Question

describe factor therom ?please​

Answer 1

Answer:

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).

Answer 2

Answer:

★ The Factor Theorem states that

(x – a) is a factor of the polynomial f(x) if and only if f(a) = 0

★ Note that the following statements are equivalent for any polynomial f(x).

• (x – a) is a factor of f(x).

• The remainder is zero when f(x) is

divided by (x – a).

• f(a) = 0.

• The solution to f(x) = 0 is a.

• The zero of the function f(x) is a.

† Example :

Question

Check whether (x + 1) is a factor of polynomial f(x)=3x⁴ + x³ – x² + 3x + 2 or not using Factor Theorem .

Solution:

=> Let f(x) = 3x⁴ + x³ – x² + 3x + 2

=> f(–1) = 3(–1)4 + (–1)3 – (–1)2 +3(–1)

+ 2

=> 3(1) + (–1) – 1 – 3 + 2 = 0

Therefore, (x + 1) is a factor of f(x)