If x-2 is a factor of 2x3-x2-px-2 a.find the value of p and factorise completly
Answers
it has given that (x - 2) is a factor of 2x³ - x² - px - 2.
To find : (a) find the value of P
(b) factorise the expression completely.
Solution : as (x - 2) is a factor of 2x³ - x² - px - 2, x = 2 will be a root of 2x³ - x² - px - 2.
i.e., 2(2)³ - (2)² - p(2) - 2 = 0
⇒16 - 4 - 2p - 2 = 0
⇒10 - 2p = 0
⇒p = 5
Therefore the value of p = 5.
now expression is, 2x³ - x² - 5x - 2
= 2x³ - 4x² + 3x² - 6x + x - 2
= 2x²(x - 2) + 3x(x - 2) + 1(x - 2)
= (x - 2)(2x² + 3x + 1)
= (x - 2)(2x² + 2x + x + 1)
= (x - 2){2x(x + 1) + 1(x + 1)}
= (x - 2)(x + 1)(2x + 1)
Therefore (x - 2)(x + 1)(2x + 1) is required answer.
also read similar questions : If (x – 1) and ( x – 2) are the factors of x^4 – px^2 + q, then the value of root(p+q) is
https://brainly.in/question/20713198
If the zeroes of the polynomial x2 +px+q are double in value to the zeroes of 2 x 2 – 5x–3,find the value of p and q
https://brainly.in/question/18676978
Step-by-step explanation:
(x – 2) is a factor of 2x
3
– x
2
+ px – 2, then
(i) find the value of p.
(ii) with this value of p, factorise the above expression completely