Advertisements
Advertisements
Question
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
Advertisements
Solution
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
Now put x = -1 in equation (i), we get
p(-1) = 2(-1)3 + 4(-1) + 6
= 2 x - 1 - 4 + 6
= -2 - 4 + 6
= -6 + 6 = 0
Since, p(-1) = 0, so by factor theorem (x = 1) is a factor of p(x).
RELATED QUESTIONS
Show that x – 2 is a factor of 5x2 + 15x – 50.
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1)x2 + nx – 18.
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = x3 − x2 − x − 1, q(x) = x − 1
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
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.
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
Find the value of 'a' if x – a is a factor of the polynomial 3x3 + x2 – ax – 81.
