Question

Factorise 6x^2 + 17x + 5 by using the "Factor Theorem"

Solve it in detail.​

Answer 1

Question :

Factorize 6x² + 17x + 5 by using the "Factor Theorem"

Solution :

What factor theorem means?

Factor theorem states that a polynomial P(x) has a factor (x - a) if and only if P(x) = 0

P(x) = 6x² + 17x + 5

Now,

⇒ P(-1/3) = 6(-1/3)² + 17(-1/3) + 5

               = 6 * (1/9) - 17/3 + 5

               = 2/3 - 17/3 + 5

               = (2 - 17 + 15)/3

               = (-15 + 15)/3

               = 0/3

               = 0

Now according to factor theorem, {x - (-1/3)} or, x + 1/3 or, (3x + 1)/3 or, (3x + 1) is a factor of P(x).     [Here, denominator '3' gets cancelled as the factor implies to 0 so it gets cancelled]

Now we have 1 factor of P(x) as (3x + 1)

P(x) = 6x² + 17x + 5

⇒ P(x) = 6x² + 2x + 15x + 5

⇒ P(x) = 2x(3x + 1) + 5(3x + 1)

⇒ P(x) = (2x + 5)(3x + 1)

Therefore,

Factors of the given polynomial = (2x + 5)(3x + 1)

Answer 2

Answer

Let p(x)=6x

2

+17x+5 the term

6

5

can be written as many terms one would be (±

2

5

,±

3

1

),(±

6

5

,±1),...……....

Let p(

3

−1

)=0 then by factor theorem

3

−1

then the other will be;

6x

2

+17x+5=(2x+5)(3x+1)