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
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1)x2 + nx – 18.
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 Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
If ax3 + 3x2 + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.
Determine the value of m, if (x + 3) is a factor of x3 – 3x2 – mx + 24
