Question

A polynomial expression is shown below.

Answer 1

The polynomial is (mx^3+3)(2x²+5x+2)-(8x^5 +20x^4)
if it is reduced to 8x^3+6x²+15x+6, so we can find the value of m

 (mx^3+3)(2x²+5x+2)-(8x^5+20x^4) = 8x^3+6x²+15x+6
2mx^5+5mx^4+2mx^3+6x²+15x+6-8x^5-20x^4=8x^3+6x²+15x+6
2mx^5+5mx^4+2mx^3=8x^3+6x²+15x+6-6x²-15x-6+ 8x^5+20x^4
=  8x^5+20x^4+8x^3= 4(2x^5+5x^4+2x^3)
finally

m(2x^5+5x^4+2x^3)=4(2x^5+5x^4+2x^3), and after simplification

C:  m=4

4. When the expression is factored x²-3x-18 completely, 

one of its factor is x-6
x²-3x-18=0
D= 9-4(-18)= 81, sqrtD=9 x=3-9/2= -6/2= -3, and x=3+9 / 2= 6
so x²-3x-18= (x-6)(x+6)