Question

question 3 of 5

select the correct answer.

simplify the following expression.
\\((3x^2 - 11x - 4) - (x - 2)(2x + 3)\\)

\\(\bigcirc\\) \\(x^2 - 12x - 10\\)
\\(\bigcirc\\) \\(x^2 - 10x + 2\\)
\\(\bigcirc\\) \\(5x^2 - 12x - 10\\)
\\(\bigcirc\\) \\(x^2 + 10x - 2\\)

Explanation:

⚡ Using what you learned: multiplying polynomials · adding and subtracting polynomials

Step 1: Expand the binomials

Multiply the two binomials in the second part of the expression:

$$ (x - 2)(2x + 3) = x(2x) + x(3) - 2(2x) - 2(3) $$

$$ = 2x^2 + 3x - 4x - 6 $$

$$ = 2x^2 - x - 6 $$

Step 2: Subtract the expanded expression

Substitute the expanded result back into the original expression and distribute the negative sign:

$$ (3x^2 - 11x - 4) - (2x^2 - x - 6) $$

$$ = 3x^2 - 11x - 4 - 2x^2 + x + 6 $$

Step 3: Combine like terms

Group and combine the terms with the same powers of \(x\):

$$ (3x^2 - 2x^2) + (-11x + x) + (-4 + 6) $$

$$ = x^2 - 10x + 2 $$

Answer:

\(x^2 - 10x + 2\) (the second option)