Question

Factor x2 + 3x + 2 A) (x + 3)(x + 1) B) (x + 2)(x + 1) C) (x + 2)(x - 1) D) (x - 2)(x + 1) E) (x - 2)(x - 1)

Answer 1

(x + 1) (x + 2)

Explanation:

x² + 3x + 2

We can Split the Middle Term of this expression to factorise it

In this technique, if we have to factorise an expression like ax² + bx + c,

we need to think of 2 numbers such that:

N₁ · N₂ = a · c = 1 · 2 = 2

And,

N₁ + N₂ = b = 3

After trying out a few numbers we get N₁ = 2 and N₂ = 1

2 · 1 = 2 and 2 + 1 = 3

x² + 3x + 2 = x² + 2x + x + 2

x (x + 2) + 1 (x + 2)

(x + 1) (x + 2) , is the factorized form.

Answer 2

(x+2)(x+1)

Explanation:

`x^(2) +3x+2`

→Multiply the first and last term's coefficient =1×2=2

Now,

→Factors of 2=2,1

→Using 2 and 1 we must add up to 3

Now we get,

`\hookrightarrow x^(2) +3x+2\\\\\hookrightarrow x^(2) +2x+x+2`

Here when we add 2x and x we get 3x.

Now,

Take common x from x²+2x as well as 1 from x+2

Then we get,

`\hookrightarrow x^(2) +2x+x+2\\\\\hookrightarrow x(x+2)+1(x+2)\\\\`

Here, x+2 is common. So we can write both of them as one.

`\hookrightarrow (x+2)(x+1)`

And it is our final answer.

Hence, the final factors are (x+2)(x+1)