Question

factor the following polynomials based on the examples shown in class. you will end up with two binomials at the end of the factoring process. there may or may not be a common factor.
show your work!!!

1. $20v^3 - 8v^2 + 15v - 6$
2. $9m^2 + 16mn - 7m - 28n$
3. $3x^3 + x^2y - 9xy^2 - 3y^3$
4. $2x^3 + 4x^2 + 3x + 6$
5. $u^3 - u^2v + uv^2 - v^3$
6. $5xy - x^2 + 10y - 2x$

Explanation:

Step1: Group polynomial terms

$(5x^2y - x^2) + (5y - 1)$

Step2: Factor out GCF from each group

$x^2(5y - 1) + 1(5y - 1)$

Step3: Factor out common binomial

$(5y - 1)(x^2 + 1)$

Answer:

$\boldsymbol{(5y - 1)(x^2 + 1)}$

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Verification of completed problems (for reference):

1. Correct: $4v^2(5v-2)+3(5v-2)=(5v-2)(4v^2+3)$
2. Correct: $4m(m+4n)-7(m+4n)=(m+4n)(4m-7)$
3. Correct: $x^2(2x+y)-3y^2(2x+y)=(2x+y)(x^2-3y^2)$
4. Correct: $4x(3x+1)+5(3x+1)=(3x+1)(4x+5)$
5. Correct: $u^2(u-v)+v^2(u-v)=(u-v)(u^2+v^2)$