Pre-calc
x - 3 is a factor of P(x) = x^3 – 7x² +15x-9
A. True
B. False

A. True
Explanation-

Let p(x) = x^3 – 7x^2 – 15x – 9

For checking that (x – 3) is a factor of p(x), we find : p(3)

p(3) = (3)^3 – 7(3)^2 + 15(3) – 9

= 27 – 63 + 45 – 9

= 72 – 72

= 0

Hence, (x – 3) is a factor of p(x).

By division of p(x) by x – 3, we get the quotient

= x^2 – 4x + 3

∴ x^3 – 7x^2 + 15x – 9

= (x – 3)(x^2 – 4x + 3)

= (x – 3)(x – 3)(x – 1)

= (x – 3)^2(x – 1)

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