factorize 144+12x+x²
Answers
Step-by-step explanation:
1.1 Factoring x2+12x+144
The first term is, x2 its coefficient is 1 .
The middle term is, +12x its coefficient is 12 .
The last term, "the constant", is +144
Step-1 : Multiply the coefficient of the first term by the constant 1 • 144 = 144
Step-2 : Find two factors of 144 whose sum equals the coefficient of the middle term, which is 12 .
-144 + -1 = -145
-72 + -2 = -74
-48 + -3 = -51
-36 + -4 = -40
-24 + -6 = -30
-18 + -8 = -26
For tidiness, printing of 24 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
x2 + 12x + 144
Answer:
x2-12x + 144 = x2-12x +36 -36 + 144 = (x-6)2 +108
x = 6 ± √-108 = 6 ± (6√3) i
(x+6 + (6√3) i)(x+6 - (6√3) i)
I don't see why they call it a perfect square trinomial unless the original expression is wrong.
A perfect square trinomial would be:
x2-24x + 144
For a perfect square trinomial ax2+bx+c, b2 must equal 4ac, which it is not for the original equation.