Question

Use the remainder theorem and the factor theorem to determine whether (y − 3) is a factor of (y4 + 2y2 − 4).

A. The remainder isn't 0 and, therefore, (y − 3) isn't a factor of (y4 + 2y2 − 4).

B. The remainder is 0 and, therefore, (y − 3) is a factor of (y4 + 2y2 − 4).

C. The remainder isn't 0 and, therefore, (y − 3) is a factor of (y4 + 2y2 − 4).

D. The remainder is 0 and, therefore, (y − 3) isn't a factor of (y4 + 2y2 − 4).

Answer 1

A. The remainder isn't 0 and, therefore, (y − 3) isn't a factor of (y4 + 2y2 − 4).

Explanation:

Use the remainder theorem and the factor theorem to determine whether (y − 3) is a factor of (y^4 + 2y^2 − 4).

y-3 is a factor then y-3=0 so y= 3

Now we plug in 3 for y in the given expression (y^4 + 2y^2 − 4)

(3)^4 + 2(3)^2 − 4= 81 + 18 -4=95

Remainder is 95

The remainder is not 0, so (y-3) is not a factor of the given expression

the remainder isn't 0 and, therefore, (y − 3) isn't a factor of (y^4 + 2y^2 − 4).