Advertisements
Advertisements
Question
Check whether 7 + 3x is a factor of 3x3 + 7x.
Advertisements
Solution 1
7 + 3x will be a factor of 3x3 + 7x only if 7 + 3x divides 3x3 + 7x leaving no remainder.
Let p(x) = 3x3 + 7x
7 + 3x = 0
⇒ 3x = −7
⇒ x = `-7/3`
∴ Required remainder
`f(7/3) = 3(-7/3)^3 + 7(-7/3)`
= `3(-343/27) - 49/3`
= `-343/9-49/3`
= `-490/9`
Since `p(-7/3)` ≠ 0
∴ 7 + 3x is not a factor of 3x3 + 7x.
Solution 2
Let us divide (3x3 + 7x) by (7 + 3x). If the remainder obtained is 0, then 7 + 3x will be a factor of 3x3 + 7x.
By long division,
As the remainder is not zero, therefore, 7 + 3x is not a factor of 3x3 + 7x.
RELATED QUESTIONS
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
Find the remainder when x4 + 1 is divided by x + 1.
Using the Remainder Theorem, factorise the following completely:
2x3 + x2 – 13x + 6
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
Find without division, the remainder in the following:
2x3 - 3x2 + 6x - 4 is divisible by (2x-3)
Using remainder theorem, find the value of m if the polynomial f(x)= x3 + 5x2 -mx +6 leaves a remainder 2m when divided by (x-1),
Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Use the Remainder Theorem to factorise the following expression:
2x3 + x2 – 13x + 6
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
(x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b.
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = 4x3 – 12x2 + 14x – 3; g(x) = 2x – 1
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x – 1
