Question

factor : 3x² + 13x - 10
factors : ( ) and ( )
no spaces in your answer.

Explanation:

Step1: Use AC method for factoring

For quadratic \(ax^2 + bx + c\) (here \(a = 3\), \(b = 13\), \(c=- 10\)), find \(ac=3\times(-10)=-30\).
Find two numbers that multiply to \(-30\) and add to \(13\). The numbers are \(15\) and \(-2\) (since \(15\times(-2)=-30\) and \(15 + (-2)=13\)).

Step2: Rewrite middle term and factor by grouping

Rewrite \(13x\) as \(15x-2x\):
\(3x^2+15x - 2x - 10\)
Group terms: \((3x^2 + 15x)+(-2x - 10)\)
Factor out GCF from each group: \(3x(x + 5)-2(x + 5)\)
Factor out \((x + 5)\): \((3x - 2)(x + 5)\)

Answer:

\(3x - 2\) and \(x + 5\)