Question

If f(x)=x^(2)-x+3, then what is the remainder when f(x) is divided by x+9?

Answer 1

To find the remainder when f(x) is divided by x+9, use polynomial long division method. The remainder is 93.

Step-by-step explanation:

To find the remainder when f(x) is divided by x+9, we can use the polynomial long division method.

1. Divide the first term of f(x), which is x^2, by the first term of x+9, which is x.
2. Write the quotient, x, above the line.
3. Multiply x+9 by x, which gives us x^2+9x.
4. Subtract x^2+9x from x^2-x+3, which gives us -10x+3.
5. Bring down the next term, which is -10x.
6. Repeat the steps by dividing -10x by x, which gives us -10.
7. Write the quotient, -10, above the line.
8. Multiply x+9 by -10, which gives us -10x-90.
9. Subtract -10x-90 from -10x+3, which gives us 93.
10. Since there are no more terms to bring down, the remainder is 93.

Therefore, the remainder when f(x) is divided by x+9 is 93.