How do you factor the expression $2 x^{2} + 3 x + 1$ $2x^2 + 3x + 1$ ?

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Answer 1 · 2016-03-16T15:56:10

$(x + 1) (2 x + 1)$ $" "(x+1)(2x+1)$

The only whole number factors of 2 is $1 \times 2$ $1 xx 2$
The only whole number factors of 1 is $1 \times 1$ $1xx1$

The constant of 1 in $2 x^{2} + 3 x + 1$ $2x^2+3x+1$ is positive

So the signs in the brackets are the same

$3 x$ $3x$ is positive which means, that as the signs are both the same, they have to be positive.

Thus our structure is: $(? + ?) (? + ?)$ $(?+?)(?+?)$

Let us insert the factors. By what was stated earlier we can only have: $(1 x + 1) (2 x + 1)$ $(1x+1)(2x+1)$

But it is considered bad practice to write $1 x$ $1x$ so we write our factorisation as:

$(x + 1) (2 x + 1)$ $" "(x+1)(2x+1)$

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