Solve: lim_(x rarr-1)(x^(4)+2x^(3)+x^(2))/(x+1)=

Factorize Numerator: Step Title: Factorize the Numerator Concise Step Description: Factorize the polynomial in the numerator. Step Calculation: x^2(x^2 + 2x + 1) = x^2(x + 1)^2 Step Output: x^2(x + 1)^2Simplify Expression: Step Title: Simplify the Expression Concise Step Description: Cancel out the common factor in the numerator and the denominator. Step Calculation: (x^2(x + 1)^2) / (x + 1) = x^2(x + 1) Step Output: x^2(x + 1)Substitute Limit Value: Step Title: Substitute the Limit Value Concise Step Description: Substitute x = -1 into the simplified expression. Step Calculation: (-1)^2(-1 + 1) = 1 * 0 = 0 Step Output: 0

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Math Problems

Algebra 2

Factor polynomials

Full solution

Q. Solve:

\lim_{x \rightarrow -1}\left(\frac{x^{4}+2x^{3}+x^{2}}{x+1}\right)=

Factorize Numerator: Step Title: Factorize the Numerator $\newline$ Concise Step Description: Factorize the polynomial in the numerator. $\newline$ Step Calculation: $x^2(x^2 + 2x + 1) = x^2(x + 1)^2$ $\newline$ Step Output: $x^2(x + 1)^2$
Simplify Expression: Step Title: Simplify the Expression $\newline$ Concise Step Description: Cancel out the common factor in the numerator and the denominator. $\newline$ Step Calculation: $(x^2(x + 1)^2) / (x + 1) = x^2(x + 1)$ $\newline$ Step Output: $x^2(x + 1)$
Substitute Limit Value: Step Title: Substitute the Limit Value $\newline$ Concise Step Description: Substitute $x = -1$ into the simplified expression. $\newline$ Step Calculation: $(-1)^2(-1 + 1) = 1 \times 0 = 0$ $\newline$ Step Output: $0$