Advertisements
Advertisements
Question
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
Advertisements
Solution
If x - y is assumed to be fsctor, then x = y. Substituting this in problerr polynomial, we get :
f(x = y) = yz (y2 - z2) + zy(z2 - y2) + yy (y2 - y2)
= yz (y2-z2) + zy(-(y2 - z2)) + 0
= yz (y2 - z2) - yz (y2 - z2) = 0
Hence , (x - y) is a factor.
APPEARS IN
RELATED QUESTIONS
If 2x + 1 is a factor of 2x2 + ax – 3, find the value of a.
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 Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
Using the Factor Theorem, show that (3x + 2) is a factor of 3x3 + 2x2 – 3x – 2. Hence, factorise the expression 3x3 + 2x2 – 3x – 2 completely.
If x + a is a common factor of expressions f(x) = x2 + px + q and g(x) = x2 + mx + n; show that : `a = (n - q)/(m - p)`
Prove by factor theorem that
(x-2) is a factor of 2x3- 7x -2
Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
The expression 2x3 + ax2 + bx - 2 leaves the remainder 7 and 0 when divided by (2x - 3) and (x + 2) respectively calculate the value of a and b. With these value of a and b factorise the expression completely.
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
Factors of 3x3 – 2x2 – 8x are ______.
