Question

Polynomials what is the product of
1/2x - 1/4 and 5x^2-2x+6

Answer 1

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

Explanation:

Given polynomials are
`(1)/(2)x-(1)/(4)` and
`5x^2-2x+6`.

Now we need to find their product which can be done as follows:

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

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

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

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

Hence final answer is
`(5)/(2)x^3-(9)/(4)x^2+(7)/(2)x-(3)/(2)`.