The expression 2x^2 + ax is equivalent to x(2x + 7) for some constant a . What is the value of a ?

The correct answer is D. Choice D is correct. It's given that 2x^2 + ax is equivalent to x(2x + 7) for some constant a . Distributing the x over each term in the parentheses gives 2x^2 + 7x , which is in the same form as the first given expression, 2x^2 + ax . The coefficient of the second term in 2x^2 + 7x is 7 . Therefore, the value of a is 7 .

Note: Enter the relationship as a regression; Desmos prints a=7.

SAT Question 49efde89: Answer, Explanation & Desmos Solution

Choice A

Choice A is incorrect. If the value of $a$ were $2$ , then $2 x^{2} + a x$ would be equivalent to $2 x^{2} + 2 x$ , which isn't equivalent to $x (2 x + 7)$ .

Choice B

Choice B is incorrect. If the value of $a$ were $3$ , then $2 x^{2} + a x$ would be equivalent to $2 x^{2} + 3 x$ , which isn't equivalent to $x (2 x + 7)$ .

Choice C

Choice C is incorrect. If the value of $a$ were $4$ , then $2 x^{2} + a x$ would be equivalent to $2 x^{2} + 4 x$ , which isn't equivalent to $x (2 x + 7)$ .

Explanation

Enter in Desmos:

Why the other choices are wrong

SAT Question 49efde89: Equivalent Expressions answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong