Problem 26
Question
Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$6 x^{3}+15 x^{2}$$
Step-by-Step Solution
Verified Answer
The factored form of the polynomial \(6x^{3}+15x^{2}\) is \(3x^{2}(2x + 5)\).
1Step 1: Identify the Greatest Common Factor
The greatest common factor (GCF) in 6x^3 and 15x^2 is 3x^2, because it is the highest degree of x that divides both terms and 3 is the largest integer that divides both coefficients.
2Step 2: Factor out the Greatest Common Factor
Factor out the GCF from each term. This can be done by dividing each term by the GCF. The result is \(3x^{2}(2x + 5)\). which is the factored form of the polynomial.
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