Advertisements
Advertisements
Question
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Advertisements
Solution
If x - 3 assumed to be factor, then x = 3. Substituting this in problem polynomial, we get:
f(3) = 3 × 3 × 3 - 3 × 3 - 9 × 3 + 9 = 0
Hence its proved that x - 3 is a factor of the polynomial.
APPEARS IN
RELATED QUESTIONS
Show that 3x + 2 is a factor of 3x2 – x – 2.
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Find the value of a , if (x - a) is a factor of x3 - a2x + x + 2.
The expression 2x3 + ax2 + bx - 2 leaves the remainder 7 and 0 when divided by (2x - 3) and (x + 2) respectively calculate the value of a and b. With these value of a and b factorise the expression completely.
Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26.
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
Determine the value of m, if (x + 3) is a factor of x3 – 3x2 – mx + 24
If both (x − 2) and `(x - 1/2)` is the factors of ax2 + 5x + b, then show that a = b
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
