Factoring a quadratic trinomial by grouping

How do you factor 2x² + 3x + 1 into two binomials?

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2x² + 3x + 1

Think of two numbers that multiply to get what 2(1) is....the outer numerical portions,and also add to get the inner coefficient, 3.  Those two numbers would be 2 and 1, therefore you split the middle term, 3x, into 2x and x to begin factoring by grouping.

2x² + 3x + 1
= 2x² + 2x + x + 1 {split the 3x into 2x and x using factoring by grouping}
= 2x(x + 1) + 1(x + 1) {factored 2x out of first two terms and 1 out of last two terms}
= (2x + 1)(x + 1) {factored (x + 1) out of the two terms}

- Algebra House