Advertisements
Advertisements
प्रश्न
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 19x + 6
Advertisements
उत्तर
Let P(x) = 3x3 + 2x2 – 19x + 6
By hit and trial method,
P(1) = 3(1)3 + 2(1)2 – 19(1) + 6
= 3 + 2 – 19 + 6
= –8 ≠ 0
P(–1) = 3(–1)3 + 2(–1)2 – 19(–1) + 6
= –3 + 2 + 19 + 6
= 24 ≠ 0
P(2) = 3(2)3 + 2(2)2 – 19(2) + 6
= 24 + 8 – 38 + 6
= 0
Thus, (x – 2) is a factor of P(x).
Now,
3x2 + 8x – 3
`x - 2")"overline(3x^3 + 2x^2 - 19x + 6)`
3x3 – 6x2
– +
8x2 – 19x + 6
8x2 – 16x
– +
– 3x + 6
– 3x + 6
+ –
0
∴ 3x3 + 2x2 – 19x + 6 = (x – 2)(3x2 + 8x – 3)
= (x – 2)(3x2 + 9x – x – 3)
= (x – 2)(3x(x + 3) – 1(x + 3))
= (x – 2)(x + 3)(3x – 1)
APPEARS IN
संबंधित प्रश्न
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
Using the remainder theorem, find the remainders obtained when x3 + (kx + 8 )x + k is divided by x + 1 and x − 2.
Hence, find k if the sum of the two remainders is 1.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
If x51 + 51 is divided by x + 1, the remainder is ______.
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
