SOLUTION: (1+x)^4+ (1+x)^3=5

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Question 1020889: (1+x)^4+ (1+x)^3=5
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
SIMPLIFY and solve according to any factoring you may find that way, OR according to trying Rational Roots Theorem.

Maybe this way should be a good path:
(1+x)^3*(1+x+1)=5
(1+x)^3(x+2)=5
No, not so good,...
Try this way:

(learn about Pascal's Triangle and the Binomial Theorem as a shortcut to the multplications)-----
%281%2B4%2Ax%2B6%2Ax%5E2%2B4%2Ax%5E3%2Bx%5E4%29%2B%281%2B3x%2B3x%5E2%2Bx%5E3%29=5
x%5E4%2B4x%5E3%2B6x%5E2%2B4x%2B1%2Bx%5E3%2B3x%5E2%2B3x%2B1=5
x%5E4%2B5x%5E3%2B9x%5E2%2B7x%2B2=5
highlight_green%28x%5E4%2B5x%5E3%2B9x%5E2%2B7x-3=0%29

Check the possible roots, -3, -1, 1, 3, and if desired, any others according to what you may be learning about polynomial functions.
(In fact, none of those will be roots. According to a graphing feature in Google, there are two real roots, and both are irrational roots.)