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.

Related questions
See all questions in Factorization of Quadratic Expressions
Impact of this question
3123 views around the world
You can reuse this answer
Creative Commons License