Answer
We factor out the given polynomial by trial and error.
Example:
3$x^{2}$ + 10 x + 8
First multiply coefficient of $x^{2}$ and constant term, then break the product of both into two factors so that the sum of both factor will be same as the product.
Here 3$\times$8 = 24
factor of 24 = 4 and 6 that sum will be 10.
3$x^{2}$ + 10 x + 8 = 3$x^{2}$ + 6 x + 4 x + 8
Take 3$x$ and 4 common
3$x^{2}$ + 6 x + 4 x + 8 = 3 x(x + 2) + 4( x + 2)
= (3 x + 4) (x + 2)
So the factor of polynomial = (3 x + 4) (x + 2)
Work Step by Step
There are many methods to factor out a polynomial.
We find out the factors of a given polynomial by trial and error.
Example:
3$x^{2}$ + 10 x + 8
First multiply coefficient of $x^{2}$ and constant term, then break the product of both into two factors so that the sum of both factor will be same as the product.
Here 3$\times$8 = 24
factor of 24 = 4 and 6 that sum will be 10.
3$x^{2}$ + 10 x + 8 = 3$x^{2}$ + 6 x + 4 x + 8
Take 3$x$ and 4 common
3$x^{2}$ + 6 x + 4 x + 8 = 3 x(x + 2) + 4( x + 2)
= (3 x + 4) (x + 2)
So the factor of polynomial = (3 x + 4) (x + 2)
