Question

Give factoring polynomials examples with complete solution​

Answer 1

To give:

Examples of factoring polynomial with complete solution

Step-by-step explanation:

Here we proceed our solution with some explained examples.

①

Let, $f(x)=x^{2}+7x+12$

• Here, $12$ can be written as $12=3\times 4$

• Also, $3+4=7$

Now, $f(x)=x^{2}+7x+12$

$\Rightarrow f(x)=x^{2}+3x+4x+12$

$\Rightarrow f(x)=x(x+3)+4(x+3)$

$\Rightarrow f(x)=(x+3)(x+4)$

$\boxed{x^{2}+7x+12=(x+3)(x+4)}$

②

Let, $f(x)=2x^{2}+5x+2$

• Here, $2\times 2=4$ and $4$ can be written as $4=4\times 1$

• Also, $4+1=5$

Now, $f(x)=2x^{2}+5x+2$

$\Rightarrow f(x)=2x^{2}+4x+x+2$

$\Rightarrow f(x)=2x(x+2)+1(x+2)$

$\Rightarrow f(x)=(x+2)(2x+1)$

$\boxed{2x^{2}+5x+2=(x+2)(2x+1)}$

Some more examples of factoring polynomials:

1. $x^{2}+x-6$
2. $x^{2}-9x+20$
3. $x^{2}+7x+6$
4. $x^{2}-2x-80$