Question
Factor completely. \( 3 r^{2}-4 r-4 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( 3 r^{2}-4 r-4=\square \) (Factor completely.) B. The trinomial is not factorable.
Ask by Ball Wood. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 3r^{2} - 4r - 4 = (3r + 2)(r - 2) \)
Solution
We can factor the quadratic 3r² - 4r - 4 by finding two numbers that multiply to (coefficient of r²) × (constant term) = 3 × (-4) = -12 and add up to the coefficient of r, which is -4.
The two numbers that work are -6 and 2 because:
-6 + 2 = -4 and -6 × 2 = -12.
Next, rewrite the middle term:
3r² - 6r + 2r - 4
Now, group the terms:
(3r² - 6r) + (2r - 4)
Factor out the greatest common factor (GCF) from each group:
3r(r - 2) + 2(r - 2)
Notice that (r - 2) is a common factor:
(3r + 2)(r - 2)
Thus, the correct factorization is:
3r² - 4r - 4 = (3r + 2)(r - 2)
Select choice A and fill in:
A. 3r² - 4r - 4 = (3r + 2)(r - 2)
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Simplify this solution Extra Insights
To factor the expression \( 3 r^{2}-4 r-4 \) completely, we look for two numbers that multiply to \( 3 \times -4 = -12 \) and add to \( -4 \). These numbers are \( -6 \) and \( 2 \). Thus, we can rewrite the expression as \( 3r^2 - 6r + 2r - 4 \). Grouping the terms, we have \( 3r(r - 2) + 2(r - 2) \), allowing us to factor by grouping: \( (3r + 2)(r - 2) \). So, the answer is: A. \( 3 r^{2}-4 r-4=(3r + 2)(r - 2) \)
