Question

verify whether (x+1),(x-2)and (x+3) are the factors of the polynomial x^3+2x^2-5x-6 without actual division​

Answer 1

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$f(x)\:=\:x^3+2x^2-5x-5$

If (x+1),(x-2)and (x+3) are the factors of the polynomial then, when we put the value of

x = -1 , 2 , -3 in the polynomial

Then we will get, f(x) = 0

Now,

$f( - 1) = {( - 1)}^{3} + 2 {( - 1)}^{2} - 5( - 1) - 6 \\ = 0 \\ \\ \: in \: the \: same \: way \: \\ f(2) = 0 \: \\ f( - 3) = 0 \\ \\ hence \: proved$