Solutions to Problem Set 15

Math 101-06

10-13-2017

[Solving by factoring]

1. Solve $x(x - 17)(x + 61) = 0$ .

The solutions are $x = 0$ , $x = 17$ , and $x = -61$ .


2. Solve $(3 x - 30)(x -
   \sqrt{11}) = 0$ .

You can factor 3 out of $3 x -
   30$ :

$$3(x - 10)(x - \sqrt{11}) = 0.$$

The solutions are $x = 10$ and $x = \sqrt{11}$ .


3. Solve $x^2 - 25 = 0$ .

$$\eqalign{ x^2 - 25 & = 0 \cr (x + 5)(x - 5) & = 0 \cr}$$

The solutions are $x = 5$ and $x = -5$ .


4. Solve $6 x^2 - 12 x = 0$ .

$$\eqalign{ 6 x^2 - 12 x & = 0 \cr 6 x (x - 2) & = 0 \cr}$$

The solutions are $x = 0$ and $x = 2$ .


5. Solve $x^2 - 11 x + 18 = 0$ .

$$\eqalign{ x^2 - 11 x + 18 & = 0 \cr (x - 2)(x - 9) & = 0 \cr}$$

The solutions are $x = 2$ and $x = 9$ .


6. Solve $x^2 - 6 x - 7 = 0$ .

$$\eqalign{ x^2 - 6 x - 7 & = 0 \cr (x + 1)(x - 7) & = 0 \cr}$$

The solutions are $x = -1$ and $x = 7$ .


7. Solve $x^2 - 10 x + 25 = 0$ .

$$\eqalign{ x^2 - 10 x + 25 & = 0 \cr (x - 5)^2 & = 0 \cr}$$

The solution is $x = 5$ .


8. Solve $x^2 + 21 = 10 x$ .

$$\eqalign{ x^2 + 21 & = 10 x \cr x^2 - 10 x + 21 & = 0 \cr (x - 3)(x - 7) & = 0 \cr}$$

The solutions are $x = 3$ and $x = 7$ .


9. Solve $5 x^3 + 35 x^2 + 50 x
   = 0$ .

$$\eqalign{ 5 x^3 + 35 x^2 + 50 x = 0 \cr 5 x (x^2 + 7 x + 10) & = 0 \cr 5 x (x + 2)(x + 5) & = 0 \cr}$$

The solutions are $x = 0$ , $x = -2$ , and $x = -5$ .


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