Advertisements
Advertisements
Question
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
Advertisements
Solution
Let P(x) = x4 + 5x2 – 5x + 1
By factor theorem, (x – 1) is a factor of P(x), if P(1) = 0
P(1) = 14 + 5 (12) – 5(1) + 1
= 1 + 5 – 5 + 1
= 2 ≠ 0
∴ (x – 1) is not a factor of x4 + 5x2 – 5x + 1
APPEARS IN
RELATED QUESTIONS
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Using the Factor Theorem, show that (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
Using the factor Theorem, show that:
2x + 7 is a factor 2x3 + 5x2 − 11x – 14. Hence, factorise the given expression completely.
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5.
If x – 2 is a factor of 2x3 - x2 - px - 2.
Find the value of p
Use factor theorem to factorise the following polynominals completely.
x3 + 2x2 – 5x – 6
If (x + 2) and (x – 3) are factors of x3 + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.
Factors of 3x3 – 2x2 – 8x are ______.
