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 – 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.
Show that x – 2 is a factor of 5x2 + 15x – 50.
Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.
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 a , if (x - a) is a factor of x3 - a2x + x + 2.
Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the above expression.
Given that x + 2 and x + 3 are factors of 2x3 + ax2 + 7x - b. Determine the values of a and b.
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?
For what value of k is the polynomial p(x) = 2x3 – kx2 + 3x + 10 exactly divisible by (x – 2)
