SAT Math · Equivalent expressions · medium

If (x-6)(x+2) = x² + bx + c for all values of x, what is the value of b - c?

If (x−6)(x+2)=x2+bx+c(x-6)(x+2) = x^2 + bx + c for all values of xx, what is the value of b−cb - c?

Answer and explanation

Answer: B: 8

Expand: (x−6)(x+2)=x2+2x−6x−12=x2−4x−12(x - 6)(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12. So b=−4b = -4 and c=−12c = -12. The question asks for b−c=−4−(−12)=−4+12=8b - c = -4 - (-12) = -4 + 12 = 8, choice B. Choice A (−16-16) is b+cb + c. Choice C (−4-4) is bb alone. Choice D (−8-8) has the wrong sign, which comes from computing c−bc - b or from subtracting without handling the double negative. Careful sign work is the whole challenge here, so write out b−cb - c with the values in parentheses.

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