3. Use the same technique as in $$ (1 $$ and 2$$ ) $$ above to factorise $$ x^{2}+3 x+ $$ Show ALL the steps (

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We are given the polynomial

$$
x^2+3x+2
$$

and we wish to factorise it using the technique of “splitting the middle term”. Follow the steps below.

1. Write down the polynomial in standard form:

$$
   x^2+3x+2
   $$

2. We look for two numbers $$a$$ and $$b$$ such that

- Their sum is equal to the coefficient of $$x$$: 
     
     $$
     a+b=3,
     $$
     
   - Their product is equal to the constant term:
     
     $$
     ab=2.
     $$

3. Checking the pairs of factors of $$2$$, we see that $$1$$ and $$2$$ work since

$$
   1+2=3 \quad\text{and}\quad 1\times2=2.
   $$

4. We split the middle term $$3x$$ as $$1x+2x$$. Thus the polynomial becomes

$$
   x^2+1x+2x+2.
   $$

5. Next, we factor by grouping. Group the first two terms and the last two terms:

$$
   (x^2+1x)+(2x+2).
   $$

6. Factor out the greatest common factor from each group:

- From $$x^2+1x$$, factor out $$x$$:
     
     $$
     x(x+1),
     $$
     
   - From $$2x+2$$, factor out $$2$$:
     
     $$
     2(x+1).
     $$

7. Now, the expression becomes

$$
   x(x+1)+2(x+1).
   $$

Notice that $$(x+1)$$ is a common factor.

8. Factor out $$(x+1)$$:

$$
   (x+1)(x+2).
   $$

Thus, the factorisation is

$$
x^2+3x+2 = (x+1)(x+2).
$$
$$ x^2 + 3x + 2 = (x + 1)(x + 2) $$

3. Use the same technique as in \( (1 \) and 2\( ) \) above to factorise \( x^{2}+3 x+ \) Show ALL the steps (

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