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# Binomial

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What number goes in the box so that the quadratic is the square of a binomial? 9x^2 + 6x + 8x - 5x^2 + ___

May 12, 2022

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Simplify the polynomial first.

$$\quad 9x^2 + 6x + 8x - 5x^2 + \underline{\phantom{\text{aaaaa}}}\\ = 4x^2 + 14x + \underline{\phantom{\text{aaaaa}}}\\$$

Note that (a + b)^2 = a^2 + 2ab + b^2. What happens if we take a = 2x?

(2x + b)^2 = 4x^2 + 4bx + b^2

There we matched the first term of the polynomial. The rest is just finding the value of b that makes the second term match, and then the answer is just b^2.

Hint: Consider the coefficient. What b would make 4b = 14?

May 12, 2022