Question

if (x-1) (x+3) are factors of x³+3x²-x-3.find another factor​

Answer 1

Step-by-step explanation:

Let p(x)=x

3

+3x

2

−x−3

p(x) is a cubic polynomial, so it may have three linear factors.

The constant term is -3. The factors of -3 are -1, 1, -3 and 3.

p(−1)=(−1)

3

+3(−1)

2

−(−1)−3=−1+3+1−3=0

∴(x+1) is a factor of p(x).

p(1)=(1)

3

+3(1)

2

−1−3=1+3−1−3=0

∴(x−1) is a factor of p(x).

p(−3)=(−3)

3

+3(−3)

2

−(−3)−3=−27+27+3−3=0

∴(x+3) is a factor of p(x).

The three factors of p(x) are (x + 1), (x - 1) and (x - 3)

∴x

3

+3x

2

−x−3=(x+1)(x−1)(x+3).

Answer 2

Answer:

(x+1)

Step-by-step explanation:

(x-1)(x+3)

=x²+3x-x-3

=x²+2x-3

now we are to multiply some quantity to make given equation

(x²+2x-3)(x+1)

=x³+2x²-3x+x²+2x-3

x³+3x²-x-3.

hence another factor is (x+1)

I think it is helpful for you