Advertisements
Advertisements
प्रश्न
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
उत्तर
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
संबंधित प्रश्न
Using the Factor Theorem, show that (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Prove by factor theorem that
(x - 3) is a factor of 5x2 - 21 x +18
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5.
Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of expression x3 + ax2 + bx - 12.
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
