+0

+2
100
2
+27

Find a polynomial $$q(x)$$ such that $$(x+1)^3+x^2\cdot q(x)$$ has degree less than $$2$$.

Nov 22, 2020

#1
+112463
+3

Here is how:

$$(x+1)^3+x^2\cdot q(x)\\ =x^3+3x^2+3x+1+x^2\cdot q(x)\\ =x^2(x+3)+3x+1+x^2\cdot q(x)\\ =x^2(x+3+q(x))+3x+1\\ if\;\;q(x)=-3-x\\ \text{Then the degree of the resuling polynomial will be 1}$$

Nov 22, 2020
#2
+27
+2

Thanks a lot!