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klio [65]
3 years ago
15

Which trinomials are prime?Choose all answers that are correct.

Mathematics
1 answer:
lbvjy [14]3 years ago
7 0

Answer:

x^2+11x+18 is prime

Step-by-step explanation:

<u>Prime Trinomials</u>

A given trinomial is prime if it cannot be factored. The general expression for a trinomial is

ax^2+bx+c

Another useful expression is

a(x-x_1)(x-x_2)

where x1 and x2 are the zeroes of the trinomial.

The zeroes can be computed by using the known formula

\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

The trinomial has two zeroes if the root can be found as a real number, that is if d is positive or zero, where

d=b^2-4ac

Let's test the four options

x^2-8x+2

a=1,b=-8,c=2

d=(-8)^2-4\cdot 1\cdot 2=56

Since d is positive, the trinomial can be factored and therefore is not prime

x^2+4x+5

a=1,b=4,c=5

d=4^2-4\cdot 1\cdot 5=-4

Since d is negative, the trinomial is prime

x^2+11x+18

a=1,b=11,c=18

d=11^2-4\cdot 1\cdot 18=49

Since d is positive, the trinomial can be factored and therefore is not prime

x^2-3x-2

a=1,b=-3,c=-2

d=(-3)^2-4\cdot 1\cdot (-2)=17

Since d is positive, the trinomial can be factored and therefore is not prime

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