What value in place of the question mark makes the polynomial below a perfect square trinomial?9x2 + ?x + 49A.126B.42C.21D.63
Question
What value in place of the question mark makes the polynomial below a perfect square trinomial?9x2 + ?x + 49A.126B.42C.21D.63
Solution
A perfect square trinomial is a trinomial that can be factored into the square of a binomial. The general form of a perfect square trinomial is (ax)² + 2abx + b².
Given the trinomial 9x² + ?x + 49, we can see that a = 3x (since (3x)² = 9x²) and b = 7 (since 7² = 49).
The middle term of a perfect square trinomial is 2ab. So, we can find the missing value by multiplying 2, a, and b:
2 * 3x * 7 = 42x
So, the missing coefficient of x is 42. Therefore, the answer is B. 42.
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