If (x – 1) and (x + 3) are the factors of x3 + 3x2 – x – 3 then

1.	If (x – 1) and (x + 3) are the factors of x3 + 3x2 – x – 3 then the other factor is …………A) x + 1 B) x – 3 C) x + 2 D) x – 1
Answer» Correct option is (A) x + 1 x = 1 & x = -3 are zeros of polynomial \(x^3 + 3x^2 – x – 3 .\) Let the other zero be x. \(\therefore\) Sum of zeros \(=\frac{\text{-coefficient of }x^2}{\text{coefficient of }x^3}\) \(=\frac{-3}1\) = -3 \(\therefore\) 1 + (-3) + \(\alpha\) = -3 \(\Rightarrow\) \(\alpha\) = -1 \(\therefore\) x = -1 is another zero of polynomial \(x^3 + 3x^2 – x – 3 .\) \(\Rightarrow\) (x+1) is a other factor of polynomial \((x^3+3x^2-x-3).\) Correct option is A) x + 1

If (x – 1) and (x + 3) are the factors of x3 + 3x2 – x – 3 then the other factor is …………A) x + 1 B) x – 3 C) x + 2 D) x – 1

Answer»

Correct option is (A) x + 1

x = 1 & x = -3 are zeros of polynomial \(x^3 + 3x^2 – x – 3 .\)

Let the other zero be x.

\(\therefore\) Sum of zeros \(=\frac{\text{-coefficient of }x^2}{\text{coefficient of }x^3}\) \(=\frac{-3}1\) = -3

\(\therefore\) 1 + (-3) + \(\alpha\) = -3

\(\Rightarrow\) \(\alpha\) = -1

\(\therefore\) x = -1 is another zero of polynomial \(x^3 + 3x^2 – x – 3 .\)

\(\Rightarrow\) (x+1) is a other factor of polynomial \((x^3+3x^2-x-3).\)

Correct option is A) x + 1