Question

Divide the following. Give your answer in the form quotient +

-20x³ +17z² + 10x
5x+2
Question Help:
=
remainder
divisor
if necessary.

Answer 1

To divide the polynomial -20x³ + 17z² + 10x by the polynomial 5x + 2, we can use long division. The quotient is -4x² + 3z² + 2x, and the remainder is -2z² + 12x.

Step-by-step explanation:

To divide a polynomial by another polynomial, we can use either long division or synthetic division. In this case, we will use long division. Let's divide the polynomial -20x³ + 17z² + 10x by the polynomial 5x + 2.

1. Divide the first term of the dividend (-20x³) by the first term of the divisor (5x). This gives us -4x².
2. Multiply the divisor (5x + 2) by the quotient we obtained in the previous step (-4x²). This gives us -20x³ - 8x².
3. Subtract this result (-20x³ - 8x²) from the dividend (-20x³ + 17z² + 10x). This gives us 0x³ + 17z² + 18x.
4. Bring down the next term of the dividend, which is 17z². We now have 17z² + 18x.
5. Divide the new dividend (17z² + 18x) by the divisor (5x + 2). This gives us 3z² + 2x.
6. Multiply the divisor (5x + 2) by the new quotient (3z² + 2x). This gives us 15z² + 6x.
7. Subtract this result (15z² + 6x) from the new dividend (17z² + 18x). This gives us -2z² + 12x.

So, the quotient is -4x² + 3z² + 2x, and the remainder is -2z² + 12x.

Learn more about Dividing polynomials