Exponents and Polynomials Factoring a univariate polynomial by grouping: Probl
Factor by grouping.
\[
2 x^{3}-5 x^{2}-6 x+15
\]
Answer
\(\boxed{(2x - 5)(x^{2} - 3)}\) is the final answer.
Step 1 ：Given the polynomial \(2 x^{3}-5 x^{2}-6 x+15\).
Step 2 ：To factor a polynomial by grouping, we first need to split the polynomial into two groups. In this case, we can group the first two terms together and the last two terms together.
Step 3 ：Then, we factor out the greatest common factor (GCF) from each group. If the resulting expressions in parentheses are the same, then we have factored correctly. If not, we need to rearrange the terms and try again.
Step 4 ：The factored form of the polynomial is \((2x - 5)(x^{2} - 3)\).
Step 5 ：\(\boxed{(2x - 5)(x^{2} - 3)}\) is the final answer.
