Easy -1.2 This is a straightforward application of the factor theorem requiring substitution of x = -2 into f(x) and solving a simple linear equation for a. It's a single-step problem testing basic recall of the factor theorem with minimal algebraic manipulation, making it easier than average.
1.
$$f ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + a x + a$$
Given that \(( x + 2 )\) is a factor of \(\mathrm { f } ( x )\), find the value of the constant \(a\).
Sets \((a+2)a = 0\) or selects a suitable method given that \((x + 2)\) is a factor of \(f(x)\). Accept either setting \(f(-2) = 0\) or attempted division of \(f(x)\) by \((x + 2)\)
dM1
Solves linear equation in \(a\). Minimum requirement is that there are two terms in \(a\) which must be collected to get \(...a = ...\)
A1
\(a = -36\)
(3 marks)
# Question 1
**M1** | Sets $(a+2)a = 0$ or selects a suitable method given that $(x + 2)$ is a factor of $f(x)$. Accept either setting $f(-2) = 0$ or attempted division of $f(x)$ by $(x + 2)$
**dM1** | Solves linear equation in $a$. Minimum requirement is that there are two terms in $a$ which must be collected to get $...a = ...$
**A1** | $a = -36$
(3 marks)
1.
$$f ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + a x + a$$
Given that $( x + 2 )$ is a factor of $\mathrm { f } ( x )$, find the value of the constant $a$.\\
\hfill \mbox{\textit{Edexcel Paper 2 Q1 [3]}}