Problem of the Week

Updated at Nov 25, 2019 11:37 AM

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Mar 24, 2025

How would you find the factors of $2{z}^{2}-17z+30$ ?

Below is the solution.

2{z}^{2}-17z+30

Split the second term in

2{z}^{2}-17z+30

into two terms.

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

2\times 30=60

Ask: Which two numbers add up to

-17

and multiply to

60

-5

and

-12

Split

-17z

as the sum of

-5z

and

-12z

2{z}^{2}-5z-12z+30

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2{z}^{2}-5z-12z+30

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

z(2z-5)-6(2z-5)

Factor out the common term

2z-5

(2z-5)(z-6)

Done