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.
Show that m − 1 is a factor of m21 − 1 and m22 − 1.
Prove by factor theorem that
(x - 3) is a factor of 5x2 - 21 x +18
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
Find the value of the constants a and b, if (x – 2) and (x + 3) are both factors of the expression x3 + ax2 + bx – 12.
If (2x – 3) is a factor of 6x2 + x + a, find the value of a. With this value of a, factorise the given expression.
If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 – 2x + a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
Determine the value of m, if (x + 3) is a factor of x3 – 3x2 – mx + 24
