3 Basic Ways to Solve a Maths Question.

1) Using 'I don't Understand' to Solve.

Given that (2x-1) and (x+1) are factors of the expression 2x^3 + px^2 + x + q, find the value of p and of q. Hence, factorise the expression completely.

Step 1: Whenever you see '... value of p and of q.', always think of 'Simultaneous Equation'.

Step 2: In Simultaneous Equation, you need 2 equations.

Step 3: Look at the questions and asked yourself, how to create 2 equations? Think Simple!

Step 4: Use Filomaths *'Agar Agar' method, and substitute x = 1/2 and x = -2 into the given equation.
If you are asking  >>>  How to know what to substitute?,
FIRST ask yourself  >>>  what else you can substitute?

Step 5: You will automatically know what to do ...

"A thousand mile begin with a single step"

NOTE: We heave specific ways to 'agar agar' to increase your accuracy. 


2) Using 'KeyWords' to help you to Solve.

Given that (2x-1) and (x+1) are factors of the expression 2x^3 + px^2 + x + q, find the value of p and of q. Hence, factorise the expression completely.

Step 1: Gather all Keywords. They are: (2x-1), (x+1), 'factors', 2x^3 + px^2 + x + q, 'value of p and of q', 'Hence' and 'factorise'.

Step 2: Let f(x) = 2x^3 + px^2 + x + q

Step 3: Let f(1/2) = 2(1/2)^3 + p(1/2)^2 + (1/2) + q

Step 4: 2(1/2)^3 + p(1/2)^2 + (1/2) + q = 0 (The word 'Factor' tells you equal to '0')

Step 5: Let f(-1) = 2(-1)^3 + p(-1)^2 + (-1) + q

Step 6: 2(-1)^3 + p(-1)^2 + (-1) + q = 0 (The word 'Factor' tells you equal to '0')

Step 7: Simultaneous Equation (The word 'value of p and of q' tells you Simultaneous)

Step 8: 'Hence' tells you you need to use what you have done previously.

Step 9: 'factorise' tells you that you will 'see' brackets at the End of Your Workings.

3) Using 'Understand' to help you to Solve.

Given that (2x-1) and (x+1) are factors of the expression 2x^3 + px^2 + x + q, find the value of p and of q. Hence, factorise the expression completely.

'expression' means an equation. 'factor' means there shall be NO REMAINDER, therefore the equation is equal to '0' when you substitute the 2 factors into it. Since there are 2 unknowns, 'p' and 'q', we need to solve using Simultaneous Substitution Method.

'Hence' means that you need to use what you have done previously and continue solving. Since the expressions has the highest power of 3 and You need the following 3 Steps to Complete factorise.
They are: Guess and Check, Long Division and Cross Product.

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