SOLUTION: The problem is x(x+1)squared(x+2)=0; 0, -1, 2. Sorry I dont know how to make an exponent on the computer. I am supposed to use the 0, -1, and 2. to determine by substitution whi

Question 143384This question is from textbook Mathmatical Analysis
: The problem is x(x+1)squared(x+2)=0; 0, -1, 2.
Sorry I dont know how to make an exponent on the computer. I am supposed to use the 0, -1, and 2. to determine by substitution which of the given numbers, if any satisfy the equation. So far I have getting that -1 and 0 work! I have a question about my work though. Am I supposed to distribute the x first or foil first? Thanks so much for your time! Tarah This question is from textbook Mathmatical Analysis

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
It doesn't matter whether you distribute the x first or use the FOIL process first -- remember the commutative property of multiplication? From a practical point of view, you will find it easier to do the FOIL thing first and then distribute the x because distributing the x is just a matter of going across the polynomial that resulted from the FOIL process and increasing the exponents on the variables by 1.

Having said all of that, you really don't need to use FOIL or distribute anything. Just remember the Zero Product Rule: if and only if or .

Applying the zero product rule to you get:

, or
=> , or
=> , (because there are 2 factors of ) or
=>

And those are all of the roots of the given equation. We are sure of this fact because we know that if you did use FOIL and distribution to multiply the factors, you would end up with a polynomial equation with as the high order term, making it a 4th degree polynomial equation. The Fundamental Theorem of Algebra tells us that a polynomial equation of degree n has exactly n roots (although some or all of them may be complex numbers). You have a 4th degree equation, and 4 roots, and all is right with the world.

Notice that -2 is a root, but 2 is not.

And one last thing: If you want to indicate an exponent on the computer, just use the caret mark (Shift-6), like this: x(x + 1)^2(x + 2).

RELATED QUESTIONS
HELLO.....I am asked to solve 2(x+1)exponent 2/3 + 3(x+1)exponent 1/3=0 by u-... (answered by Fombitz)

i do not know how to solve equations where there is a negative exponent. im sorry, i... (answered by jim_thompson5910)

well i hav a question about 2x2+15x-8=0 the 2 next to x is an exponent sorry i dont know... (answered by checkley71)

Draw The circle (uhm...i really dont know what to do and i need your help...uhm, you dont (answered by venugopalramana)

Quadratic equations. Solve for x value. Sorry I don't know the sign/symbol for square on (answered by ewatrrr,TimothyLamb)

don't know how to type exponent. the equation is x squared plus 0x minus 1 equals 0. i... (answered by Earlsdon)

need to solve for an "X" exponent: 2 (x power) = 1/4 I know the answer but dont... (answered by ikdeep)

I am supposed to solve this problem by completing the square: (x squared) + 11x +... (answered by LifeDeathnCandy)

{{{ log( 3,x ) }}} ^2 + {{{ log( 3,x^2) }}} -3 = 0 What is x? Basically, this question (answered by josgarithmetic)