Question

Divide 15x^4 - 5x^3 - 10x^2 by -5x^2

Answer 1

To divide the given polynomial by -5x^2, you divide each term's coefficient by -5 and subtract 2 from each term's exponent, resulting in -3x^2 + x + 2.

Step-by-step explanation:

To divide the polynomial 15x^4 - 5x^3 - 10x^2 by -5x^2, you perform division of exponentials by dividing the digit terms of the numerator by the digit term of the denominator and subtracting the exponents of the exponential terms.

Here are the steps:

1. Divide the coefficient of each term by -5.
2. Subtract 2 from the exponent of each x term, because you're dividing by x^2.

The results are:

• 15x^4 divided by -5x^2 is -3x^(4-2), which simplifies to -3x^2.
• -5x^3 divided by -5x^2 is x^(3-2), which simplifies to x.
• -10x^2 divided by -5x^2 is 2x^(2-2), which simplifies to 2.

So the final answer is -3x^2 + x + 2.