identity

In O level Additional Mathematics, there is a small section on Identity inside the topic of Factor & Remainder Theorem. Today I am going to share with you the 2 different approaches to solve this kind of questions.

Substitution Method (My preferred method)

I am going to use the question below to show you the step by step solutions of both methods.

Given that [pmath]3x^2+x-2=A(x-1)(x+2)+B(x-1)+C[/pmath] for all values of x, find the value of A, of B and of C.

Let x = 1,

[pmath]3+1-2 = C[/pmath]

[pmath]C=2[/pmath]

Let x = -2,

[pmath]3(4)-2-2 = B(-3) + 2[/pmath]

[pmath]B= -2[/pmath]

Let x = 0,

[pmath]-2 = -2A+ 2 + 2[/pmath]

[pmath]A = 3[/pmath]

Thus A = 3, B = -2 and C = 2

Concept behind the Subsitution method: The value of x choosen will cause one or more of the unknowns to be "cancel off", leaving just 1 unknown left. For example, when I choose x = 1 in the first subsituition, A & B are eliminated, allowing me to find 'C'.

Comparing Coefficients Method

Given that [pmath]3x^2+x-2=A(x-1)(x+2)+B(x-1)+C[/pmath] for all values of x, find the value of A, of B and of C.

By comparing coefficient of [pmath]x^2[/pmath]:

LHS: 3 = A => A = 3

By comparing coefficient of [pmath]x[/pmath]:

LHS: 1 = 2A - A + B => B = -2

By comparing coefficient of [pmath]x^0[/pmath]:

LHS: -2 = -2A - B + C => C = 2

Thus A = 3, B = -2 and C = 2

Concept behind the Comparing Coefficient method: Expansion is usually required on one side of the equation. It takes up time. The reason for the insignificant working shown is due to the fact that the expansion is done mentally instead of written. This method is highly recommended if there is more than 1 unknown other than x on the left hand side of the equation. For example, there's an unknown 'D' on the left hand side of the equation.

Which method do you usually use? And which method does your school teach you? Leave me your answer in the comment section below.

I was doing Factor, Remainder Theorem with one of my students. She's a brilliant girl but has yet to achieve the results she truly deserves. I think she knows the reasons clearly :-)

She likes to do things her way.

And I am totally fine with students having their own style. Afterall, my best method might not be their best method. However, if their style is not helping them in terms of scoring, time management..., this is where I step in to influence and get them to better understand how my strategy (usually a much shorter way as I am a lazy person :-)) might help them to understand and get the answer faster and easily.

I get them to buy my idea. And most of the time, my idea sells out :)

Today post will be on Identity covered with Factor-Remainder Theorem.

There are 2 main methods to solve the question. And for me, I choose the "lazy" method again. Simply because it is easy, fast and accurate!

Who else wants to be like me? "Lazy" strategy which is easy, fast and accurate!

O level A-Math: 2 Different Approaches To Solve Identity Question In Factor - Remainder Theorem

Does Stubborness Earn You More Marks?