1. Look at the two terms in the expression: 12t and 4t³.
2. Find the highest common factor (HCF) of the numerical coefficients (12 and 4).
3. Find the highest common factor of the algebraic parts (t and t³).
4. Combine these to find the overall HCF of the two terms.
5. Place the HCF outside a pair of brackets.
6. Divide each of the original terms by the HCF and place the results inside the brackets.
Full Answer
To factorise fully, we need to find the highest common factor (HCF) of the terms 12t and 4t³.
First, let's look at the numerical coefficients, 12 and 4. The HCF of 12 and 4 is 4.
Next, let's look at the variable parts, t and t³. The HCF of t and t³ is t (the lowest power of t present in both terms).
So, the overall HCF of the expression is 4t.
Now, we take this HCF outside a bracket and divide each original term by it:
12t ÷ 4t = 3
4t³ ÷ 4t = t²
Putting it all together, we get:
12t + 4t³ = 4t(3 + t²)
Common mistakes
✗ Only partially factorising, e.g., 4(3t + t³) or t(12 + 4t²).
✗ Incorrectly dividing the terms inside the bracket, e.g., 4t(3t + t²).
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