ANSWER
[tex]2x^3+\text{ 10x}^2\text{ +14x + 70 = 2\lbrack\lparen x}^2\text{ + 7\rparen\lparen x + 5\rparen\rbrack}[/tex]
EXPLANATION
Given polynomial function
[tex]2x^3\text{ + 10x}^2\text{ + 14x + 70}[/tex]
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
[tex]\begin{gathered} 2x^3\text{ + 10x}^2\text{ + 14x + 70} \\ \frac{2x^3}{2}\text{ + }\frac{10x^2}{2}+\text{ }\frac{14x}{2}\text{ + }\frac{70}{2} \\ x^3\text{ + 5x}^2\text{ + 7x + 35} \end{gathered}[/tex]
Step 2: Factor the simplified expression in step 1
[tex]\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}[/tex]
Hence, the correct answer is option D
