Factorization of Tinomials and Polynomials

By GCF

100

Factor out the GCF of:

14n²+10n

2n(7n+5)

200

Factor out the GCF of:

12x⁵-18x³-3x²

3x²(4x³-6x-1)

300

Factor out the GCF of:

15x³y²+10x²y⁴

5x²y²(3x+2y²)

400

Factor out the GCF of:

22x⁵y⁷-14x³y⁸+18x⁶y⁴

2x³y⁴(11x²y³-7y⁴+9x³)

500

Factor out the GCF and simplify the expression:

(6x+4)(-2m-7)-m(6x+4)-(6x+4)

(6x+4)(-3m-8)

Trinomials with a=1

100

Factor completely:

x²+6x+9

(x+3)²

200

Factor completely:

x²-10x+25

(x-5)²

300

Factor completely:

m²n²+16mn+39

(mn+13)(mn+3)

400

Factor completely:

4a^4/5-20a^2/5+24

Hint: Remember GCF first!!

4(a^2/5-2)(a^2/5-3)

500

Factor completely:

-2w²-10w+168

Hint: Remember GCF first!!

-2(w+12)(w-7)

Trinomials with a>1

100

Select the trinomial that is the product of 2 binomials with OPPOSITE SIGNS in the last term:

a. 10a²+5a+15

b. 10a²-5a+15

c. 10a²-5a-15

Trinomial C

Because the sign of its last term is negative.

When sign of the last term is positive both binomials keep the sign of the middle term of the trinomial.

200

Factor completely:

5x²-17x+6

(5x-2)(x-3)

300

Factor completely:

12z²+7z-10

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

400

Factor completely:

10x^2a+11x^a-6

(5x^a-2)(2x^a+3)

500

Factor completely:

9x³-57x²+60x

Hint: Remember GCF first!!

3x(3x-4)(x-5)

Polynomials

100

Factor completely:

ax+ay+bx+by

(a+b)(x+y)

200

Factor completely:

6n²x-5x-6n²+5

(x-1)(6n²-5)

300

Factor completely:

24bx-12by-16kx+8ky

Hint: Remember GCF first!!

4(3b-2k)(2x-y)

400

Factor completely:

3ax²-6a+3x²-6

Hint: Remember GCF first!!

3(a+1)(x²-2)

500

Factor completely:

3x²y³+6x²y²-21x²y²-42x²y

Hint: Remember GCF first!!

3x²y(y+2)(y-7)

Random!

100

Factor completely the following difference of squares:

4y²-25

(2y+5)(2y-5)

200

Factor completely by grouping:

bz+z-bm-m

(b+1)(z-m)

300

Factor completely:

15z²-2z-8

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

400

Factor completely the following addition of cubes:

64x³+27y⁶

Remember it comes from a binomial times a special trinomial

(4x+3y²)(16x²-12xy²+9y⁴)

500

Factor completely the first trinomial and then the resulting difference of squares:

(x²-6xy+9y²)-16m²

=(x-3y)²-16m²

=(x-3y+4m)(x-3y-4m)