Advertisements
Advertisements
प्रश्न
Factorize of the following polynomials:
4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
Advertisements
उत्तर
Let ` f(x) = 4x^3 + 20x^2 + 33x+ 18` be the given polynomial.
Therefore (2x + 3)is a factor of the polynomial f(x).
Now,
`f(x)= 2x^2 (2x + 3)+7x(2x + 3) + 6(2x + 3)`
`=(2x + 3){2x^2 + 4x 3x + 6}`
`= (2x + 3){2x^2 + 4x + 3x + 6}`
` = (2x + 3)(2x + 3)(x + 2)`
Hence (x +2),(2x+3) and (2x + 3 ) are the factors of polynomial f(x).
APPEARS IN
संबंधित प्रश्न
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
f(x) = 3x3 + x2 − 20x +12, g(x) = 3x − 2
f(x) = x3 − 6x2 + 11x − 6, g(x) = x2 − 3x + 2
Show that (x − 2), (x + 3) and (x − 4) are factors of x3 − 3x2 − 10x + 24.
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
Using factor theorem, factorize each of the following polynomials:
x3 + 6x2 + 11x + 6
y3 − 2y2 − 29y − 42
Find the remainder when x3 + 4x2 + 4x − 3 is divided by x.
If f(x) = x4 − 2x3 + 3x2 − ax − b when divided by x − 1, the remainder is 6, then find the value of a + b
