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Wize High School Grade 11 Math Textbook > Factoring Polynomials

Factoring Summary + Extra Practice

Factoring Perfect Square TrinomialsPrevious Section
Operations with RadicalsNext Section
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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^2
→ The factored form is (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^2 or a2−2ab+b2a^2-2ab+b^2
→ The factored form is (a+b)2(a+b)^2 or (a−b)2(a-b)^2

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

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

Practice: Factoring

Factor all of the following polynomials fully.

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

b) x2+2x−35x^2+2x-35

c) 6x2−11x+46x^2-11x+4

d) −5x2−20x+105-5x^2-20x+105

e) 8x2−88x^2-8

f) −6x2+34x+12-6x^2+34x+12

g) x2−14x+49x^2-14x+49

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

Practice: Factoring

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

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.

Practice: Factoring

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