Advertisements
Advertisements
Question
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
Options
Yes
No
Nothing can be said
None of the above is true
Advertisements
Solution
Yes
Explanation:
Let f(x) = x3 – 4x2 – 11x + 30
Here f(2) = 23 – 4 × 22 – 11 × 2 + 30
= 8 – 16 – 22 + 30
= 0
∴ x – 2 is a factor of f(x)
RELATED QUESTIONS
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)`
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
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
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
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.
If x – 2 is a factor of 2x3 - x2 - px - 2.
with the value of p, factorize the above expression completely.
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x2 – Kx + 6 = 0. Also, find the other root of the equation.
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
If p(a) = 0 then (x – a) is a ___________ of p(x)
