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Which value of b would make 16x? - bx + 25 a perfect square trinomial?

a. 4
b. 5
C. 20
d. 40

1 Answer

4 votes

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Answer:

d. 40

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

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