Advertisements
Advertisements
Question
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Advertisements
Solution
If p - q is assumed to be factor, then p = q. Substituting this in problem polynomial, we get:
f(p = q) = (p - r)3 + (r - p )3
= (p-r)3+ (- (p - r))3
= (p - r)3 - (p - r)3
= 0
Hence, (p - q) is a factor.
APPEARS IN
RELATED QUESTIONS
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1)x2 + nx – 18.
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
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 by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Show that (x – 1) is a factor of x3 – 5x2 – x + 5 Hence factorise x3 – 5x2 – x + 5.
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
