the directions are perform the indicated divisions.
so the problem is:
(x^2-2x-35)/(x+5)
so these are the steps i took:
(-36x^3)/(6x)=
so my answer was:
-6x^2
Nope. Factor the numerator, one of the factors will be x+5, which will divide out.
To perform the division of polynomials, we use the process called polynomial long division. Here are the steps to divide the polynomial (x^2 - 2x - 35) by (x + 5):
Step 1: Set the division problem up in the long division format:
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(x + 5) | (x^2 - 2x - 35)
Step 2: Divide the first term of the numerator (x^2) by the first term of the denominator (x), which gives us x. Write the result above the line:
x
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(x + 5) | (x^2 - 2x - 35)
Step 3: Multiply the divisor (x + 5) by the quotient (x), which gives us (x^2 + 5x). Write this product below the numerator polynomial, aligning the terms according to their degree:
x
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(x + 5) | (x^2 - 2x - 35)
-(x^2 + 5x)
Step 4: Subtract the product from the numerator polynomial. This step eliminates the first term of the numerator:
x
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(x + 5) | (x^2 - 2x - 35)
-(x^2 + 5x)
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- 7x - 35
Step 5: Bring down the next term from the numerator (- 7x) and repeat the dividing process:
x - 7
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(x + 5) | (x^2 - 2x - 35)
-(x^2 + 5x)
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- 7x - 35
- (- 7x - 35)
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0
Step 6: Once the degree of the remaining term is less than the degree of the divisor, the division is completed. In this case, the remaining term is 0. This means that (x + 5) divides evenly into (x^2 - 2x - 35).
Therefore, the final result of the polynomial division is x - 7.