Precalculus Examples

$x = - 3$ , $x = 3$ , $x = 7$

Since the roots of an equation are the points where the solution is $0$ , set each root as a factor of the equation that equals $0$ .

$(x - (- 3)) (x - 3) (x - 7) = 0$

Simplify.

Tap for more steps...

Expand $(x + 3) (x - 3)$ using the FOIL Method.

Tap for more steps...

Apply the distributive property.

$(x (x - 3) + 3 (x - 3)) (x - 7) = 0$

Apply the distributive property.

$(x x + x \cdot - 3 + 3 (x - 3)) (x - 7) = 0$

Apply the distributive property.

$(x x + x \cdot - 3 + (3 x + 3 \cdot - 3)) (x - 7) = 0$

Remove parentheses.

$(x x + x \cdot - 3 + 3 x + 3 \cdot - 3) (x - 7) = 0$

Simplify and combine like terms.

Tap for more steps...

Simplify each term.

Tap for more steps...

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Combine $x$ and $x$

Tap for more steps...

Raise $x$ to the power of $1$ .

$(x x + x \cdot - 3 + 3 x + 3 \cdot - 3) (x - 7) = 0$

Raise $x$ to the power of $1$ .

$(x x + x \cdot - 3 + 3 x + 3 \cdot - 3) (x - 7) = 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{1 + 1} + x \cdot - 3 + 3 x + 3 \cdot - 3) (x - 7) = 0$

Add $1$ and $1$ .

$(x^{2} + x \cdot - 3 + 3 x + 3 \cdot - 3) (x - 7) = 0$

Move $- 3$ to the left of the expression $x \cdot - 3$ .

$(x^{2} - 3 \cdot x + 3 x + 3 \cdot - 3) (x - 7) = 0$

Multiply $- 3$ by $x$ .

$(x^{2} - 3 x + 3 x + 3 \cdot - 3) (x - 7) = 0$

Multiply $3$ by $- 3$ .

$(x^{2} - 3 x + 3 x - 9) (x - 7) = 0$

Add $- 3 x$ and $3 x$ .

$(x^{2} + 0 - 9) (x - 7) = 0$

Add $x^{2}$ and $0$ .

$(x^{2} - 9) (x - 7) = 0$

Expand $(x^{2} - 9) (x - 7)$ using the FOIL Method.

Tap for more steps...

Apply the distributive property.

$x^{2} (x - 7) - 9 (x - 7) = 0$

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 7 - 9 (x - 7) = 0$

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 7 + (- 9 x - 9 \cdot - 7) = 0$

Remove parentheses.

$x^{2} x + x^{2} \cdot - 7 - 9 x - 9 \cdot - 7 = 0$

Simplify each term.

Tap for more steps...

Multiply $x^{2}$ by $x$ by adding the exponents.

Tap for more steps...

Combine $x^{2}$ and $x$

Tap for more steps...

Raise $x$ to the power of $1$ .

$x^{2} x + x^{2} \cdot - 7 - 9 x - 9 \cdot - 7 = 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 1} + x^{2} \cdot - 7 - 9 x - 9 \cdot - 7 = 0$

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 7 - 9 x - 9 \cdot - 7 = 0$

Move $- 7$ to the left of the expression $x^{2} \cdot - 7$ .

$x^{3} - 7 \cdot x^{2} - 9 x - 9 \cdot - 7 = 0$

Multiply $- 7$ by $x^{2}$ .

$x^{3} - 7 x^{2} - 9 x - 9 \cdot - 7 = 0$

Multiply $- 9$ by $- 7$ .

$x^{3} - 7 x^{2} - 9 x + 63 = 0$

Enter YOUR Problem