Which expression is equivalent to x^2 - 9x + 20? | SAT Equivalent expressions Question, Answer Explained

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Which expression is equivalent to $x^2 - 9x + 20$ ?

$(x - 2)(x - 10)$

$(x - 4)(x - 5)$

$(x + 4)(x - 5)$

$(x + 4)(x + 5)$

Show answer and explanation

Answer: B

Look for two numbers whose product is $20$ and whose sum is $-9$ . These are $-4$ and $-5$ , so $x^2 - 9x + 20 = (x - 4)(x - 5)$ . Check: $(x - 4)(x - 5) = x^2 - 5x - 4x + 20 = x^2 - 9x + 20$ .

Choice D has the right product, $20$ , but its middle term is $+9x$ , not $-9x$ .

Why the other choices are wrong

A. -2 and -10 multiply to 20 but add to -12, so the middle term would be -12x.
C. 4 and -5 add to -1 and multiply to -20, which gives x² - x - 20.
D. 4 and 5 multiply to 20 but add to +9, so the middle term would be +9x.

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