Question

question 4 of 5

select the correct answer.

simplify the following polynomial expression.

\\3x(4x + 5) - 4(-x - 3)(2x - 5)\\

• \\4x^2 + 59x + 60\\
• \\20x^2 + 59x - 15\\
• \\20x^2 + 19x - 60\\
• \\4x^2 + 19x + 15\\

Explanation:

⚡ Using what you learned: multiplying polynomials

Step 1: Expand the first term

$$ 3x(4x + 5) = 12x^2 + 15x $$

Step 2: Multiply the binomials in the second term

$$ (-x - 3)(2x - 5) = -2x^2 + 5x - 6x + 15 = -2x^2 - x + 15 $$

Step 3: Distribute the constant factor

$$ -4(-2x^2 - x + 15) = 8x^2 + 4x - 60 $$

Step 4: Combine like terms

$$ (12x^2 + 15x) + (8x^2 + 4x - 60) = 20x^2 + 19x - 60 $$

Answer:

\(20x^2 + 19x - 60\)