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6.4.6 Practice

Algebra 16.4.6 Practice

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Complete the following questions to practice the skills you have learned in this lesson.

For questions 1 – 3, find the GCF of each set of expressions.

$12m^2n^3, 30m^5n^3$

$6m^2n^3$
$2m^5n^3$
$3m^2n^3$
$6m^3n^3$

$28x^2y^4,42x^4y^4$

$27p^2q^3,45p^3q^4,9p^4q^3$

$9p^3q^3$
$9p^2q^3$
$27p^2q^3$
$9pq^3$

For questions 4 – 6, factor the expression.

$15x^3y − 3x^2y^2 + 6xy^3$

$−7a^3 + 21a^2 − 14a$

$−7a(a^2 − 3a + 2)$
$−7a^2(a − 1)$
$7a(a^2 − 3a + 2)$
$−7(a^2 − 3a + 2)$

$8n(n − 4) + 5(n − 4)$

$(8n − 4)(n + 5)$
$(n − 4)(8n + 5)$
$(n − 4)(8n − 5)$
$(n + 4)(8n + 5)$

For questions 7–10, factor by grouping

$u^2 − u + 6u − 6$

$(u − 1)(u + 6)$
$(u + 1)(u − 6)$
$(u − 1)(u − 6)$
$(u + 1)(u + 6)$

$16q^2 + 20q − 28q − 35$

$(4q − 5)(4q − 7)$
$(4q + 5)(4q − 7)$
$(4q − 5)(4q + 7)$
$(4q + 5)(4q + 7)$

$r^2 − 3r − r + 3$

$(r + 3)(r − 1)$
$(r − 3)(r + 1)$
$(r + 3)(r + 1)$
$(r − 3)(r − 1)$

$6y^2 + 7y + 24y + 28$

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
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- Section URL: https://openstax.org/books/algebra-1/pages/6-4-6-practice

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