Advertisements
Advertisements
Question
Prove by factor theorem that
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
Advertisements
Solution
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
3x - 2 = 0 ⇒ x = `2/3`
Substituting this value, we get
`"f" (2/3) = 18 xx (2/3) xx (2/3) xx (2/3) - 3 xx (2/3) xx (2/3) + 6 xx (2/3) - 8`
`= 16/3 - 4/3 + 4 - 8`
`= 4 + 4 - 8`
= 0
Hence (3x - 2) Is a factor of 18x3 - 3x2 + 6x -8.
APPEARS IN
RELATED QUESTIONS
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 Factor Theorem, show that (3x + 2) is a factor of 3x3 + 2x2 – 3x – 2. Hence, factorise the expression 3x3 + 2x2 – 3x – 2 completely.
Show that m − 1 is a factor of m21 − 1 and m22 − 1.
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence factorise the given expression completely, using the factor theorem.
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
x – 1 is a factor of 8x2 – 7x + m; the value of m is ______.
Factors of 4 + 4x – x2 – x3 are ______.
