Question

explain the process of transforming x^2 + 8x + 15 into factored form by completing the sentence starters to find the factors i first try to find....next, I think about...The equivalent expression in factored form is.... To check that the factors are correct, I can...

Answer 1

To find the factor first try to find two such number whose product is equal to 15x^2 and sum is equal to 8x. Such numbers are 5x and 3x.

Evaluate the factor of the equation.

`\begin{gathered} x^2+8x+15=x^2+5x+3x+15 \\ =x(x+5)+3(x+5) \\ =(x+5)(x+3) \end{gathered}`

The equivalent expression is (x+5)(x+3).

To check the factors are correct multiply the factors then original equation is obtained.

`\begin{gathered} (x+5)(x+3)=x\cdot x+3\cdot x+5\cdot x+5\cdot3 \\ =x^2+3x+5x+15 \\ =x^2+8x+15 \end{gathered}`

So factors are correct.