SOLUTION: Factor the polynomial 15s^3-21s^2+18s

Question 215406: Factor the polynomial
15s^3-21s^2+18s
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
Factor the polynomial

Step 1. Factor out 3s in the three terms. That is,

Step 2. Need to find two integers m and n such that their product is mn=5*6=30 and their sum is m+n=-7.

Step 3. After several tries, the numbers are no numbers that satisfy step 2. Note if equation was then the numbers would be -10 and 3 for the quadratic expression. We can factor with grouping where and

.

Then the factor for this changed problem yields:

Step 4. We can use the quadratic formula given as

where a=5, b=-7 and c=6.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -71 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -71 is + or - .

The solution is

Here's your graph:

Step 5. We have imaginary results for this example and there are no real solutons.

I hope the above steps and explanation were helpful.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonmetry please visit http://www.FreedomUniversity.TV/courses/Trignometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

RELATED QUESTIONS
factor... (answered by MathLover1)

factor... (answered by ReadingBoosters)

Factor... (answered by jim_thompson5910)

(21s^4+49s^3-35s^2) /... (answered by tangled_mind)

factor completely... (answered by mananth)

14s^2-21s=0 (answered by ReadingBoosters)

Please help me solve this equation: Factor the trinomial s^2-15s+50 (answered by nadinadan,Earlsdon)

what are the factors of... (answered by mananth)

Factor the polynomial twice. First use a common factor with a positive coefficient,... (answered by josgarithmetic)