What value in place of the question mark makes the polynomial below a perfect square trinomial?9x2 + ?x + 49A.21B.126C.42D.63SUBMITarrow_backPREVIOUS
Question
What value in place of the question mark makes the polynomial below a perfect square trinomial?
A. 21
B. 126
C. 42
D. 63
SUBMIT arrow_back PREVIOUS
Solution
The polynomial is a perfect square trinomial if it can be written in the form (ax+b)^2.
The general form of a perfect square trinomial is a^2 + 2ab + b^2.
Given the trinomial 9x^2 + ?x + 49, we can see that a^2 = 9x^2 and b^2 = 49.
Taking the square root of a^2 and b^2, we get a = 3x and b = 7.
Substituting a and b into 2ab gives us 23x7 = 42x.
Therefore, the value that should replace the question mark to make the polynomial a perfect square trinomial is 42x.
So, the correct answer is C. 42.
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