Question

if F(x)= 5x^2+ X - 18 has (5x-9) as one linear factor then the other linear factor is

wrong ans or rubbish will be reported
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Answer 1

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 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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