Advertisements
Advertisements
प्रश्न
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
उत्तर
Let P(x) = x3 + 5x2 – 10x + 4
By factor theorem (x – 1) is a factor of P(x), if P(1) = 0
P(1) = 13 + 5(12) – 10(1) + 4 = 1 + 5 – 10 + 4
P(1) = 0
∴ (x – 1) is a factor of x3 + 5x2 – 10x + 4
APPEARS IN
संबंधित प्रश्न
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.
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)`
What should be subtracted from 3x3 – 8x2 + 4x – 3, so that the resulting expression has x + 2 as a factor?
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.
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
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.
Factors of 3x3 – 2x2 – 8x are ______.
