How do you factor the trinomial $2 x^{2} - 5 x + 3$ $2x^2-5x+3$ ?

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How do you factor the trinomial $2 x^{2} - 5 x + 3$ $2x^2-5x+3$ ?

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Answer 1 · 2016-03-19T21:44:07

$(x - 1) (2 x - 3)$ $(x-1)(2x-3)$

Explanation:

Given : $2 x^{2} - 5 x + 3$ $2x^2-5x+3$ , this quadratic equation can be factored, if I can find two numbers which multiply together to equal $6$ $6$ and add together to equal $- 5$ $-5$ . I can, and they are $- 3$ $-3$ and $- 2$ $-2$ . So now I will use them to expand the original expression.
$2 x^{2} - 5 x + 3$ $2x^2 -5x+3$
$2 x^{2} - 2 x - 3 x + 3$ $2x^2-2x -3x+3$

Notice that I have rewritten the term $- 5 x$ $-5x$ as the sum of $- 2 x + (- 3 x)$ $-2x + (-3x)$ . Now I will do some simple factoring:

$2 x (x - 1) - 3 (x - 1)$ $2x(x-1) -3(x-1)$ . Notice that $(x - 1)$ $(x-1)$ is a common term, so I can factor it and get the solution.

$(x - 1) (2 x - 3)$ $(x-1)(2x-3)$

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How do you factor the trinomial $2 x^{2} - 5 x + 3$ $2x^2-5x+3$ ?

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How do you factor the trinomial $2 x^{2} - 5 x + 3$ $2x^2-5x+3$ ?