if F(x)= 5x^2+ X - 18 has (5x-9) as one linear factor then the other linear factor is
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Answers
Answer:
here 5x-9
is one factor so
F(X)=5xx+10x-9x-18
F(X)=5x(X+2)-9(X+2)
=(5x-9)(X+2)
so other factor will be ( X+2)
Answer:
The second linear factor of the polynomial f(x) = 5x²+ x - 18 is (x+2)
Step-by-step explanation:
Given,
One linear factor of the polynomial is F(x)= 5x²+ x - 18 is (5x-9)
To find,
The other factor
Solution:
The given polynomial is f(x) =5x²+ x - 18, this is a quadratic polynomial in variable 'x'
To get the factors of the polynomial, we should factorize f(x)
To factorize 5x²+ x - 18 by splitting the middle term, we should find two integers such that
sum of the numbers = +1
product of the numbers = (-90)
Two such numbers are (+10) and (-9)
Then the given polynomial can be expressed as
5x²+ x - 18 = 5x²+ 10x - 9x - 18
=5x(x+2) - 9(x+2)
= (5x-9)(x+2)
The factors of the polynomial 5x²+ x - 18 are (5x-9) and (x+2)
Given, one linear factor is 5x-9, the required answer is (x+2)
∴ The second linear factor of the polynomial f(x) = 5x²+ x - 18 is (x+2)
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