Advertisements
Advertisements
प्रश्न
Factorize completely using factor theorem:
2x3 – x2 – 13x – 6
Advertisements
उत्तर
Let f(x) = 2x3 – x2 – 13x – 6
By hit and trial method
Put x = – 2
f(–2) = 2(–2)3 – (–2)2 – 13(–2) – 6
= – 16 – 4 + 26 – 6
= 0
`\implies` (x + 2) is a factor of f(x)
∴ Dividing f(x) by (x + 2)
`x + 2")"overline(2x^3 - x^2 - 13x - 6)(2x^2 - 5x - 3`
2x3 + 4x2
– –
–5x2 – 13x – 6
–5x2 – 10x
+ +
–3x – 6
–3x – 6
+ +
x
So, 2x3 – x2 – 13x – 6 = (x + 2)(2x2 – 5x – 3)
= (x + 2){2x2 – 6x + x – 3}
= (x + 2){2x (x – 3) + 1(x – 3)}
= (x + 2)(x – 3)(2x + 1)
APPEARS IN
संबंधित प्रश्न
Given that x – 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.
If the polynomials ax3 + 4x2 + 3x - 4 and x3 - 4x + a leave the same remainder when divided by (x - 3), find the value of a.
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x3 + ax2 − 2x + a + 4
Show that x2 - 9 is factor of x3 + 5x2 - 9x - 45.
If (x – 2) is a factor of 2x3 – x2 + px – 2, then
(i) find the value of p.
(ii) with this value of p, factorise the above expression completely
Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorize the given polynomial completely.
If (x + 3) and (x – 4) are factors of x3 + ax2 – bx + 24, find the values of a and b: With these values of a and b, factorise the given expression.
f 2x3 + ax2 – 11x + b leaves remainder 0 and 42 when divided by (x – 2) and (x – 3) respectively, find the values of a and b. With these values of a and b, factorize the given expression.
