Question

question
factor the trinomial:
$3x^2 + 26x + 35$
answer attempt 1 out of 2

Explanation:

Step1: Identify coefficients

For trinomial \(3x^2 + 26x + 35\), \(a = 3\), \(b = 26\), \(c = 35\).

Step2: Find two numbers

Find two numbers that multiply to \(a\times c=3\times35 = 105\) and add to \(b = 26\). The numbers are \(21\) and \(5\) (since \(21\times5 = 105\) and \(21 + 5 = 26\)).

Step3: Split the middle term

Rewrite the trinomial as \(3x^2+21x + 5x + 35\).

Step4: Factor by grouping

Group the first two and last two terms: \((3x^2 + 21x)+(5x + 35)\). Factor out common factors from each group: \(3x(x + 7)+5(x + 7)\).

Step5: Factor out the common binomial

Factor out \((x + 7)\) to get \((3x + 5)(x + 7)\).

Answer:

\((3x + 5)(x + 7)\)