MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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)

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)