Question

for what value of a, x-a is a factor of the polynomial x³ -ax²-2x +5a - 7​

Answer 1

The point of the Factor Theorem is the reverse of the Remainder Theorem: If you synthetic-divide a polynomial by x = a and get a zero remainder, then, not only is x = a a zero of the polynomial (courtesy of the Remainder Theorem), but x – a is also a factor of the polynomial (courtesy of the Factor Theorem)....

factor x-t for a polynomial would divide the polynomial leaving ZERO remainder.

Moreover, the factor theorem would solve this question easily. The factor theorem states that if x-t is a factor of P(x), then P(t)= 0. In other words t must be a root of the polynomial.

Thus, 125 – 75 + 5a - 10= 0

Solving for a is pretty simple. Then a= -8.

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Answer 2

Answer:

I hope you get your answer