Question

algebra 2
© 2025 kuta software llc all rights reserved.
dividing with polynomials: long division
factor each completely.

1. 3a⁴ - 5a³ - 50a²
2. 7x² - 71x + 72

Explanation:

Step1: Factor out GCF

$3a^4 - 5a^3 - 50a^2 = a^2(3a^2 - 5a - 50)$

Step2: Factor quadratic trinomial

Find two numbers: $10$ and $-15$, since $10 \times (-15) = -150$ and $10 + (-15) = -5$
$3a^2 - 5a - 50 = 3a^2 + 10a - 15a - 50 = a(3a + 10) - 5(3a + 10) = (3a + 10)(a - 5)$
Combine with GCF: $a^2(3a + 10)(a - 5)$

Step3: Factor second expression GCF

$7x^2 - 71x + 72$ has no common GCF, move to factoring trinomial

Step4: Factor quadratic trinomial

Find two numbers: $-8$ and $-63$, since $-8 \times (-63) = 504$ and $-8 + (-63) = -71$
$7x^2 - 71x + 72 = 7x^2 - 63x - 8x + 72 = 7x(x - 9) - 8(x - 9) = (7x - 8)(x - 9)$

Answer:

1. $a^2(3a + 10)(a - 5)$
2. $(7x - 8)(x - 9)$