Question

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

Answer 1

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

Answer 2

(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