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
If 2x + 1 is a factor of 2x2 + ax – 3, find the value of a.
Using the factor Theorem, show that:
2x + 7 is a factor 2x3 + 5x2 − 11x – 14. Hence, factorise the given expression completely.
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
Use factor theorem to factorise the following polynominals completely. x3 – 13x – 12.
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
If ax3 + 3x2 + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
Factors of 4 + 4x – x2 – x3 are ______.
