Question

select the correct answer.

what is the simplest form of this expression?

\\((2x + 1)(x^2 - 9x + 11)\\)

\\(\bigcirc\\) \\(2x^3 - 19x^2 + 11x + 11\\)

\\(\bigcirc\\) \\(2x^3 - 17x^2 + 13x + 11\\)

\\(\bigcirc\\) \\(2x^3 + 18x^2 + 22x + 11\\)

\\(\bigcirc\\) \\(2x^3 - 18x^2 - 9x + 11\\)

Explanation:

⚡ Using what you learned: multiplying polynomials

Step 1: Distribute the terms

Multiply each term in the first polynomial by each term in the second polynomial:

$$ (2x + 1)(x^2 - 9x + 11) = 2x(x^2 - 9x + 11) + 1(x^2 - 9x + 11) $$

$$ = (2x^3 - 18x^2 + 22x) + (x^2 - 9x + 11) $$

Step 2: Combine like terms

Group and combine the terms with the same exponents:

$$ 2x^3 + (-18x^2 + x^2) + (22x - 9x) + 11 $$

$$ = 2x^3 - 17x^2 + 13x + 11 $$

Answer:

\( 2x^3 - 17x^2 + 13x + 11 \) (the second option)