Exercise 11 Page 224

The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is - x. Because of the order of the terms, it will be easier to visualize if we factor out the -1 and the x separately.

- x^2+3x

FactorOutNegSign

Factor out a minus sign

-(x^2-3x)

SplitIntoFactors

Split into factors

-(x* x-3* x)

FactorOut

Factor out x

- x(x-3)

The factored form of - x^2+3x is - x(x-3). Note that it is one of many correct ways to rewrite the expression.

Checking Our Answer

Check your answer ✓

To check our answer, we can apply the Distributive Property and compare the result with the given expression.

- x(x-3)

Distr

Distribute - x

- x(x)-3(- x)

MultNegNegOnePar

- a(- b)=a* b

- x(x)+3x

Multiply

Multiply

- x^2+3x

After applying the Distributive Property, the result is the same as the given expression. Therefore, we can be sure our solution is correct!