Ace the Accuplacer 2026: Unleash Your Algebra Advanced Powers!

To divide the polynomial \( 6x^4 + 11x^2 - 10 \) by \( 2x^2 + 5 \), we can utilize polynomial long division.

First, we write down the division setup as we would with numerical long division. We start with the leading term of the dividend, \( 6x^4 \), divided by the leading term of the divisor \( 2x^2 \). This gives us \( 3x^2 \), which we place as the first term of our quotient.

Next, we multiply \( 3x^2 \) by \( 2x^2 + 5 \), resulting in \( 6x^4 + 15x^2 \). We subtract this product from the original polynomial:

\[

(6x^4 + 11x^2 - 10) - (6x^4 + 15x^2) = 11x^2 - 15x^2 - 10 = -4x^2 - 10.

\]

Now, we repeat the division process using the leading term \( -4x^2 \). We divide this by \( 2x^2 \),