Question

1. (01.06 lc) simplify (x - 4)(x² + 3x + 5). (5 points) x³ + 7x² + 17x - 20 x³ + 7x² - 7x - 20 x³ - x² + 17x - 20 x³ - x² - 7x - 20

Explanation:

Step1: Distribute $x$ to the trinomial

$x(x^2 + 3x + 5) = x^3 + 3x^2 + 5x$

Step2: Distribute $-4$ to the trinomial

$-4(x^2 + 3x + 5) = -4x^2 - 12x - 20$

Step3: Combine all resulting terms

$x^3 + 3x^2 + 5x - 4x^2 - 12x - 20$

Step4: Combine like terms

$x^3 + (3x^2 - 4x^2) + (5x - 12x) - 20 = x^3 - x^2 - 7x - 20$

Answer:

$\boldsymbol{x^3 - x^2 - 7x - 20}$ (the fourth option)