Question

difficulty:
factorise completely ((x + 2)^2 + 3(x + 2) + 2.
a ((x + 1)(x + 2)
b ((x + 2)(x + 3)
c ((x + 3)(x + 4)
d ((x - 1)(x - 2))

Explanation:

Step1: Let \( y = x + 2 \)

Substitute \( y \) into the expression: \( y^{2}+3y + 2 \)

Step2: Factorise \( y^{2}+3y + 2 \)

Find two numbers that multiply to \( 2 \) and add to \( 3 \), which are \( 1 \) and \( 2 \). So, \( y^{2}+3y + 2=(y + 1)(y + 2) \)

Step3: Substitute back \( y = x + 2 \)

\( (x + 2+1)(x + 2 + 2)=(x + 3)(x + 4) \)

Answer:

C. \((x + 3)(x + 4)\)