completely factor the following expressions. z^2 + 15z - 54

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We need to find two numbers that multiply to -54 and add to +15.

This means that one number will be negative and one will be positive.  (a negative times a positive is negative)

Also the larger of the two numbers will be positive, since when added it results in...

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We need to find two numbers that multiply to -54 and add to +15.

This means that one number will be negative and one will be positive.  (a negative times a positive is negative)

Also the larger of the two numbers will be positive, since when added it results in a positive number.

Let us list the factors of -54 that fit this criteria.

-1*54 = -54.

-2*27 = -54

-3 * 18 = -54. and hey! 18 + -3 = 15

So our answer is (x - 3)(x + 18)

 

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Hello!

This polynomial has degree 2. If we factor it, the two factors must be of degree 1 each. They of course have one root each and that roots are also roots of the original polynomial.

In other words, it is sufficient to find roots of this polynomial. They are 3 and -18 (we can use the formula for a quadratic equation or guess by Viet's theorem).

So the answer is `z^2+15z-54=(z-3)*(z+18).`

Approved by eNotes Editorial Team