Question

Which expression is equivalent to

2x ²−x+18?
A. 2(x−12) ²

B. 2(x−14) ²

C. 2(x−18)²

D. 2(x−11) ²

Answer 1

The expression 2x²−x+18 can be factored to (2x−9)(x−2). The equivalent expression is 5x²−40x+85.

Step-by-step explanation:

The expression 2x²−x+18 can be factored to (2x−9)(x−2). Therefore, to find an equivalent expression, we need to square the factors.

Using the FOIL method, we get (2x−9)² = (2x)²−2(2x)(9)+(9)² = 4x²−36x+81.

Similarly, (x−2)² = (x)²−2(x)(2)+(2)² = x²−4x+4.

Therefore, the equivalent expression to 2x²−x+18 is 4x²−36x+81+x²−4x+4 = 5x²−40x+85.