Question
Factor. \( 9 r^{2}-3-26 r \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( 9 r^{2}-3-26 r=\square \) (Type your answer in factored form. Simplify your answer.) B. The trinomial is not factorable.
Ask by Fuentes Gibbs. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 9r^{2} - 3 - 26r = (9r + 1)(r - 3) \)
Solution
To factor the expression 9r² - 3 - 26r, it helps to first rewrite it in standard form (in descending order of degree):
9r² - 26r - 3
We need to find two numbers that multiply to (9 × -3 = -27) and add to -26. Notice that:
(-27) × (1) = -27 and (-27) + 1 = -26
Now rewrite the middle term using these two numbers:
9r² - 27r + r - 3
Group the terms:
(9r² - 27r) + (r - 3)
Factor out the common factors in each group:
9r(r - 3) + 1(r - 3)
Now factor out the common binomial factor (r - 3):
(r - 3)(9r + 1)
Thus, the answer is:
A. 9r² - 3 - 26r = (9r + 1)(r - 3)
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To factor \( 9r^{2} - 26r - 3 \), we can start by rearranging it into standard form: \( 9r^{2} - 26r - 3 = 9r^{2} + 0r - 26r - 3 \). Next, we look for two numbers that multiply to \( 9 \times (-3) = -27 \) and add up to \(-26\). The correct pair of factors is \(-27\) and \(1\). So, rewriting the middle term: \( 9r^{2} - 27r + r - 3 \). Now, group the terms: \( (9r^{2} - 27r) + (r - 3) \). Factoring each group gives us: \( 9r(r - 3) + 1(r - 3) \). Now we can factor out the common term \((r - 3)\): \( (r - 3)(9r + 1) \). Thus, the factored form of \( 9r^{2} - 26r - 3 \) is \( (r - 3)(9r + 1) \), making the answer A. \( 9r^{2}-3-26 r=(r - 3)(9r + 1) \).
