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The learner will factor out the largest monomial factor in a polynomial.

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Factoring: Set 1 Polynomials Containing a Common Factor

Factor $21a^2bc^2 + 15a^3b^2c^3 - 18a^4bc^5$ completely.

$3a^2bc^2(7 + 5abc + 6a^2c^3)$
$a^2bc^2(21 + 15abc - 18a^2c^3)$
$3abc(7ac + 5a^2bc^2 - 6a^3c^4)$
$3a^2bc^2(7 + 5abc - 6a^2c^3)$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $3x(x + 7) + 5(x + 7)$ completely.

$3x^2 + 21x + 5x + 35$
$3x^2 + 26x + 35$
$(x + 7)(3x + 5)$
$(3x + 5)(x + 7)^2$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $-3x^2 + 9x - 15$ completely so the leading coefficient of the polynomial factor is positive.

$-(3x^2 - 9x + 15)$
$-3(x + 5)(x - 1)$
$-(3x^2 + 9x - 15)$
$-3(x^2 - 3x + 5)$
$-3(x^2 + 3x - 5)$
$-(3x + 5)(x - 3)$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $12x^2y + 18xy^3 - 24x^4y^2$ completely.

$2xy(6x + 9y^2 - 12x^3y)$
$6xy(2x + 3y^2 - 4x^3y)$
$6(2x^2y + 3xy^3 - 4x^4y^2)$
$6xy(2x - 3y^{2} + 4x^3y)$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $-5x + 9$ completely so the leading coefficient of the polynomial factor is positive.

$-(5x + 9)$
$-1(-5x - 9)$
$-1(9 - 5x)$
$-(5x - 9)$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $b(3b + 1) - 3b - 1$ completely.

$(3b + 1)(b + 1)$
$(3b^2 + b)(3b - 1)$
cannot be factored
$(3b + 1)(b - 1)$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $3abc + 6a + 12ab$ completely.

$3(abc + 2a + 4ab)$
$3ab(c + 2a + 4)$
$a(3bc + 6 + 12b)$
$3a(bc + 2 + 4b)$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $16x - 49y$ completely.

cannot be factored
$(4x + 7y)(4x - 7y)$
$16(x - 3y)$
$-33(x - y)$
$4x - 7y$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $5xy - 7y$ completely.

cannot be factored
$-2xy$
$y(5x - 7)$
$x(5y - 7)$
$-35xy^{2}$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $2x^{2} + 8x^{5}$ completely.

$2(x^{2} + 4x^{5})$
$2x^2(1 + 4x^3)$
$2x(x + 4x^4)$
$x^2(2 + 8x^3)$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $12x - 3$ completely.

$3(4x - 0)$
cannot be factored
$3(4x - 1)$
$3(4x)$
$9x$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $17x -136xy^2$ completely.

$x(17 - 136y^2)$
$x(17 - 136xy^2)$
cannot be factored
$17x(1 - 8y^2)$
$x(136y^2 - 17)$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $y(y - 5) - 7(y - 5)$ completely.

$(y - 5)(y - 7)$
$y^2 - 5y - 7y +35$
$7y(y - 5)$
$(y - 7)(y - 5)^2$

Question 1 of 10

Factoring: Set 1 Polynomials Containing a Common Factor

Factor $3x + 3y$ completely.

$6xy$
$9xy$
$3(x + y)$
$9(x + y)$
$6(x + y)$
cannot be factored

Question 1 of 10

Author

Kevin Ritzman

Published: 4/9/2014

Last Updated: 4/9/2014

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Factoring: Set 1 Polynomials Containing a Common Factor by Fox Valley Technical College is licensed under a Creative Commons Attribution 3.0 Unported License.