Advertisements
Advertisements
Question
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
Advertisements
Solution
p(x) = 2x3 − x2 − 45
Divisor = q(x) = x − 3
∴ Let x = 3
∴ p(3) = 2 × (3)3 − (3)2 − 45
= 2 × 27 − 9 − 45
= 54 − 54
= 0
So, by factor theorem q(x) = x − 3 is a factor of polynomial p(x) = 2x3 − x2 − 45.
APPEARS IN
RELATED QUESTIONS
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Using the Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
What should be subtracted from 3x3 – 8x2 + 4x – 3, so that the resulting expression has x + 2 as a factor?
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
If (x - 2) is a factor of x3 − mx2 + 10x − 20 then find the value of m.
Show that m − 1 is a factor of m21 − 1 and m22 − 1.
Use the factor theorem to determine that x - 1 is a factor of x6 - x5 + x4 - x3 + x2 - x + 1.
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the above expression.
If x – 2 is a factor of 2x3 - x2 - px - 2.
with the value of p, factorize the above expression completely.
If (2x – 3) is a factor of 6x2 + x + a, find the value of a. With this value of a, factorise the given expression.
If both (x − 2) and `(x - 1/2)` is the factors of ax2 + 5x + b, then show that a = b
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
Which of the following is a factor of (x – 2)2 – (x2 – 4)?
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
