Factor completely: 20 x+x^(2)-x^(3) Answer:

Factor out 'x': First, we should look for any common factors in all terms of the polynomial 20x + x^2 - x^3. We can see that each term has an 'x' in it, so we can factor out an 'x' from the entire polynomial. Calculation: x(20 + x - x^2)Rearrange terms in descending order: Now we have x(20 + x - x^2). We should rearrange the terms inside the parentheses in descending order of the powers of x. Calculation: x(-x^2 + x + 20)Factor quadratic expression: Next, we need to factor the quadratic expression -x^2 + x + 20. To do this, we look for two numbers that multiply to -20 (the product of the coefficient of x^2, which is -1, and the constant term, which is 20) and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 5 and -4. Calculation: -x^2 + x + 20 = -(x^2 - x - 20) = -(x - 5)(x + 4)Combine factored terms: Finally, we combine the factored quadratic with the 'x' we factored out in the first step. Calculation: x * -(x - 5)(x + 4) = -x(x - 5)(x + 4)

Home

Math Problems

Calculus

Find derivatives of using multiple formulae

Full solution

Q. Factor completely:

\newline

20 x+x^{2}-x^{3}

\newline

Answer:

Factor out 'x': First, we should look for any common factors in all terms of the polynomial $20x + x^2 - x^3$ . $\newline$ We can see that each term has an 'x' in it, so we can factor out an 'x' from the entire polynomial. $\newline$ Calculation: $x(20 + x - x^2)$
Rearrange terms in descending order: Now we have $x(20 + x - x^2)$ . We should rearrange the terms inside the parentheses in descending order of the powers of $x$ . $\newline$ Calculation: $x(-x^2 + x + 20)$
Factor quadratic expression: Next, we need to factor the quadratic expression $-x^2 + x + 20$ . To do this, we look for two numbers that multiply to $-20$ (the product of the coefficient of $x^2$ , which is $-1$ , and the constant term, which is $20$ ) and add up to $1$ (the coefficient of $x$ ). $\newline$ The numbers that satisfy these conditions are $5$ and $-4$ . $\newline$ Calculation: $-x^2 + x + 20 = -(x^2 - x - 20) = -(x - 5)(x + 4)$
Combine factored terms: Finally, we combine the factored quadratic with the $x$ we factored out in the first step. $\newline$ Calculation: $x \cdot -(x - 5)(x + 4) = -x(x - 5)(x + 4)$