Advertisements
Advertisements
प्रश्न
Show that x – 2 is a factor of 5x2 + 15x – 50.
Advertisements
उत्तर
(x – a) is a factor of a polynomial f(x) if the remainder, when f(x) is divided by (x – a), is 0, i.e., if f(a) = 0.
f(x) = 5x2 + 15x – 50
f(2) = 5(2)2 + 15(2) – 50
= 20 + 30 – 50
= 0
Hence, x – 2 is a factor of 5x2 + 15x – 50
संबंधित प्रश्न
Show that 3x + 2 is a factor of 3x2 – x – 2.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 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.
Given that x + 2 and x + 3 are factors of 2x3 + ax2 + 7x - b. Determine the values of a and b.
If (x + 2) and (x – 3) are factors of x3 + ax + b, find the values of a and b. With these values of a and b, 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.
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
