Use the factor theorem to prove that 2x+1 is a factor of f(x)=6x^2-5x^2-12x-4

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2 Answers

The question is wrong. It should be f(x)=6x³-5x²-12x-4.

When 2x+1=0, x=-½.

2x+1 is a factor if f(-½)=0. Let’s see:

6(-½)³-5(-½)²-12(-½)-4=-3/4-5/4+6-4=-2+6-4=0.

So 2x+1 is a factor.

by Top Rated User (796k points)

Assuming f(x)=6x^3-5x^2-12x-4

Using rational root test:

we know p/q: ±1/1,±1/2,±1/3,±1/6,±2/1,±2/2,±2/3,±2/6,±4/1,±4/2,±4/3,±4/6 are the test candidates.

Since we have to prove 2x+1 is a factor of f(x)

we check x=-1/2,

so f(-1/2) = 6x^3-5x^2-12x-4 = 6(-1/2)^3-5(-1/2)^2-12(-1/2)-4 =0

Since f(-1/2) =0

so, x - (-1/2) =  x + 1/2 = (2x +1)/2 is a root.

therefore, 2x+1 is a root of f(x)

 

 

 

by Level 6 User (19.5k points)

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