Question

Is x-3 a factor of the polynomial p(x)=2x4-9x3+15x2-22x+12 and for waht reason

Answer 1

Yes, (x - 3) is a factor of the given polynomial.

If (x - 3) was a factor of the polynomial, then 3 would be one of the zeros of the function. That means if you input 3 into the function, you will get an output of zero.

In this case, inputting 3 does produce 0. Therefore, it is a factor.

Answer 2

(x - 3) is a factor of polynomial function p(x).

Explanation:

If (x - 3) is a factor of the polynomial function

p(x) =
`2x^(4)-9x^(3)+15x^(2)-22x+12`

Then x = 3 will be one of the zeros of this polynomial function and by plug-in the value of x, function p(x) will be zero.

p(3) =
`2(3)^(4)-9(3)^(3)+15(3)^(2)-22(3)+12`

= 2×81 - 9×27 + 15×9 - 66 + 12

= 162 - 243 + 135 - 66 + 12

= 0

Therefore, (x - 3) is a factor of polynomial function p(x).