Advertisements
Advertisements
प्रश्न
Show that 3x + 2 is a factor of 3x2 – x – 2.
Advertisements
उत्तर
(x – a) is a factor of a polynomial f(x) if the remainder, when f(x) is divided by (x – a), is 0, i.e., if f(a) = 0.
f(x) = 3x2 – x – 2
`f((-2)/3) = 3((-2)/3)^2 - ((-2)/3) - 2`
= `3 xx 4/9 + 2/3 - 2`
= `4/3 + 2/3 - 2`
= `6/3 - 2`
= 2 – 2
= 0
Hence, 3x + 2 is a factor of 3x2 – x – 2
APPEARS IN
संबंधित प्रश्न
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.
If 2x + 1 is a factor of 2x2 + ax – 3, find the value of a.
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
Prove by factor theorem that
(x-2) is a factor of 2x3- 7x -2
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of expression x3 + ax2 + bx - 12.
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
Which of the following is a factor of (x – 2)2 – (x2 – 4)?
