Question

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x2 - 3x + 22

Answer 1

how do I go about solving this?

Answer 2

See if (4x^2-3x+22)/(x-2) has a remaineder. This is the same as seeing if 2 is a zero of the polynomial

Answer 3

The factor theorem states that a polynomial has x-k as a factor if and only if f(k) = 0

Answer 4

So x-2 is a factor of your polynomial only if you replace x with 2 and get 0

Answer 5

Well I did get a remainder for (4x^2-3x+22)/(x-2)...

Answer 6

You did not need to divide. To use the factor theorem follow Mertsj's method

Answer 7

I replaced the 2s, and got 32 not zero...