Question

1. a.apr.1

rewrite this polynomial function in standard form using the box method or distributive property.
(x-3)(2x-1)(x+4)

1. rei.c.7

Explanation:

Step1: Multiply first two binomials

First, multiply \((x - 3)\) and \((x + 4)\) using the box method (or distributive property). From the box, we get \(x^2 + 4x - 3x - 12 = x^2 + x - 12\).

Step2: Multiply the result with the third binomial

Now, multiply \((x^2 + x - 12)\) with \((2x - 1)\).
Using distributive property:
\(x^2(2x - 1)+x(2x - 1)-12(2x - 1)\)
\(= 2x^3 - x^2 + 2x^2 - x - 24x + 12\)

Step3: Combine like terms

Combine the like terms:
\(2x^3 + (-x^2 + 2x^2)+(-x - 24x)+12\)
\(= 2x^3 + x^2 - 25x + 12\)

Answer:

\(2x^3 + x^2 - 25x + 12\)