Algebra Extra Credit

Completing The Square

100

Rewrite the function by completing the square.

f(x)=x²-8x-51

f(x)=(x−4)²−67

200

Rewrite the equation by completing the square.

x² -4x-32=0 

(x-2)²=36

300

Rewrite the function by completing the square.

f(x)=x²+20x+40

f(x)=(x+10)²-60

400

Rewrite the function by completing the square.

x²+4x-21=0

(x+2)²=25

500

Rewrite the function by completing the square.

x²+3x-28=0

(x+ 3/2)²=121/4

Add & Subtract Polynomials

100

(7x²−3x+10)−(−4x²+6x−4)

11²−9x+14

200

(6x²+3x−9)−(−2x²+4x−1)

8x²−x−8

300

(−8r²+11r−6)+(−7r²−9r+14)

−15r²+2r+8

400

(4a³−3a−8)−(a−5)

4a³−4a−3

500

(8x²−6x+2)−(3x²+7x−4)

5x²−13x+6

Multiplying Polynomials

100

Multiply the Polynomial

−p²(p²−p−1)

-p⁴+p³+p²

200

Multiply the polynomial

(k²−5k−2)(k²+2)

k⁴-5k³-10k-4

300

Multiply the Polynomial

(y²−9)(y²−4)

y⁴-13y²+36

400

Multiply the polynomial

(1−4m)(m²−3m+8)

-4m³+13m²-35m+8

500

Multiply the Polynomial 

(1+x)(x²−5x−6)

x³-4x²-11x-6

Dividing Polynomials

100

Divide the polynomial

2x⁴-3x/x

2x³-3

200

Divide the polynomial

2x⁵+5x³/x

2x⁴+5x²

300

Divide the polynomial

2x³−5x²+x/x

2x²−5x+1

400

Divide the polynomial

3x⁵+x4−4x²/x

3x⁴+x³−4x

500

Divide the polynomial

4x³−x²+3/x 

4x²−x+ 

3/x

Polynomial Factorization

100

Factor completely.

7x⁵−21x⁴+14x³

7x³(x−1)(x−2)

200

Factor completely.

x⁵−x⁴+3x−3

(x−1)(x⁴+3)

300

Factor completely.

(x²+x−6)(2x²+4x)

2x(x+3)(x−2)(x+2)

400

Factor the polynomial by its greatest common monomial factor.

44k⁵−66k⁴+77k³

11k³(4k²−6k+7)

500

Factor the polynomial by its greatest common monomial factor.

9m³−27m

9m(m²−3)