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

Question

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

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

Identify the coefficients.
For a quadratic expression in the form $ax^2 + bx + c$ , we have $a=2$ , $b=5$ , and $c=2$ .
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.
Rewrite the middle term using these two numbers.
$2x^2 + 5x + 2 = 2x^2 + 1x + 4x + 2$
Factor by grouping.
Group the terms and factor out the common factors from each group.
$(2x^2 + x) + (4x + 2)$ $x(2x + 1) + 2(2x + 1)$
Factor out the common binomial.
$(2x + 1)(x + 2)$
The factored form of $2x^2 + 5x + 2$ is $(2x + 1)(x + 2)$ .

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