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Chapter 7: Problem 22

Factorise \(t^{3}+3 t^{2}+2 t\).

Short Answer

Expert verified
Answer: The factorised form of the given expression is \(t(t + 2)(t + 1)\).

Step by step solution

01

Identify the common factor

Observe the three terms in the expression: \(t^3\), \(3t^2\), and \(2t\). All of them have a common factor of \(t\).
02

Factor out the common factor

Now, we need to factor out the common factor "t" from each term: \(t(t^2 + 3t + 2)\).
03

Factorise the quadratic expression

Now, we need to factorise the remaining quadratic expression \((t^2 + 3t + 2)\). To do this, find two numbers that multiply to 2 and add to 3. In this case, these numbers are 2 and 1. So, we can rewrite the quadratic expression as \((t + 2)(t+1)\).
04

Write the final factorised expression

Finally, combine the common factors and the factored quadratic expression to get the complete factorised expression: \(t(t + 2)(t + 1)\).

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