Question

Find the product of the given polynomials

Answer 1

Option A:

$-2x^2+19x-24$

Step-by-step explanation:

Given polynomials are (5x + 8 – 6x) and (4 + 2x –7).

Let us first simplify the expression:

Combine like terms.

(5x + 8 – 6x) = (5x – 6x + 8) = –x + 8

(4 + 2x –7) = (4 – 7 + 2x) = –3 + 2x

Product of (5x + 8 – 6x) and (4 + 2x –7)

              = (5x + 8 – 6x)(4 + 2x –7)

              = (–x + 8)(–3 + 2x)

Multiply each term of one expression with each term of the other expression.

              = (–x)(–3) + (–x)(2x) + 8(–3) + 8(2x)

              $=3x-2x^2-24+16x$

Combine like terms and add.

              $=(3x+16x)-2x^2-24$

              $=19x-2x^2-24$

Arranging the equation, starting with highest power.

              $=-2x^2+19x-24$

Hence, the product of the two given polynomials is $-2x^2+19x-24.$