Question
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Tutor-Verified Answer
Answer
\(9f^2 + 7f - 2 = (f + 1)(9f - 2)\)
Solution
Factor the expression \( 9f^2+7f-2 \).
Factor the expression by following steps:
- step0: Factor:
\(9f^{2}+7f-2\)
- step1: Rewrite the expression:
\(9f^{2}+\left(-2+9\right)f-2\)
- step2: Calculate:
\(9f^{2}-2f+9f-2\)
- step3: Rewrite the expression:
\(f\times 9f-f\times 2+9f-2\)
- step4: Factor the expression:
\(f\left(9f-2\right)+9f-2\)
- step5: Factor the expression:
\(\left(f+1\right)\left(9f-2\right)\)
The factored form of the expression \(9f^2+7f-2\) is \((f+1)(9f-2)\).
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Simplify this solution Mind Expander
To factor the quadratic expression \( 9f^{2} + 7f - 2 \) completely, we'll look for two numbers that multiply to \( 9 \times -2 = -18 \) and add to \( 7 \). The numbers \( 9 \) and \( -2 \) fit these criteria. We can split the middle term: \( 9f^{2} + 9f - 2f - 2 \). Now, group the terms: \( (9f^{2} + 9f) + (-2f - 2) \). Factor out the common terms in each group: \( 9f(f + 1) - 2(f + 1) \). Now, notice that \( f + 1 \) is a common factor: \( (9f - 2)(f + 1) \). Thus, the complete factorization of \( 9f^{2} + 7f - 2 \) is \( (9f - 2)(f + 1) \).
