How do I factorize \(2t^2 + 5t + 2\)?

To factorise the quadratic 2t² + 5t + 2, find two numbers that multiply to 4 and add to 5, then rewrite the middle term and factor by grouping to get (t + 2)(2t + 1).

To factorise the quadratic expression 2t² + 5t + 2, you need to look for two numbers that multiply to 2 times 2 (the coefficient of t² and the constant term), which is 4, and add up to 5 (the coefficient of t). These two numbers are 1 and 4. We can then write the middle term 5t as 4t + t.
Now the expression can be rewritten as:
2t² + 4t + t + 2
Next, factor by grouping:
Group the first two terms and the last two terms: (2t² + 4t) + (t + 2)
Factor out the common factor in each group: 2t(t + 2) + 1(t + 2)
Now, you have a common binomial factor of (t + 2), so factor this out: (t + 2)(2t + 1)
Therefore, the factorised form of 2t² + 5t + 2 is (t + 2)(2t + 1).

Answered by Vickynehra | 2024-06-24

To factorize the expression 2 t 2 + 5 t + 2 , first find two numbers that multiply to 4 (the product of 2 and 2 ) and add to 5 . Rewrite the middle term as 4 t + 1 t , then group and factor to achieve the final factored form ( t + 2 ) ( 2 t + 1 ) .
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Answered by Vickynehra | 2024-09-05