10.1 Homework Problems: Factoring Polynomials

1. Find the GCF of each set of terms

a. {9,14,22}

b. {5, 15, 20}

c. {6, 20, 42}

d. {8a³, 16a⁴, 20a²}

e. {26ab², 39a²b, 52a²b²}

f. {8x²y³, 32x²y, 64x²y²}

2. Simplify each expression

a. [latex]\frac{9x^5}{3x^2}[/latex]

b. [latex]\frac{21x^4y^3}{-3xy^2}[/latex]

c. [latex]\frac{-36x^2y}{-12xy^3}[/latex]

d. [latex]\frac{-144x^3y^7}{72x^8y^2}[/latex]

3. Complete the factoring

a. 13ab² + 13ab = 13ab ( _______________ )

b. – 5xy² – 20x²y – 5xy = –5xy (_______________)

4. Factor each of the polynomials by finding the GCF

a. 11x – 121

b. 10x²y – 25xy

c. 6x²y – 25xy

d. – 56x⁴z³ – 98x³z⁴ – 35x²z⁵

5. Factor each expression by grouping

a. 7y²(y +3) + 2(y +3)

b. 10y(2y +3) – 7(2y +3)

c. bx + b + cx + c

d. 5xy + yz – 20x – 4z

e. 10xy – 2y² + 7yz – 35xz

f. 5xy + 6uv – 3vy–10ux

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