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Polynomial Zeros and Multiplicity Factoring

Authored by Anthony Clark

Mathematics

11th Grade

CCSS covered

Polynomial Zeros and Multiplicity Factoring
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10 questions

Show all answers

1.

HOTSPOT QUESTION

1 min • 1 pt

Plot all the zeros (x-intercepts) of the polynomial in the interactive graph.

p(x)=(x+2)(2x+7)(x−1)(x−3)p\left(x\right)=\left(x+2\right)\left(2x+7\right)\left(x-1\right)\left(x-3\right)

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

What could be the equation of p ?

p(x)=(x−5)(3x−2)(x+2)p\left(x\right)=\left(x-5\right)\left(3x-2\right)\left(x+2\right)

p(x)=(x−5)(2x−3)(x+2)p\left(x\right)=\left(x-5\right)\left(2x-3\right)\left(x+2\right)

p(x)=(x+5)(2x+3)(x−2)p\left(x\right)=\left(x+5\right)\left(2x+3\right)\left(x-2\right)

p(x)=(x+5)(3x+2)(x−2)p\left(x\right)=\left(x+5\right)\left(3x+2\right)\left(x-2\right)

Tags

CCSS.HSA.APR.B.3

3.

DROPDOWN QUESTION

1 min • 1 pt

Given the factored form of the polynomial f(x)=(x+2)2(x−5)f\left(x\right)=\left(x+2\right)^2\left(x-5\right) , describe the behavior at the roots. The graph will ​ (a)   at x = -2 because its multiplicity is ​ (b)   . The graph will ​ (c)   at x = 5 because its multiplicity is ​ (d)   .​

bounce

cut

squiggle

2

1

0

5

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

Even

Odd

None

Tags

CCSS.HSF-IF.C.7C

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

-4, -1, 3

3, -3, 4, 1

4, 1, -3

3, -4, -1, 3

Tags

CCSS.HSF-IF.C.7C

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

f(x)= x2(x – 2)3(x – 7)

Find and select each real zero and its multiplicity

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

2 (Mult of 3), 7 (mult 1)

0, 2, 7

2 (mult of 2), 7 (mult of 3)

Tags

CCSS.HSF-IF.C.7C

7.

FILL IN THE BLANKS QUESTION

1 min • 1 pt

Find the zeros of the function by factoring f(x)=x3−5x2+6xf\left(x\right)=x^3-5x^2+6x  . Write your answers from least to greatest, separated by a space.

(a)  

Tags

CCSS.HSF-IF.C.7C

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