Question

1/2x - 1/4 and 5x^2 - 2x + 6 ( show in standard form and explain how did you get it)

Answer 1

The standard form is given by(As highest degree is 2 we will take till degree 2 i.e quadratic)

• ax²+bx+c

So

#1

• 1/2x-1/4
• 0x²+1/2x-1/4

Multiply 4

• 0x²+2x-1

Here

• a=0
• b=2
• c=-1

#2

• 5x²-2x+6

Already in standard form

• a=5
• b=-2
• c=6

Answer 2

`(5)/(2)x^3-(9)/(4)x^2+(7)/(2)x-(3)/(2)`

Explanation:

The product of the two expressions is:

`\left((1)/(2)x-(1)/(4)\right)(5x^2-2x+6)`

`=(1)/(2)x(5x^2-2x+6)-(1)/(4)(5x^2-2x+6)`

`=(5)/(2)x^3-(2)/(2)x^2+(6)/(2)x-(5)/(4)x^2+(2)/(4)x-(6)/(4)`

`=(5)/(2)x^3-x^2-(5)/(4)x^2+3x+(1)/(2)x-(3)/(2)`

`=(5)/(2)x^3-(9)/(4)x^2+(7)/(2)x-(3)/(2)`