SOLUTION: I need to verify whether each equation is an identity or not by substituting -1, 0, and 1 for X. Lesson 9.4 extra practice in the back of the book. Problem #7. x^+4x+3=(

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to verify whether each equation is an identity or not by substituting -1, 0, and 1 for X. Lesson 9.4 extra practice in the back of the book. Problem #7. x^+4x+3=(      Log On


   

Question 130039This question is from textbook Algebra 1
: I need to verify whether each equation is an identity or not by substituting -1, 0, and 1 for X.
Lesson 9.4 extra practice in the back of the book.
Problem #7. x^+4x+3=(x+1)(x+3) This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B4x%2B3=%28x%2B1%29%28x%2B3%29 Start with the given equation


%28-1%29%5E2%2B4%28-1%29%2B3=%28-1%2B1%29%28-1%2B3%29 Plug in x=-1


1%2B4%28-1%29%2B3=%28-1%2B1%29%28-1%2B3%29 Square -1 to get 1


1-4%2B3=%28-1%2B1%29%28-1%2B3%29 Multiply


0=%280%29%282%29 Combine like terms


0=0 Multiply. So the solution x=-1 works

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x%5E2%2B4x%2B3=%28x%2B1%29%28x%2B3%29 Start with the given equation


%280%29%5E2%2B4%280%29%2B3=%280%2B1%29%280%2B3%29 Plug in x=0


0%2B4%280%29%2B3=%280%2B1%29%280%2B3%29 Square 0 to get 0


0%2B0%2B3=%280%2B1%29%280%2B3%29 Multiply


3=%281%29%283%29 Combine like terms


3=3 Multiply. So the solution x=0 works



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x%5E2%2B4x%2B3=%28x%2B1%29%28x%2B3%29 Start with the given equation


%281%29%5E2%2B4%281%29%2B3=%281%2B1%29%281%2B3%29 Plug in x=1


1%2B4%281%29%2B3=%281%2B1%29%281%2B3%29 Square -1 to get 1


1%2B4%2B3=%281%2B1%29%281%2B3%29 Multiply


8=%282%29%284%29 Combine like terms


8=8 Multiply. So the solution x=1 works


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Since more than one solution works, this equation is an identity



Note:

Another way you can prove that the equation is an identity is to foil the right side and simplify.