High School

The polynomial [tex]2025x + 26x^8[/tex] is equivalent to the product of [tex](5x + 4)[/tex] and which of the following binomials?

A. [tex]4x^7[/tex]
B. [tex]5x^7[/tex]
C. [tex]5x^9[/tex]
D. [tex]4x^9[/tex]

Answer :

Final answer:

To find the binomial that, when multiplied by (5x + 4), gives you the polynomial 2025x + 26x^8, you can use polynomial long division. The resulting binomial is (405x + 324).

Explanation:

To find the binomial that, when multiplied by (5x + 4), gives you the polynomial 2025x + 26x^8, we need to divide the polynomial by (5x + 4) using polynomial long division. Here's how:

  1. First, divide the first term of the polynomial, 2025x, by the first term of the binomial, 5x. This gives you 405x as the first term of the quotient.
  2. Next, multiply the entire binomial, (5x + 4), by 405x. This gives you 2025x^2 + 1620x.
  3. Subtract this product from the original polynomial: (2025x + 26x^8) - (2025x^2 + 1620x).
  4. Continue this process until you can no longer divide.

When you divide the polynomial by (5x + 4), you will find that the quotient is 405x + 324. Therefore, the polynomial 2025x + 26x^8 is equivalent to the product of (5x + 4) and (405x + 324).

Learn more about Polynomial Division here:

https://brainly.com/question/36507743

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