Advertisements
Advertisements
प्रश्न
Factorise:
2x3 – 3x2 – 17x + 30
उत्तर
Let p(x) = 2x3 – 3x2 – 17x + 30
Constant term of p(x) = 30
∴ Factors of 30 are ±1, ±2, ±3, ±5, ±6, ±10, ±15, ±30
By trial, we find that p(2) = 0, so (x – 2) is a factor of p(x) ...[∵ 2(2)3 – 3(2)2 – 17(2) + 30 = 16 – 12 – 34 + 30 = 0]
Now, we see that 2x3 – 3x2 – 17x + 30
= 2x3 – 4x2 + x2 – 2x – 15x + 30
= 2x2(x – 2) + x(x – 2) – 15(x – 2)
= (x – 2)(2x2 + x – 15) ...[Taking (x – 2) common factor]
Now, (2x2 + x – 15) can be factorised either by splitting the middle term or by using the factor theorem.
Now, (2x2 – x – 15) = 2x2 + 6x – 5x – 15 ...[By splitting the middle term]
= 2x(x + 3) – 5(x + 3)
= (x + 3)(2x – 5)
∴ 2x3 – 3x2 – 17x + 30 = (x – 2)(x + 3)(2x – 5)
APPEARS IN
संबंधित प्रश्न
Identify polynomials in the following:
`q(x)=2x^2-3x+4/x+2`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`r(x)=3x^2+4x^2+5x-7`
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
Show that (x + 4) , (x − 3) and (x − 7) are factors of x3 − 6x2 − 19x + 84
For what value of a is (x − 5) a factor of x3 − 3x2 + ax − 10?
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
x3 − 3x2 − 9x − 5
x4 + 10x3 + 35x2 + 50x + 24
2x4 − 7x3 − 13x2 + 63x − 45
Factorise the following:
a4 – 3a2 + 2
