x4 + 11x3 + 33x2 + 24x +23 (Called the dividend.)
x+6 (Called the divisor.)
_______x3 + 5x2 + 3x + 6
x + 6 |x4 + 11x3 + 33x2 + 24x +23
2. -(x4 + 6x3) | | |
3. 5x3 + 33x2 | |
4. -(5x3 + 30x2) | |
5. 3x2 + 24x |
6. -(3x2 + 18x) |
7. 6 x + 23
8. -(6x + 36)
You have an x4 expression divided by an x expression.
1. What multiplied by x will give x4? -> x3. Write x3 up top above the x3 term in the dividend.
2. Multiply x3 times (x + 6) and write below the corresponding terms -> x4 + 6x3
3. Subtract the terms-you are left w/5x3. Bring down 33x2. Now you have 5x3 + 33x2.
4. What multiplied by x will give 5x3? 5x2. Put 5x2 on & top multiply it by x + 6 = 5x2 + 30x2. Write it below the 5x3 + 33x2.
5. Subtract the terms-you're left w/3x2. Bring down 24x. Now you have 3x2 + 24x.
6. What multiplied by x will give 3x2? Put 3x on & top multiply it by x + 6 = 3x2 + 18x. Write this below the 3x2 + 24x.
7. Subtract the terms-you're left w/6x. Bring down 23. Now you have 6x + 23.
8. What multiplied by x will give 6x? 6. Put 6 on & top multiply by x + 6 = 6x + 36. Write this under 6x + 23.
9. Subtract the terms-you're left w/-13. This is your remainder.
10. Your answer is x3 + 5x2 + 3x + 6 R -13
(x3 + 5x2 + 3x + 6 is called the quotient and -13 is the remainder.)
It helps to write all of this down yourself while you follow along with the reasoning.
I've numbered each step in the problem and numbered each step. These should match up. Let me know if you can follow it this way.