Question

(15x³-7x²-7x+4)÷(5x²+x) Your answer should give the quotient and the remainder.

Answer 1

The quotient of the polynomial division (15x³-7x²-7x+4) ÷ (5x²+x) is 3x-2 with a remainder of -5x+4, computed through a series of division, multiplication, and subtraction steps.

Step-by-step explanation:

To divide the polynomial (15x³-7x²-7x+4) by (5x²+x), you can use long division. Here's how you would compute the quotient and the remainder step by step:

1. Divide the first term of the numerator by the first term of the denominator: 15x³ ÷ 5x² = 3x. This is the first term of the quotient.
2. Multiply the entire denominator by this term and subtract from the numerator: (5x²+x)(3x) = 15x³+3x², then 15x³-7x² - (15x³+3x²) = -10x².
3. Bring down the next term of the numerator to get -10x²-7x.
4. Divide -10x² by 5x² to get -2. This is the next term of the quotient.
5. Multiply the entire denominator by this new term and subtract from the new numerator: (5x²+x)(-2) = -10x²-2x, then -10x²-7x - (-10x²-2x) = -5x.
6. Bring down the next term of the numerator to get -5x+4.
7. Since 5x² cannot divide into -5x, the division stops here and -5x+4 is the remainder.

The quotient is 3x-2 and the remainder is -5x+4.