to factorize the expression 2x2 + 5x + 2.

I will solve question 7(a) from the image.

The question asks to factorize the expression $2x^2 + 5x + 2$.

Step 1: Identify the coefficients. For a quadratic expression in the form $ax^2 + bx + c$, we have $a=2$, $b=5$, and $c=2$.

Step 2: Find two numbers that multiply to $ac$ and add to $b$. Here, $ac = 2 \times 2 = 4$. We need two numbers that multiply to 4 and add to 5. These numbers are 1 and 4.

Step 3: Rewrite the middle term using these two numbers. $2x^2 + 5x + 2 = 2x^2 + 1x + 4x + 2$

Step 4: Factor by grouping. Group the terms and factor out the common factors from each group. $(2x^2 + x) + (4x + 2)$ $x(2x + 1) + 2(2x + 1)$

Step 5: Factor out the common binomial. $(2x + 1)(x + 2)$

The factored form of $2x^2 + 5x + 2$ is $(2x + 1)(x + 2)$.

The final answer is $\boxed{(2x + 1)(x + 2)}$.