Question

Use long division to determine if x+5 is a factor of the following polynomial. Explain how you know. 3x^3+7x^2-103x-35

Answer 1

To determine if x+5 is a factor of the polynomial 3x^3+7x^2-103x-35, we can use long division. After performing the division, we find that there is a remainder, indicating that x+5 is not a factor of the polynomial.

Step-by-step explanation:

To determine if x+5 is a factor of the polynomial 3x^3+7x^2-103x-35, we can use long division. Here is how:

1. Divide the first term of the polynomial, 3x^3, by x+5. The result is 3x^2.
2. Multiply the divisor, x+5, by the quotient obtained in the previous step, 3x^2, and subtract it from the polynomial. This gives us 4x^2-103x-35.
3. Repeat the process by dividing the first term of the new polynomial, 4x^2, by x+5. The quotient is 4x.
4. Multiply the divisor, x+5, by the quotient obtained in the previous step, 4x, and subtract it from the new polynomial. This results in -503x-35.
5. The remaining polynomial, -503x-35, cannot be further divided by x+5. Therefore, x+5 is not a factor of the polynomial 3x^3+7x^2-103x-35.