Advertisements
Advertisements
Question
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
Advertisements
Solution
Let the number to be subtracted be k and the resulting polynomial be f(x), then
f(x) = 2x3 – 5x2 + 5x – k
Since, 2x – 3 is a factor of f(x),
Now, converting 2x – 3 to factor theorem
`f(3/2)` = 0
⇒ 2x3 – 5x2 + 5x – k = 0
⇒ `2(3/2)^3 - 5(3/2)^2 +5(3/2) -k` = 0
⇒ `2 xx (27)/(8) - 5 xx (9)/(4) + 5 xx (3)/(2) - k` = 0
⇒ `(27)/(4) - (45)/(4) + (15)/(2) - k` = 0
⇒ 27 – 45 + 30 – 4k = 0
⇒ –4k + 12 = 0
⇒ k = `(-12)/(-4)`
⇒ k = 3.
APPEARS IN
RELATED QUESTIONS
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
What should be subtracted from 3x3 – 8x2 + 4x – 3, so that the resulting expression has x + 2 as a factor?
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
If ax3 + 3x2 + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.
If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 – 2x + a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.
Determine the value of m, if (x + 3) is a factor of x3 – 3x2 – mx + 24
If p(a) = 0 then (x – a) is a ___________ of p(x)
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
