p(x)=2x³-x²-45,q(x)=x-3 By using factor theorem in the following examples, determine whether q(x) is a factor p(x) or not
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Answered by
3
P(x) = 2x^3 - x^2 - 45
q(x) = x-3
On putting x = 3
P(3) = 2(3)^3 - (3)^2 - 45
=> P(3) = 54 - 9 - 45
=> P (3) = 54 - 54
=> P(3) = 0
=> q(x) is a factor of P(x)
q(x) = x-3
On putting x = 3
P(3) = 2(3)^3 - (3)^2 - 45
=> P(3) = 54 - 9 - 45
=> P (3) = 54 - 54
=> P(3) = 0
=> q(x) is a factor of P(x)
Answered by
3
***********************************
Factor Theorem :
If ( x - a ) is a factor of a
polynomial p(x) then
p(a) = 0
***********************************
Given q(x)=(x-3) is a factor of
p(x) = 2x³-x²-45
Now ,
p(3) = 2×3³ - 3² - 45
= 54 - 9 - 45
= 54 - 54
= 0
Therefore ,
p(3) = 0 ,
q(x) is a factor of p(x).
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