Question

1. 2x² + 5x + 2

Explanation:

Step1: Identify $a$, $b$, $c$

For $2x^2 + 5x + 2$, $a = 2$, $b = 5$, $c = 2$.

Step2: Find two numbers

Find two numbers that multiply to $a\times c = 2\times2 = 4$ and add to $b = 5$. The numbers are $4$ and $1$.

Step3: Split the middle term

Rewrite the middle term: $2x^2 + 4x + x + 2$.

Step4: Factor by grouping

Group the first two and last two terms: $(2x^2 + 4x) + (x + 2)$. Factor out common factors: $2x(x + 2) + 1(x + 2)$.

Step5: Factor out the common binomial

Factor out $(x + 2)$: $(2x + 1)(x + 2)$.

Answer:

$(2x + 1)(x + 2)$