Wize High School Grade 10 Math Textbook > Factoring Polynomials

 Factoring Summary
When asked to factor a polynomial fully, try these in order:

1. Check to see if there is a common factor among all of the term 
→ Write the GCF in front of the brackets and divide all terms inside the bracket by the GCF

2. Check to see if there are common factors in the pairs of terms 
→ Try factoring by grouping

3. Check to see if there is a difference of squares a2−b2a^2-b^2a2−b2  
→ The factored form is (a−b)(a+b)(a-b)(a+b)(a−b)(a+b)

4. Check to see if there is a perfect square trinomial a2+2ab+b2a^2+2ab+b^2a2+2ab+b2 or a2−2ab+b2a^2-2ab+b^2a2−2ab+b2 
→ The factored form is (a+b)2(a+b)^2(a+b)2 or (a−b)2(a-b)^2(a−b)2

5. If we have a simple trinomial x2+bx+cx^2+bx+cx2+bx+c 
→ Find two numbers m, nm,~ nm, n that multiply to ccc and add to bbb
→ The factored form is (x+m)(x+n)(x+m)(x+n)(x+m)(x+n)

6. If we have a harder trinomial ax2+bx+cax^2+bx+cax2+bx+c 
→ Find two numbers m, nm,~nm, n that multiply to acacac and add to bbb
→ Decompose the trinomial into ax2+mx+nx+cax^2+mx+nx+cax2+mx+nx+c
→ Factor this by grouping the terms in pairs

Practice: Factoring
Factor all of the following polynomials fully.

a) 2x2+4x2x^2+4x2x2+4x

b) x2+2x−35x^2+2x-35
x2+2x−35

c) 6x2−11x+46x^2-11x+46x2−11x+4

d) −5x2−20x+105-5x^2-20x+105−5x2−20x+105

e) 8x2−88x^2-88x2−8

f) −6x2+34x+12-6x^2+34x+12−6x2+34x+12

g) x2−14x+49x^2-14x+49x2−14x+49

h) 18x2+12x+218x^2+12x+218x2+12x+2

I don't know

Practice: Factoring
Factor 2x4−322x^4-322x4−32 fully. Then explain why it is fully factored.

Enter the FULLY factored form

⭐Make sure you know how to explain why this is fully factored on a test or exam! Check your explanation with the solution.

I don't know

Practice: Factoring
Select ALL expressions that are fully factored.

⭐Make sure you can also explain why an expression is fully factored or is not fully factored.

A) 2x(x−1)2x(x-1)2x(x−1)

B) (−3x+1)(x−8)(-3x+1)(x-8)(−3x+1)(x−8)

C) (2x−4)2(2x-4)^2(2x−4)2

D) (3−x)(5x−10)(3-x)(5x-10)(3−x)(5x−10)

E) (x2−9)(x2+9)(x^2-9)(x^2+9)(x2−9)(x2+9)

F) (x−1)(x2+1)(x-1)(x^2+1)(x−1)(x2+1)

I don't know

Practice: Factoring
A community pool is being built, and here is the blueprint for the pool.

The pool is the shaded blue area. The inner and outer perimeter of this pool is a square.

a) Write an expression representing the area of the pool. Do NOT simplify anything!

b) Factor the expression representing the area of the pool. Simplify each factor as much as possible.

c) Expand and simplify the expression representing the area of the pool.

a) Do not simplify your answer.

b) Simplify each factor as much as possible.

c) Simplify the entire expression as much as possible.

I don't know

Practice: Factoring
The volume of a rectangular prism is V=3x3+9x2+6xV=3x^3+9x^2+6xV=3x3+9x2+6x.
a) Factor this expression fully.
b) Based on the expression found in part a), if x=4x=4x=4, what are the dimensions of this prism?
c) Are these the only possible dimensions this prism can have?

a) Enter your answer in the form

V=...

b) Separate the meansurements with commas and no spaces in between (for example 1,2,3 or 4,6,7)

c) Check your answer with the solution

I don't know

Extra Practice

Factoring (Review)

Practice: Factoring
Factor 625x4−16y4625x^4-16y^4625x4−16y4

Factoring (Review)

Practice: Factoring
Factor 27x3−y327x^3-y^327x3−y3

Factoring (Review)

Practice: Factoring
Factor 5x2−31x+65x^2-31x+65x2−31x+6

Factoring (Review)

Practice: Factoring
Factor 3x2−13x−103x^2-13x-103x2−13x−10

Factoring

Practice: Factoring
Factor x2−10x+21x^2-10x+21x2−10x+21

Factoring

Practice: Factoring
Factor x2−9x−10x^2-9x-10x2−9x−10