Question

A polynomial expression is shown below.
(mx³ + 3)(2x² + 5x + 2) - (8x⁵ + 20x⁴)
The expression is simplified to 8x³ + 6x² + 15x + 6. What is the value of m?

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)

Answer 2

The value of the m in the polynomial expression for which the simplified expression is 8x³ + 6x² + 15x + 6 is 4.

What is the simplified form of a equation?

Simplified form of an equation is the simplest way of expression the equation, which is obtained by applying the required operations of mathematics.

A polynomial expression is shown below.

$(mx^3 + 3)(2x^2 + 5x + 2) - (8x^5 + 20x^4)$

The expression is simplified to the following expression,

$8x^3 + 6x^2 + 15x + 6$

As the equation is a simplified expression of the given polynomial. Thus, both the equation are same.

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

Open the brackets and simplify it further,

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

On comparing both side of the equation, the value of m we get is,

$m=4$

Thus, the value of the m in the polynomial expression for which the simplified expression is 8x³ + 6x² + 15x + 6 is 4.

Learn more about the simplified form here;

https://brainly.com/question/1597694