Name: Review of Chapter 8

Lesson 8-1

Standard Form — writing all polynomial answers so that the degrees are in decreasing order.

Which are In s andard form? If it is not in standard form, rewrite it.

5x 2 + 6x - 3x2 + x3 + I 8x 3 - 2x +1

Names based on Degrees — match the letters to the right with the correct name

constant

—L— quadraticA cubic

fourth degree

A. 4x 3 + 2x 2 + x —4

B. 8

D. 3x4 + 2x

E. x 2 + x — 4

Names based on Terms — match the letters to the right with the correct name

e- monomial—A— binomial

trinomial

polynomial with 4 terms

Adding Polynomials

A. 2x 2 + x

B. 6X3 — x 2 + 3x — 2

C. 4x2

D. 5x4 -7x+8

Example:

Add:

(3X2 + 4X 2) + (7X2 - - 5) = 10x2 — 5x-3

(8x 3 + 5x2 — 2x) + (2x3 — 9x + 2) = I OX + 5x + a

(9x2 — 8x— 5) + (x2 — OX —IOx + a

Subtracting Polynomials

Example:

Subtract:

(9x 2 + 3x + 1) — (5x2 — 4x + 6) = 4x 2 + 7x — 5

(6x 3 + 2x2 -4x) - (8x3 + 2x - 1) = ax + ax - (ax

(x2 -3x- 1) - (6x 2 -5x

Lesson 8-2

Multiplying a Monomial with Polynomials

Example:

Multiply:

Find the GCF

Example:

Multiply:

Factor

Example:

Factor completely:

Lesson 8-3

FOIL

Example:

FOIL:

2x(6x2 + 9x - 5) = 12x3 + 18x2 - lox

3x2 (4x3 + 5x2 -2) = I ax 4- | 5x ¯ COX

-2x(7x2 -9x2 + 3) = q x Cox

8x3 + 12x2 + 20x the GCF is 4x

9xS + 12X3 + 6X2

10x3 + 15x2 + 5

the GCF is

the GCF is

8x3 + 12x2 + 20x = 4x(2x2 + 3x + 5)

+ 12x3 = (3 X 3 3xz

10x3y6 +15x2y4 +5x 3y3 = SX

5

LIX

4- 3N + X

(3x+ 5) = 6x 2 - + 4x - 10 = 6x 2 - lix - 10

Multiplying a Binomial by a Trinomial

Example: (x + 3)(2x2 + 4x + 5) = 2x3 + 4x 2 + 5x + 6x2 + 12x + 15

= 2x3 + 10x2 + 17x+ 15

FOIL: (w + + 3w — 2) == w3+üW Z +lOvu-8

3 —13K

Lesson 8-4

Special Case: The Square of a Binomial

Example:

Simplify:

(W 4) 2 = (W +

(x

+ 4) = W 2 + 4W + 4W + 16 = W 2

-z X 2 -ax-ax

X

+ 16

X a—c/ x + Ll

LIX

Finding the Area of the Shaded Region

(2x — = (ax

Example: Large Rectangle:

2X+4

Small Rectangle:

6x2 — 2x + 12x —4

6x2 + 10x — 4

2x(x + 1)

2x2 + 2x

Subtract the Two: (6x2 + lox — 4) — (2x2 + 2x)

Area of the Shaded Region: 4x 2 + 8x — 4

Find the area of the shaded region:

I-a-re X -

x

CoX 2 -6x

X ea)

- (x i +

Lesson 8-5

Factoring x2 + bx + cIf the "a" term is a 1, you can use the short cut method where you multiply to "cj' and add to "b". Don't forgetto look for a GCF first.

Example:

Factor:

Lesson 8-6

x 2 — 1 Ix + 24

X2 + 8X + 15 =

2x2 + 4x - 30 =

What two numbers multiply to 24?

And also add to -11?

Use -8 and -3.

x 2 + llxy + 24y2 =

Factoring ax2 + bx + cIf the "a" term is NOT a 1, you use the guess and check method where you plug in factors of "a" into the firstpart of each binomial and factors of "c" into the last part of each binomial. Then test that the outer and innermultiples would add to get "b". Don't forget to look for a GCF first.

Example: 3x2 +4x — 15 Possible factors of 3)(2.•3, 1, x

Possible factors of -15:-5, 3, 5, -3, 15, 1, -15, -1

9x — 5x = 4x

Factor:

— LIX

9x2 3C3b<

Lesson 8-7

Special Case: Factoring a Difference of SquaresDon't forget to look for a GCF first.

Example:

Simplify:

4x 2 -25 = (2x- + 5)

9x2 — = - 10)

18x2 — 2 = l)

a(qxa-l)

STEPS WHEN FACTORING:

1. Is there a GCF?

2. Is it a difference of squares?

3. Is the "a" term 1? Use the short cut method.

4. Is the "a" term not 1? Use guess and check.

5. Are there 4 terms? Use factor by grouping.

Lesson 8-8

Factoring by Grouping: Factoring 4 Term PolynomialsDon't forget to look for a GCF first.

Example:

Factor:

11x 3 — 9x2 + 1 Ix — 9

(11x 3 — — 9)

x 2 (11x — 9) + I(llx - 9)

(lix — + 1)

15X3 + 40X2 + 3X +

(14x3 —35x2 C 7 x a

What are the possible dimensions for thi rectangular prism?

ax ax z

16x 4 + 8x 3 + 20x 2 + lox =

1) x2 +17x+72

STEPS WHEN FACTORING:

1. Is there a GCF?

2. Is it a difference of squares?

3. Is the "a" term 1? Use the short cut method.

4. Is the "a" term not 1? Use guess and check.

5. Are there 4 terms? Use factor by grouping.

Factor each of these completely.

2) 4x 2 —16x+7 3) 6x 4 + 15x 3 - 9x 2 4) 9x4 + 12x 3 — 18x2 — 24x

3x a (ax 5K -3) 34- X a — ),tqx

(ax - -ax

5) 49x 2 — 121 6) 2x2+ — 70

ax-Il8) 6x2 —600 9) 6x2 + 25xy -F 11y2

100)

2

22>.eY

-to

3) -a(3x Q))

7) — lox —28

a(xa-sx-lcl)

10) 27x 3 + 36x 2 12x— 16