# Algebra

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Explain why x^2 +5x + 8 is prime(not factorable) How do you know?
Give 2 examples of a prime polynomial(can't be both binomials)
Give 2 examples of polynomials that are not prime(they can't be both binomials),factor them,explain what you did to factor them.
How would you explain to another student how to decide if any given polynomial is prime of not? Thanks

• Algebra -

a x^2 + b x + c

if sqrt (b^2-4ac) is a whole number then you can factor the quadratic

In this case b^2-4ac = 25 - 32 = -7
sqrt(-7) is an imaginary number so you can not factor this with whole numbers.

To make up some you can factor, do it backwards
for example
(x-1)(x-2) = x^2 -3x + 2
You know you can factor that.
Now one way to make up some you can not factor use big numbers at the end so that 4ac is positive and bigger than b^2
x^2 + 5 x + 100

• Algebra -

Damon, Thanks for your help. Appreciate it.

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