Ch 7 Polynomial Review

Basic Operations

100

(4x³-4x²+1)+(5x²-2x+6)

4x³+x²-2x+7

200

(6k³-2k²+7)-(-3k³+k²-k+9)

9k³-3k²+k-2

300

3n(4n-6w)

12n²-18nw

400

(4t-5)(3t+2)

12t²-7t-10

500

(3x-5y)²

9x²-30xy+25y²

Factoring Trinomials a=1

100

=x²-9x-10

=(x-10)(x+1)

200

=h²+3h-70

=(x+10)(x-7)

300

=-y²-13y-40

=-(x+8)(x+5)

400

=5a²+60a+100

=5(a+10)(a+2)

500

=x²+14xy+45y²

=(x+9y)(x+5y)

Factoring Trinomials a>1

100

=2x²+5x-3

=(2x-1)(x+3)

200

=24x²+17x+3

=(3x+1)(8x+3)

300

=-3x²-4x+15

=-(x+3)(3x-5)

400

=-16x²+20x+6

=-2(2x-3)(4x+1)

500

=15x²-2x-24

=(5x+6)(3x-4)

Solving Equations

100

Solve for r:

2r²-10r=0

r=0 or r=5

200

Solve for v:

4v²=8v

v=0 or v=2

300

Solve for n:

n²+7n+15=5

n=-5 or n=-2

400

Solve for r:

5r²-44r+120=-30+11r

r=6 or r=5

500

Solve for x:

36x²-49=0

x=⁷/₆ or x=^-7/₆

Factor Completely

100

=y³-9y²+y-9

=(y-9)(y²+1)

200

=q²+q+5pq+5p

=(q+1)(q+5p)

300

=36a⁴-4a²

=4a²(3a+1)(3a-1)

400

=h³+4h²-25h-100

=(h+4)(h+5)(h-5)

500

Solve for y

4y³-7y²+28=16y

y=⁷/₄ or y=-2 or y=2