Problem of the Week

Updated at May 27, 2019 2:37 PM

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Mar 24, 2025

How would you find the factors of $15{t}^{2}+t-2$ ?

Below is the solution.

15{t}^{2}+t-2

Split the second term in

15{t}^{2}+t-2

into two terms.

Multiply the coefficient of the first term by the constant term.

15\times -2=-30

Ask: Which two numbers add up to

1

and multiply to

-30

6

and

-5

Split

t

as the sum of

6t

and

-5t

15{t}^{2}+6t-5t-2

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15{t}^{2}+6t-5t-2

Factor out common terms in the first two terms, then in the last two terms.

3t(5t+2)-(5t+2)

Factor out the common term

5t+2

(5t+2)(3t-1)

Done