Advertisements
Advertisements
प्रश्न
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Advertisements
उत्तर
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
संबंधित प्रश्न
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.
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
If x – 2 is a factor of 2x3 - x2 - px - 2.
Find the value of p
Show that 2x + 7 is a factor of 2x3 + 5x2 - 11 x - 14. Hence factorise the given expression completely, using the factor theorem.
x – 1 is a factor of 8x2 – 7x + m; the value of m is ______.
Factors of 4 + 4x – x2 – x3 are ______.
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
