Question

What is the quotient of the following division problem? x 1 startlongdivisionsymbol x squared 3 x 2 endlongdivisionsymbol. minus x squared x to get a remainder of 0 ) 2 x 2. minus 2 x 2 to get a remainder of 0 and a quotient of x 2. x 2 x 1 x2 3x 2 0

Answer 1

The quotient of the provided division in which binomial is divided by a quadratic equation is x+2.

What is the quotient?

Quotient is the resultant number which is obtained by dividing a number with another. Let a number a is divided by number b. Then the quotient of these two number will be,

$q=\dfrac{a}{b}$

Here, (a, b) are the real numbers.

The given division expression is,

$\dfrac{x^2+3x+2}{x+1}$

Let the quotient of this division problem is f(x). Thus,

$f(x)=\dfrac{x^2+3x+2}{x+1}$

Factor the numerator expression as,

$f(x)=\dfrac{x^2+2x+x+2}{x+1}\\f(x)=\dfrac{x(x+2)+1(x+2)}{x+1}\\f(x)=\dfrac{(x+2)(x+1)}{x+1}\\f(x)={x+2}$

Thus, the quotient of the provided division in which binomial is divided by a quadratic equation is x+2.

Learn more about the quotient here;

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