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
4t(3 + t²)
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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