Question

factor the trinomial: $2x^2 + 15x + 28$

Explanation:

Step1: Identify \(a\), \(b\), \(c\)

For \(2x^2 + 15x + 28\), \(a = 2\), \(b = 15\), \(c = 28\).

Step2: Find \(ac\) and factors

\(ac = 2\times28 = 56\). Find two numbers that multiply to \(56\) and add to \(15\). The numbers are \(7\) and \(8\) (since \(7\times8 = 56\) and \(7 + 8 = 15\)).

Step3: Split the middle term

Rewrite the trinomial as \(2x^2 + 7x + 8x + 28\).

Step4: Factor by grouping

Group the first two and last two terms: \((2x^2 + 7x) + (8x + 28)\). Factor out the GCF from each group: \(x(2x + 7) + 4(2x + 7)\).

Step5: Factor out the common binomial

Factor out \((2x + 7)\) to get \((2x + 7)(x + 4)\).

Answer:

\((2x + 7)(x + 4)\)