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
well, if 9 is one factor of 36, the other is 4.
So, since you have +5x, you need
(x+9)(x-4)
To find the binomial that you can multiply with (x + 9) to get the product x^2 + 5x - 36, you can use the method of long division.
Step 1: Arrange the polynomial in descending order:
x^2 + 5x - 36
Step 2: Identify the leading term of the dividend (x^2) and the divisor (x) and determine what you need to multiply the divisor by to get the leading term of the dividend. In this case, the leading term of the dividend is x^2 and the divisor is (x + 9), so we need to multiply (x + 9) by x to get x^2.
x <- Quotient term for step 3
_________________
x + 9 | x^2 + 5x - 36
- (x^2 + 9x)
____________
-4x - 36
Step 3: Divide the x term in the dividend (5x) by the divisor (x + 9), which gives you the next term of the quotient. In this case, 5x divided by (x + 9) is 5.
x + 5 <- Quotient term for step 4
_________________
x + 9 | x^2 + 5x - 36
- (x^2 + 9x)
____________
-4x - 36
Step 4: Multiply the quotient term (x + 5) by the divisor (x + 9) and subtract it from the dividend. In this case, (x + 5) multiplied by (x + 9) is (x^2 + 14x + 45).
x + 5
_________________
x + 9 | x^2 + 5x - 36
- (x^2 + 9x)
____________
-4x - 36
- ( -4x - 36)
____________
0
Step 5: If the resulting polynomial is zero, then the binomial you multiplied by is the correct answer. In this case, the resulting polynomial is zero, indicating that the binomial (x + 5) is the correct answer.
Therefore, the binomial you can multiply by (x + 9) to get the product x^2 + 5x - 36 is B. x + 5.