Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let f(x)= x3 – 2x2 – 9x + 18
x – 2 = 0 `\implies` x = 2
∴ Remainder = f(2)
= (2)3 – 2(2)2 – 9(2) + 18
= 8 – 8 – 18 +18
= 0
Hence, (x – 2) is a factor of f(x).
Now, we have:
x2 – 9
`x - 2")"overline(x^3 - 2x^2 - 9x + 18)`
x3 – 2x2
– +
– 9x + 18
– 9x + 18
+ –
0
∴ x3 – 2x2 – 9x + 18 = (x – 2)(x2 – 9)
= (x – 2)(x + 3)(x – 3)
APPEARS IN
संबंधित प्रश्न
Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
Find the value of m ·when x3 + 3x2 -m x +4 is exactly divisible by (x-2)
Find the value of a , if (x - a) is a factor of x3 - a2x + x + 2.
If (x - 2) is a factor of the expression 2x3 + ax2 + bx - 14 and when the expression is divided by (x - 3), it leaves a remainder 52, find the values of a and b.
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
Find the value of the constants a and b, if (x – 2) and (x + 3) are both factors of the expression x3 + ax2 + bx – 12.
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.
