Question

exponents and polynomials
factoring a quadratic with leading coefficient greater than 1: problem typ...
factor.
$8x^2 - 22x + 5$

Explanation:

Step1: Multiply a and c

For quadratic \(ax^2 + bx + c\) (here \(a = 8\), \(b=-22\), \(c = 5\)), calculate \(a\times c=8\times5 = 40\).

Step2: Find factors of 40

Find two numbers that multiply to 40 and add to \(b=-22\) (note signs: both negative since product positive and sum negative). The numbers are \(-20\) and \(-2\) (\(-20\times -2 = 40\), \(-20 + (-2)=-22\)).

Step3: Split middle term

Rewrite the quadratic as \(8x^2-20x - 2x + 5\).

Step4: Group and factor

Group terms: \((8x^2 - 20x)+(-2x + 5)\). Factor out GCF from each group: \(4x(2x - 5)-1(2x - 5)\).

Step5: Factor out common binomial

Factor out \((2x - 5)\): \((4x - 1)(2x - 5)\).

Answer:

\((4x - 1)(2x - 5)\)