomial probability relation :
P(x =r) = nCr * p^r * (1 - p)^(n - r)
(a) Find P(r = 0).
P(r = 0) = 5C0 * 0.3^0 * (0.7)^(5- 0)
= 1 * 1 * 0.16807
= 0.16807
(b) Find P(r ≥ 1) by using the complement rule
P(r ≥ 1) = 1 - P(r = 0)
P(r ≥ 1) = 1 - 0.16807
P(r ≥ 1) = 0.83193
How many ways can Rudy choose 4 pizza toppings from a menu of 14 toppings if each topping can only be chosen once
Answers
Answer:
24,024
Step-by-step explanation:
Calculation for How many ways can Rudy choose 4 pizza toppings from a menu of 14 toppings
The 4 pizza toppings from a menu of 14 toppings will be 14,13,12,11
Hence,
14*13*12*11=24,024
Therefore the numbers of way Rudy can choose 4 pizza toppings from a menu of 14 is 24,024
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Answer:yes your Most definitely correct
Step-by-step explanation:
jester has a piece of wood measuring 1 and 2/3 m.he needs to cut in pieces measuring 3/4 m. long.how many pieces of wood did jester cut.
Answers
Answer:
2
Step-by-step explanation:
Given that,
Jester has a piece of wood measuring 1 and 2/3 m = 5/3 m
He needs to cut in pieces measuring 3/4 m
We need to find the number of pieces. Let there are x no. of pieces.
[tex]x=\dfrac{\dfrac{5}{3}}{\dfrac{3}{4}}\\\\=\dfrac{5}{3}\times \dfrac{4}{3}\\\\=2.23\[/tex]
or
x = 2
So, he will cut it into approx 2 pieces.
there are 36 playing tag at recess. this is 6 times as many playing hopscotch. which model shows this comparison?
i got the top one to the left (checking my answer)
Answers
Answer:
The top left one is correct.
Step-by-step explanation:
We can rewrite this as an algebraic expression simply so it's easier to read.
Let's say hopscotch is [tex]h[/tex]. Tag is 6 times [tex]h[/tex], or [tex]6h[/tex].
That means for every 1 unit of hopscotch, there are 6 units of tag.
The top left one is correct.
1 hours 20 min : 2 hours ratio
Answers
1:20 i think sooo.Je suis américain et habite dans les montagnes vertes du vermont . Je premier apprend français il y a un an parce que c'est un beau langue . Oui, je sais mon français est mauvais, mais J'aime l'apprendre . Je suis dix-sept et j'ai un chien blanc petit . Ma famille l'appelle snowball et il est tres gentil . Mon préféré endroit en la monde est les montagnes car ils sont très beau dans tout quatre saisons . Merci pour votre temps et au revoir .
PRE CALC ON EDGE PLEASE HELP 100 PTS!!! IM TIMED
Answers
Answer:
The last option
Step-by-step explanation:
a is the hypotenuse, x is the adjacent, h is the opposite.
a^2 = h^2 + x^2
Subtract x^2 from both sides
h^2 = a^2 - x^2
Please gimme brainliest
The angle measurements in the diagram are represented by the following expressions.
B
А
Solve for x and then find the measure of
Answers
Answer:
[tex]x = 20^{\circ}[/tex]
[tex]\angle A = 150^{\circ}[/tex]
Step-by-step explanation:
Given
[tex]\angle A = 8x - 10[/tex]
[tex]\angle B = 3x + 90[/tex]
See attachment
From the attachment A and B are vertically opposite.
This implies that:
[tex]\angle A = \angle B[/tex]
Substitute values for A and B
[tex]8x - 10 = 3x + 90[/tex]
Collect Like Terms
[tex]8x - 3x = 10 + 90[/tex]
[tex]5x = 100[/tex]
Solve for x
[tex]x = \frac{100}{5}[/tex]
[tex]x = 20^{\circ}[/tex]
Substitute 20 for x in [tex]\angle A = 8x - 10[/tex]
[tex]\angle A = 8 * 20 - 10[/tex]
[tex]\angle A = 150^{\circ}[/tex]
Evaluate x - 20 when x=3
Answers
Answer:
-17
Step-by-step explanation:
Plug in 3:
3 - 20 =
Solve:
3-20 = -17
Answer:
-17
Step-by-step explanation:
I replaced 3 for x, I solved the equation 3-20, which is equal to -17