How do you factor #4x^2-5x+7#?

1 Answer
Steve M
Dec 5, 2016

It does not factorise

Explanation:

The rule to factorise any quadratic is to find two numbers such that

#"product" = x^2 " coefficient "xx" constant coefficient"#
#"sum" \ \ \ \ \ \ = x " coefficient"#

So for #4x^2-5x+7# we seek two numbers such that

#"product" = 4*17 = 28#
#"sum" \ \ \ \ \ \ = -5#

So if we looks at the factors of #28# and compute their sum we get (as the sum is negative and the product is positive then both factors must be negative);

# {: ("factor1", "factor2", "sum"), (-28,-1,-29), (-14,-2,-16), (-7,-4,-11) :} #

So as you can see we cannot find two such factors, and so we conclude the expression cannot be factorised

This approach works for all quadratics (assuming it does factorise) , The middle step in the last section can usually be skipped with practice.

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