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
(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.
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
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Find the value of a , if (x - a) is a factor of x3 - a2x + x + 2.
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
Show that (x – 1) is a factor of x3 – 5x2 – x + 5 Hence factorise x3 – 5x2 – x + 5.
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
