Advertisements
Advertisements
Question
By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
Solution
Let x + 3 = 0 then x = – 3
Substituting the value of x in f(x)
f(x) = 2x2 + 5x – 3
= 2(–3)2 + 5(–3) –3
f(–3) = 18 – 15 – 3 = 0
∵ Remainder = 0,
then x + 3 is a factor
Again let 2x - 1 = 0,
then x = `(1)/(2)`
Substituting the value of x in f(x),
f(x) = 2x2 + 5x – 3
`f(1/2) = 2(1/2)^2 + 5(1/2) -3`
= `2 xx (1)/(4) + (5)/(2) - 3`
= `(1)/(2) + (5)/(2) - 3` = 0
∵ Remainder = 0,
∴ 2x – 1 is also a factor
Hence, proved.
APPEARS IN
RELATED QUESTIONS
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.
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1)x2 + nx – 18.
If x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
(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) is a factor of x3 − mx2 + 10x − 20 then find the value of m.
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = x3 − x2 − x − 1, q(x) = x − 1
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Use the factor theorem to determine that x - 1 is a factor of x6 - x5 + x4 - x3 + x2 - x + 1.
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.
Factors of 3x3 – 2x2 – 8x are ______.
