PolynomialsPolynomials

GCGCFFGreatest Common Factor

What is a GCF of a

polynomial?

GCF with VariablesNote: With variables, the GCF will always be the smallest exponent of a common variable

Examples:12x3, 16x2

45a5, 50a7

GCF = 4x2

GCF = 5a5

Factor out the GCFFactor out the GCF

•Put the GCF outside of (parenthesis).

•Divide each term by the GCF.

•You will always have the same numbers of terms you start with

16x2 – 8x8x(2x – 1)

10x – 10y10(x – y)

8r2 – 24r8r(r – 3)

6n2 + 15n3n(2n + 5)

6x3 – 9x2 + 3x

3x(2x2 – 3x + 1)

2a3 – 6a2a(a2 – 3)

8y3 – 20y2 + 12y

4y(2y2 – 5y + 3)

7x3 – 28x2

7x2(x – 4)

4m3 – 20m

4m(m2 – 5)

3x(x + 2) – 2(x + 2)

(x + 2)(3x – 2)

5z(z – 6) + 4(z – 6)

(z – 6)(5z + 4)

GroupinGroupingg

Steps to Factor by Grouping 4 terms

1. Group the 1st two terms and the 2nd two terms

2. Factor out the GCF of each group

3. Write down the common parenthesis4. In another parenthesis, write the GCFs5. Check to see if the parenthesis can factor again

x3 + 12x2 – 3x – 36

x2(x + 12) – 3(x + 12)(x + 12)(x2 – 3)

y3 – 14y2 + y – 14(y3 – 14y2) + (y – 14)y2(y – 14) + 1(y – 14)(y – 14)(y2 + 1)

m3 – 6m2 + 2m – 12(m3 – 6m2) + (2m –

12)m2(m – 6) + 2(m – 6)(m – 6)(m2 + 2)

p3 + 9p2 + 4p + 36(p3 + 9p2) + (4p + 36)p2(p + 9) + 4(p + 9)(p + 9)(p2 + 4)

x3 + x2 + 5x + 5(x3 + x2) + (5x + 5)x2(x + 1) + 5(x + 1)(x + 1)(x2 + 5)

x3 – 3x2 – 5x + 15(x3 – 3x2) + (-5x + 15)x2(x – 3) – 5(x – 3)(x – 3)(x2 – 5)

3x3 – 3x2 + x – 1(3x3 – 3x2) + (x – 1)

3x2(x – 1) + 1(x – 1)(x – 1)(3x2 + 1)

t2 + 2t + 3kt + 6k

(t + 2)(t + 3k)

x2 + 3x + xk + 3k

(x + 3)(x + k)

ad + 3a – d2 – 3d

(d + 3)(a – d)

2ab + 14a + b + 7

(b + 7)(2a + 1)

CW/HW - TextbookCW/HW - Textbook

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