Question

What is the factored form of his expression ? 2x^3+5x^2+6x+15

Answer 1

The given expression is:

`2x^3+5x^2+6x+15`

It is required to write the expression in factored form.

`\begin{gathered} \text{ Factor out }x^2\text{ in the first two terms of the expression:} \\ x^2(2x+5)+6x+15 \end{gathered}`

Next, factor out 3 in the last two terms of the expression:

`x^2(2x+5)+3(2x+5)`

Factor out the binomial 2x+5 in the expression:

`(2x+5)(x^2+3)`

The expression in factored form is (2x+5)(x²+3).