Review of Factoring Unit R Lesson 2

Factoring The process of finding polynomials whose product equals a given polynomial is called factoring. Since 4𝑥+12=4 𝑥+3 , both 4 and 𝑥+3 are called factors of 4𝑥+12. Also, 4 𝑥+3 is called the factored form of 4x+12.

Irreducible Polynomial A polynomial that cannot be written as a product of two polynomials with integer coefficients is a prime or irreducible polynomial.

Factor Out the Greatest Common Factor 6 𝑥 2 𝑦 3 +9𝑥 𝑦 4 +18 𝑦 5

Factor Out the Greatest Common Factor 9 𝑦 5 + 𝑦 2

Factor Out the Greatest Common Factor 6 𝑥 2 𝑡+8𝑥𝑡+12𝑡

Factor Out the Greatest Common Factor 14 𝑚 4 𝑚+1 −28 𝑚 3 𝑚+1 −7 𝑚 2 𝑚+1

Factoring by Grouping When a polynomial has more than three terms, it can sometimes be factored using factoring by grouping.

Factor by grouping. 𝑎𝑥+𝑎𝑦+6𝑥+6𝑦

Factor by grouping. 𝑚 𝑝 2 +7𝑚+3 𝑝 2 +21

Factor by grouping. 2 𝑦 2 +𝑎𝑧−2𝑧−𝑎 𝑦 2

Factor by grouping. 4 𝑥 3 +2 𝑥 2 −2𝑥−1

Factoring Trinomials Factoring is the opposite of multiplication. Therefore, factoring requires using FOIL in reverse.

Factor the trinomial. 4 𝑦 2 −11𝑦+6

Factor the trinomial. 6 𝑝 2 −7𝑝−5

Factor the trinomial. 16 𝑦 3 +24 𝑦 2 −16𝑦

Factoring Special Products Perfect Square Trinomials 𝑥 2 +2𝑥𝑦+ 𝑦 2 = 𝑥+𝑦 2 𝑥 2 −2𝑥𝑦+ 𝑦 2 = 𝑥−𝑦 2

Factor the perfect square trinomial. 16 𝑝 2 −40𝑝𝑞+25 𝑞 2

Factor the perfect square trinomial. 169 𝑥 2 +104𝑥 𝑦 2 +16 𝑦 4

Difference of Squares 𝑥 2 − 𝑦 2 = 𝑥+𝑦 𝑥−𝑦

Factor the polynomial. 4 𝑚 2 −9

Factor the polynomial. 256 𝑘 4 −625 𝑚 4

Factor the polynomial. 𝑎+2𝑏 2 −4 𝑐 2

Factor the polynomial. 𝑥 2 −6𝑥+9− 𝑦 4