What is the remainder when x3+4x2−7x−10 is divided by x+4?
any number is the answer but i dont know the formula can someone help please and thanks
using the Remainder Theorem, that would be f(-4) = -64+64+28-10 = 18
it was a timed test but im sure someone in the future would use this
To find the remainder when dividing a polynomial by another polynomial, you can use polynomial long division. Here's how you can find the remainder when dividing the polynomial x^3 + 4x^2 - 7x - 10 by x + 4:
Step 1: Arrange the terms of the dividend (x^3 + 4x^2 - 7x - 10) in descending order of exponents.
Step 2: Begin the division by considering the highest degree term in the dividend and the divisor. In this case, it is x^3 divided by x. The result is x^2.
Step 3: Multiply the entire divisor (x + 4) by the result in Step 2 (x^2). The product is x^3 + 4x^2.
Step 4: Subtract the product obtained in Step 3 from the dividend. (x^3 + 4x^2 - (x^3 + 4x^2) = -7x - 10).
Step 5: Shift the subtraction result (or what remains after Step 4) one degree to the left and repeat Steps 2-4 until the subtraction result has a degree lower than the divisor.
In this case, the result of Step 4 (-7x - 10) is a polynomial of degree 1, which is less than the degree of the divisor x + 4. Therefore, we stop the division.
The remainder is the expression obtained after the final subtraction, which is -7x - 10.
In conclusion, the remainder when dividing x^3 + 4x^2 - 7x - 10 by x + 4 is -7x - 10.