Question

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

Answer 1

Answer:

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

Step-by-step 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).

Answer 2

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.