When polynomial P is divided by x^2-x-6, the remainder is 4x-7, what is P(2) and P(3)?

Question

When polynomial P is divided by
`x^2-x-6`, the remainder is 4x-7, what is P(2) and P(3)?

Answer 1

If polynomial P is divided by x - 2, and the remainder is 4x - 7, then you can use the Remainder Theorem to find P(2) and P(3).

The Remainder Theorem states that when you divide a polynomial P(x) by (x - a), the remainder is P(a). In this case, a = 2.

So, to find P(2), substitute x = 2 into the remainder, which is 4x - 7:
P(2) = 4(2) - 7
P(2) = 8 - 7
P(2) = 1

To find P(3), you can do the same:
P(3) = 4(3) - 7
P(3) = 12 - 7
P(3) = 5

So, P(2) = 1 and P(3) = 5.