# The blank in the statement “The solutions of the equation x 2 ( x − 4 ) = 0 are ____”. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.5, Problem 3E

(a)

To determine

## To fill: The blank in the statement “The solutions of the equation x2(x−4)=0 are ____”.

Expert Solution

The complete statement is “The solutions of the equation x2(x4)=0 are x=0or x=4_”.

### Explanation of Solution

Property used:

Zero-product property:

If ab=0, then a=0orb=0, or both.

Calculation:

Use zero product property, to calculate the solutions of the equation x2(x4)=0.

x2(x4)=0x2=0or(x4)=0x=0andx=4

Thus, the complete statement is “The solutions of the equation x2(x4)=0 are x=0or x=4_”.

(b)

To determine

### To fill: The blank in the statement “To solve the equation x3−4x2=0, we _____ the left-hand side”.

Expert Solution

The complete statement is “To solve the equation x34x2=0, we factor_ the left-hand side”.

### Explanation of Solution

Note that, the expression on the left side of a quadratic equation in the standard form ax2+bx+c=0,a0 can be factored into the product of two first-degree polynomials.

Then, by using the zero-product property set each factor equal to zero. Then, the resulting equations are solved to obtain the given quadratic equation.

Thus, the given equation can be solved by factoring the expression x34x2 as follows.

x34x2=0x2(x4)=0[Takex2ascommon factor]x2=0orx4=0[Zeroproductproperty]x=0orx=4

Therefore, the complete statement is “To solve the equation x34x2=0, we factor_ the left-hand side”.

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