Given that $(x + 3)$ is a factor of $f(x)$, find the value of the constant $a$ - Edexcel - A-Level Maths Pure - Question 3 - 2019 - Paper 2

Since $(x + 3)$ is a factor, we can substitute $x = -3$ into $f(x)$:

$f(-3) = 3(-3)^3 + 2a(-3)^2 - 4(-3) + 5a$

Calculating each term:

• $3(-3)^3 = 3(-27) = -81$
• $2a(-3)^2 = 2a(9) = 18a$
• $-4(-3) = 12$
• $5a = 5a$

Hence,

$f(-3) = -81 + 18a + 12 + 5a$

We combine like terms:

$f(-3) = 18a + 5a - 81 + 12 = 23a - 69$

Setting this equal to zero (as $(x + 3)$ is a factor):

$23a - 69 = 0$