Question

When the polynomial 2x⁴+16x³+42x²+36x is divided by (x+3) what is the quotient?

Answer 1

Dividing the polynomial 2x⁴+16x³+42x²+36x by (x+3), the quotient is 2x³+10x²+12x+6.

Step-by-step explanation:

When dividing the polynomial 2x⁴+16x³+42x²+36x by (x+3), we can use polynomial long division. Here is the step-by-step process:

1. Start by dividing 2x⁴ by x, which gives us 2x³.
2. Multiply (x+3) by 2x³ to get 2x⁴+6x³.
3. Subtract 2x⁴+6x³ from 2x⁴+16x³ to get 10x³.
4. Bring down the next term, which is 42x².
5. Divide 10x³ by x, which gives us 10x².
6. Multiply (x+3) by 10x² to get 10x³+30x².
7. Subtract 10x³+30x² from 10x³+42x² to get 12x².
8. Bring down the next term, which is 36x.
9. Divide 12x² by x, which gives us 12x.
10. Multiply (x+3) by 12x to get 12x³+36x.
11. Subtract 12x³+36x from 12x³+42x² to get 6x.
12. Bring down the next term, which is 0.
13. Divide 6x by x, which gives us 6.
14. Multiply (x+3) by 6 to get 6x+18.
15. Subtract 6x+18 from 6x to get -18.

The quotient is 2x³+10x²+12x+6, and the remainder is -18.