QuestionAugust 25, 2025

33. 4x^2+16x-48 36. 6x^2+25x-9

33. 4x^2+16x-48 36. 6x^2+25x-9
33. 4x^2+16x-48 36. 6x^2+25x-9

Solution
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Answer

4(x + 6)(x - 2); (3x - 1)(2x + 9) Explanation 1. Factor the first quadratic expression For 4x^{2}+16x-48, factor out the greatest common factor, which is 4: 4(x^2 + 4x - 12). Now, factor the quadratic x^2 + 4x - 12 into (x + 6)(x - 2). 2. Factor the second quadratic expression For 6x^{2}+25x-9, use the AC method. Multiply a \cdot c = 6 \cdot (-9) = -54. Find two numbers that multiply to -54 and add to 25, which are 27 and -2. Rewrite as 6x^2 + 27x - 2x - 9. Factor by grouping: 3x(2x + 9) - 1(2x + 9) = (3x - 1)(2x + 9).

Explanation

1. Factor the first quadratic expression<br /> For $4x^{2}+16x-48$, factor out the greatest common factor, which is 4: $4(x^2 + 4x - 12)$. Now, factor the quadratic $x^2 + 4x - 12$ into $(x + 6)(x - 2)$.<br /><br />2. Factor the second quadratic expression<br /> For $6x^{2}+25x-9$, use the AC method. Multiply $a \cdot c = 6 \cdot (-9) = -54$. Find two numbers that multiply to -54 and add to 25, which are 27 and -2. Rewrite as $6x^2 + 27x - 2x - 9$. Factor by grouping: $3x(2x + 9) - 1(2x + 9) = (3x - 1)(2x + 9)$.
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