Advertisements
Advertisements
प्रश्न
Show that 2x + 7 is a factor of 2x3 + 5x2 - 11 x - 14. Hence factorise the given expression completely, using the factor theorem.
Advertisements
उत्तर
If 2x + 7 in factor of 2x3 + 5x2 - 11 x - 14 then on putting 2x + 7 = 0
x = `-(7)/(2)`
`f(-7/2)` = 0
= `2(-7/2)^3 + 5(-7/2)^2 -11(7/2)-14`
= `(-343)/(4) + (245)/(4) + (77)/(4) -14`
= `(-399)/(4) + (245 + 154)/(4)`
= `(-399 + 399)/(4)` = 0
Hence 2x + 7 is one factor.
Now 2x3 + 5x2 - 11x - 14
= x2 (2x + 7) -x (2x + 7) -2 (2x + 7)
= (2x + 7) (x2 - x - 2)
= (2x + 7) (x2 + x - 2x - 2)
= (2x + 7) [x (x + 1) -2 (x + 1)]
= (2x + 7) (x - 2) (x + 1).
संबंधित प्रश्न
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.
Prove by factor theorem that
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the above expression.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
If x – 2 is a factor of 2x3 - x2 - px - 2.
Find the value of p
By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
Use factor theorem to factorise the following polynominals completely.
x3 + 2x2 – 5x – 6
Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26.
If p(a) = 0 then (x – a) is a ___________ of p(x)
