Question

question
factor the trinomial:
$5x^2 + 42x + 49$

Explanation:

Step1: Identify coefficients

For trinomial \(ax^2 + bx + c\) (here \(a = 5\), \(b = 42\), \(c = 49\)), find two numbers that multiply to \(a\times c=5\times49 = 245\) and add to \(b = 42\).
The numbers are \(35\) and \(7\) (since \(35\times7 = 245\) and \(35 + 7 = 42\)).

Step2: Split the middle term

Rewrite the trinomial as \(5x^2+35x + 7x + 49\).

Step3: Group and factor

Group the first two and last two terms: \((5x^2 + 35x)+(7x + 49)\).
Factor out common factors from each group: \(5x(x + 7)+7(x + 7)\).

Step4: Factor out the common binomial

Factor out \((x + 7)\) to get \((5x + 7)(x + 7)\).

Answer:

\((5x + 7)(x + 7)\)