Question

What polynomial will produce the sum 7x^2-x+3 when added to 3x^2-5x+4

Answer 1

`4x^2 + 4x - 1`

Explanation:

Let f(x) =
`7x^2 - x + 3`, g(x) =
`3x^2 - 5x + 4`, and let h(x) be the polynomial that we have to find.

From the question we know that,

f(x) = g(x) + h(x)

Subtract both sides by g(x),

f(x) - g(x) = h(x)

So h(x)

= f(x) - g(x)

=
`7x^2 - x + 3 - 3x^2 + 5x - 4`

=
`4x^2 + 4x - 1`