Name the binomial you can multiply by (x + 9) to get the product x^2 + 5x - 36.
A. 4 - x
B. x + 6
C. x - 4
D. x - 6
Y = x^2+5x-36 = 0
-36 = -4*9, -4+9 = 5 = B.
(x-4)(x+9) = 0.
To find the binomial that can be multiplied by (x + 9) to get the given product x^2 + 5x - 36, we can use the method of factoring.
First, we will multiply the binomial (x + 9) with each of the answer choices and see which one gives us the desired result.
A. (x + 9)(4 - x) = 4x - x^2 + 36 - 9x = -x^2 - 5x + 36 (not the desired result)
B. (x + 9)(x + 6) = x^2 + 6x + 9x + 54 = x^2 + 15x + 54 (not the desired result)
C. (x + 9)(x - 4) = x^2 - 4x + 9x - 36 = x^2 + 5x - 36 (the desired result)
D. (x + 9)(x - 6) = x^2 - 6x + 9x - 54 = x^2 + 3x - 54 (not the desired result)
From the above calculations, we can see that only option C, (x - 4), when multiplied by (x + 9), gives us the desired result x^2 + 5x - 36.
Therefore, the correct answer is C. x - 4.