Question

How do you factor the expression ${x^2}$ + $3x$ + 2?

Answer 1

Hint: Use Algebraic Identity –
$(x + a)$ $(x + b)$= ${x^2}$+$(a + b)x$+$ab$

Complete step by step solution:
To factorize the given algebraic equation ${x^2}$ + $3x$ + 2
We can use the identity - $(x + a)$ $(x + b)$= ${x^2}$+$(a + b)x$+$ab$
So, in above equation after comparing the coefficient of x and constant,
We will get $(a + b)$ = 3 and
$ab$= 2
So, $a$ and $b$ must be the number which can give sum as 3 and product as 2
So, $a$ and $b$ will be 1 and 2.

Therefore, by putting $a$= 1 and $b$= 2, we get
${x^2}$ + (1+2) $x$ + $(1\times2)$
= $(x + 1)$$(x + 2)$

Note: We can also write $a$= 2 and $b$= 1 and we get the factor as
$(x + 2)$ $(x + 1)$
This we got by putting $a$= 2 and $b$= 1.