Question

Factor completely 2x^3 + 10x^2 + 14x + 70(2x^2 + 14)(x + 5)(x^2 + 7)(2x + 10)2(x^3 + 5x^2 + 7x + 35)2[(x^2 + 7)(x + 5)]

Answer 1

`2x^3+\text{ 10x}^2\text{ +14x + 70 = 2\lbrack\lparen x}^2\text{ + 7\rparen\lparen x + 5\rparen\rbrack}`

Step-by-step explanation

Given polynomial function

`2x^3\text{ + 10x}^2\text{ + 14x + 70}`

To factor the given polynomial function, follow the steps below

Step 1: Divide the expression through by 2 in order to make sure that the coefficient of x^3 is 1

`\begin{gathered} 2x^3\text{ + 10x}^2\text{ + 14x + 70} \\ (2x^3)/(2)\text{ + }(10x^2)/(2)+\text{ }(14x)/(2)\text{ + }(70)/(2) \\ x^3\text{ + 5x}^2\text{ + 7x + 35} \end{gathered}`

Step 2: Factor the simplified expression in step 1

`\begin{gathered} \text{ x}^3\text{ + 5x}^2\text{ + 7x + 35} \\ \text{ Factor}^\text{ x}^2\text{ out in the expression} \\ x^2(x\text{ + 5\rparen + 7\lparen x + 5\rparen} \\ \text{ \lparen x}^2\text{ + 7\rparen \lparen x + 5\rparen} \\ 2[(x^2\text{ +7\rparen\lparen x + 5\rparen\rbrack} \end{gathered}`

Hence, the correct answer is option D