Question

factor trinomials (a>1) level 1
score: 4/6 penalty: 1 off
question
factor the trinomial:
5x² + 42x + 49
answer attempt 1 out of 2

Explanation:

Step1: Identify coefficients

For trinomial \(5x^2 + 42x + 49\), \(a = 5\), \(b = 42\), \(c = 49\).

Step2: Find two numbers

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 \(35 + 7 = 42\)).

Step3: Split the middle term

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

Step4: Factor by grouping

Group the first two and last two terms: \(5x(x + 7)+7(x + 7)\).

Step5: Factor out common binomial

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

Answer:

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