9514 1404 393
Answer:
d. 40
Step-by-step explanation:
Consider the square ...
(px +q)² = (px)² +2(px)(q) +q² = p²x² +2pqx +q²
Comparing this to your expression, you see ...
16 = p² ⇒ p = ±4
25 = q² ⇒ q = ±5
-b = 2pq = 2(±4)(±5) = ±40
The expression is a perfect square trinomial when b = 40.
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Additional comment
When the linear term has a negative coefficient, we know the signs of the binomial terms are different. We conventionally write the square with the constant term in the binomial being negative:
16x² -40x +25 = (4x -5)²
