Roots of Polynomials

Presentation

•

Mathematics

•

9th - 11th Grade

•

Medium

•

CCSS

HSA-REI.B.4B, HSA.APR.B.2, HSF-IF.C.7C

Standards-aligned

jill parker

Used 6+ times

FREE Resource

6 Slides • 26 Questions

Roots of Polynomials

by jill parker

Solving by factoring

Here is an example on how to factor using the grouping technique.

Multiple Choice

Factor completely:
2x³+ 5x² - 8x - 20

(x² - 4)(2x + 5)

(2x - 5)(x² + 4)

(2x² - 4)(x + 5)

(x - 2)(x + 2)(2x + 5)

Multiple Choice

WHAT FACTORING TECHNIQUE do YOU HAVE TO USE TO SOLVE FOR THE FACTORS OF 27a³-729?

FACTORING BY GCF

DIFFERENCE OF TWO SQUARES

DIFFERENCE OF TWO CUBES

DIAMOND AND BOX METHOD

Multiple Choice

What are the remaining factors for

(x³ +x² -17x +15) if (x -1) is a factor? (hint: use synthetic division)

(x-1) (x+5) (x-3)

(x-1) (x+5) (x + 3)

(x+1) (x+5) (x-3)

(x+1) (x-5) (x-3)

Multiple Choice

What is the first step in solving
(x + 2)(x - 3) = 0 ?

Plug in zero for x

Solve for x

FOIL

Set each binomial factor equal to zero

Solve by Factoring

Here is an example on how to solve a polynomial by factoring

Multiple Choice

What are the solutions to this equation? (x-3)(x+2)=0

x=3,-2

x=-3,2

x=2,3

x=3,2

Multiple Choice

What are the zeros in (x-5)(x+4)

4 and -5

5 and -4

-4 and -5

no zeros

Multiple Choice

Write x³ + 9x² + 18x in factored form

x(x + 6)(x + 3)

x(x + 9)(x + 2)

x(x + 6)

x(x - 6)(x - 3)

Fill in the Blanks

Type answer...

Multiple Choice

Solve x² + x – 72 = 0.

x = -8

x = -8 or x = 9

x = 8 or x = -9

x = 9

Multiple Choice

Solve b²+25b=0

b= 0 and b = 25

b= 0 and b= -25

b= -5 and b= 5

b=5 an b=-2.5

Remember synthetic division?

The example shows a reminder of how to use synthetic division. You may have to refer to your notes for further examples.

Multiple Choice

Is (x-1) a factor of f(x)= x³-8x²+14x-4?

Yes, (x-1) is a factor. There is a remainder.

No, (x-1) is not a factor. The remainder is zero.

Yes, (x-1) is a factor. The remainder is zero.

No, (x-1) is not a factor. There is a remainder.

Multiple Choice

What are the three factors for P(x) = (x³ +x² -17x +15)?

(x-1) (x+5) (x-3)

(x-1) (x+5) (x + 3)

(x+1) (x+5) (x-3)

(x+1) (x-5) (x-3)

Multiple Choice

Decide if (x+3) is a factor of 3x³+10x²-x-12

Yes, it is a factor!

No, it is not a factor!

Multiple Choice

Solve for the values of x:

(2x - 1)(x + 4) = 0

x = 1/2, -4

x = 1/2, 4

x = 2, -4

x = -2 4

Multiple Choice

Find the correct statement about the zeros.

−5 is a zero with multiplicity 1

−5 is a zero with multiplicity 2

−2 is a zero with multiplicity 1

2 is a zero with multiplicity 2

Multiple Choice

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

-2, 7 multiplicity 3

-2, 7, 3

2, -7 multiplicity 3

2, -7, 3

Multiple Choice

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

±1, ±8

±1, ±2, ±4, ±8

±1, ±2, ±4

1, 2, 4, 8

Fill in the Blanks

Type answer...

Multiple Choice

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

Multiple Choice

(-2.55, 0), (2.55, 0)

(-3, 0), (-2, 0), (2, 0), (3, 0)

(0, 36)

(0, -3), (0, -2), (0, 2), (0, 3)

Multiple Choice

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

Multiple Choice

Identify the zeros:

x=-2, x=-1, x=0

x=-2, x=0

x=-1, x=0, x=2

x=-2, x=0, x=1

Multiple Choice

Which of the following could be the equation of this graph in factored form? (Careful-pay attention to multiplicity.)

f(x) = (x-4)(x-1)²(x+2)(x+4)

f(x) = (x-4)(x+1)²(x+2)(x+4)

f(x) = (x-4)(x-1)²(x-2)(x+4)

f(x) = (x+4)(x+1)²(x-2)(x-4)

Multiple Select

Check any statements below that are true about the graph provided.

This polynomial is degree 3

X= 0 is a root

The factor (x-2)^2 would be part of the equation

X = 3 is a root

This polynomial has a negative lead coefficient.

Multiple Choice

Factor: x⁴-x³-9x²+9x=0 when -3 is a root

x(x-3)(x-1)(x+1)=0

2x(x-3)(x+2)(x+3)=0

x(x-3)(x-1)(x+3)=0

x(x-3)(x+1)(x+3)=0

Poll

How good do you feel about finding zeros (solutions) to a polynomial equation?

I know it cold!

I am almost there.

Somewhat happy about it, maybe watch another video.

I need to review my notes, watch a video and do more practice.

On the last slide is a web page which shows a unique way to find zeros of a polynomial. Probably not the way it is done in your notes, but worth a look if you understand the process.

Finding Zeros of a Polynomial - High School Math

You can open this webpage in a new tab.

Roots of Polynomials

by jill parker

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Roots of Polynomials

Roots of Polynomials

​Solving by factoring

​Solve by Factoring

​Remember synthetic division?

Roots of Polynomials

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Solving by factoring

Solve by Factoring

Remember synthetic division?