Question

So confused! I have the answer, but can't understand the explanation. Please help...

A polynomial expression is show below.
(mx^3+3)(2x^2+5x+2)-(8x^5+20x^4)
The expression is simplified to 8x^3+6x^2+15x+6. What is the value of m?
The answer is 4 because in the simplified answer, there is no x^5 we assume that
2mx^5 - 8x^5 = 0x^5
2m x^5=8x^5
2m=8
m=4

Answer 1

(mx³ + 3)(2x² + 5x + 2) - (8x⁵ + 20x⁴) = 8x³ + 6x² + 15x + 6
(mx³(2x² + 5x + 2) + 3(2x² + 5x + 2)) - (8x⁵ + 20x⁴) = 8x³ + 6x² + 15x + 6
(mx³(2x²) + mx³(5x) + mx³(2) + 3(2x²) + 3(5x) + 3(2)) - (8x⁵ + 20x⁴) = 8x³ + 6x² + 15x + 6
(2mx⁵ + 5mx⁴ + 2mx³ + 6x² + 15x + 6) - (8x⁵ + 20x⁴) = 8x³ + 6x² + 15x + 6
(2mx⁵ + 5mx⁴ + 2mx³ + 6x² + 15x + 6) - 8x⁵ - 20x⁴ = 8x³ + 6x² + 15x + 6 - 6x² - 15x - 6 - 6x² - 15x - 6
(2m(x⁵) + 5m(x⁴) + 2m(x³)) - 8x⁵ - 20x⁴ = 8x³
(2x⁵ + 5x⁴ + 2x³)m - 8x⁵ - 20x⁴ = 8x³
10x⁵ - 15x⁴)m = 8x

Answer 2

`(mx^3+3)*(2x^2+5x+2)-(8x^5+20x^4)=8x^3+6x^2+15x+6 \\ (mx^3*2x^2)+(mx^3*5x)+(mx^3*2)+(3*2x^2)+(3*5x)+(3*2) \\ -8x^5-20x^4=8x^3+6x^2+15x+6\\ \\ 2mx^5+5mx^4+2mx^3+6x^2+15x+6-8x^5-20x^4 \\ =8x^3+6x^2+15x+6 \\ \\ (2m-8) x^(5) +(5m-20) x^(4) +2mx^3+6x^2+15x+6 \\ =8x^3+6x^2+15x+6 \\ \\ (2m-8) x^(5) +(5m-20) x^(4) +(2m-8)x^3=0 \\ (m-4) 2x^(5) +(m-4) 5x^(4) +(m-4)2 x^3=0 \\ (m-4)( 2x^(5) + 5x^(4) +2 x^3)=0 \\ m=4`