Question

practice: multiplying polynomials
name: tyler weiboa date: -20-2025
directions: multiply. write each answer in standard form.
1 monomial × trinomial
-3x²(x² + 4x - 5)
2 monomial × trinomial
5x(2x² - x + 6)
3 binomial × binomial
(x + 7)(x - 3)
4 binomial × binomial
(3x - 2)(2x + 5)
5 trinomial × binomial
(x² + x - 4)(2x + 1)

Explanation:

Problem 1: $-3x^2(x^2 + 4x - 5)$ (assuming the first term inside the trinomial is $x^2$ as the original might have a typo)

Step1: Distribute $-3x^2$

Multiply $-3x^2$ with each term in the trinomial:
$-3x^2 \cdot x^2 + (-3x^2) \cdot 4x + (-3x^2) \cdot (-5)$
$= -3x^{4} - 12x^{3} + 15x^{2}$

Step1: Distribute $5x$

Multiply $5x$ with each term in the trinomial:
$5x \cdot 2x^2 + 5x \cdot (-x) + 5x \cdot 6$
$= 10x^{3} - 5x^{2} + 30x$

Step1: Use FOIL method

Multiply First, Outer, Inner, Last terms:
First: $x \cdot x = x^2$
Outer: $x \cdot (-3) = -3x$
Inner: $7 \cdot x = 7x$
Last: $7 \cdot (-3) = -21$

Step2: Combine like terms

$x^2 - 3x + 7x - 21 = x^2 + 4x - 21$

Answer:

$-3x^4 - 12x^3 + 15x^2$

Problem 2: $5x(2x^2 - x + 6)$