Question
Factor out the GCF from the polynomial. \[ 8 x^{3}+16 x^{4}-28 x^{2}+12 \]
Ask by Greene Stewart. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Factor out the GCF to get \( 4(2x^{3}+4x^{4}-7x^{2}+3) \).
Solution
Factor the expression \( 8x^3+16x^4-28x^2+12 \).
Factor the expression by following steps:
- step0: Factor:
\(8x^{3}+16x^{4}-28x^{2}+12\)
- step1: Factor the expression:
\(4\left(2x^{3}+4x^{4}-7x^{2}+3\right)\)
The GCF of the polynomial \(8x^{3}+16x^{4}-28x^{2}+12\) is 4. Factoring out the GCF, we get:
\[ 4(2x^{3}+4x^{4}-7x^{2}+3) \]
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Simplify this solution Beyond the Answer
To factor out the greatest common factor (GCF) from the polynomial \(8 x^{3}+16 x^{4}-28 x^{2}+12\), we first identify the GCF of the coefficients. The coefficients are \(8, 16, -28,\) and \(12\). The GCF of these numbers is \(4\). Now, we can factor \(4\) out of each term in the polynomial: \[ 8 x^{3} + 16 x^{4} - 28 x^{2} + 12 = 4(2 x^{3} + 4 x^{4} - 7 x^{2} + 3) \] Thus, the factored form of the polynomial is: \[ 4(2 x^{3} + 4 x^{4} - 7 x^{2} + 3) \]
