Option A:
[tex]-2x^2+19x-24[/tex]
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)
[tex]=3x-2x^2-24+16x[/tex]
Combine like terms and add.
[tex]=(3x+16x)-2x^2-24[/tex]
[tex]=19x-2x^2-24[/tex]
Arranging the equation, starting with highest power.
[tex]=-2x^2+19x-24[/tex]
Hence, the product of the two given polynomials is [tex]-2x^2+19x-24.[/tex]
