Advertisements
Advertisements
प्रश्न
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
Advertisements
उत्तर
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
संबंधित प्रश्न
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Show that x – 2 is a factor of 5x2 + 15x – 50.
Using the factor Theorem, show that:
2x + 7 is a factor 2x3 + 5x2 − 11x – 14. Hence, factorise the given expression completely.
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
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 whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
Which of the following is a factor of (x – 2)2 – (x2 – 4)?
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
