Algebra Examples

$f (x) = (x + 1) (x - 3) (x - 4)$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Expand $(x + 1) (x - 3)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$(x (x - 3) + 1 (x - 3)) (x - 4)$

Step 1.1.2

Apply the distributive property.

$(x \cdot x + x \cdot - 3 + 1 (x - 3)) (x - 4)$

Step 1.1.3

Apply the distributive property.

$(x \cdot x + x \cdot - 3 + 1 x + 1 \cdot - 3) (x - 4)$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $x$ by $x$ .

$(x^{2} + x \cdot - 3 + 1 x + 1 \cdot - 3) (x - 4)$

Step 1.2.1.2

Move $- 3$ to the left of $x$ .

$(x^{2} - 3 \cdot x + 1 x + 1 \cdot - 3) (x - 4)$

Step 1.2.1.3

Multiply $x$ by $1$ .

$(x^{2} - 3 x + x + 1 \cdot - 3) (x - 4)$

Step 1.2.1.4

Multiply $- 3$ by $1$ .

$(x^{2} - 3 x + x - 3) (x - 4)$

Step 1.2.2

Add $- 3 x$ and $x$ .

$(x^{2} - 2 x - 3) (x - 4)$

Step 1.3

Expand $(x^{2} - 2 x - 3) (x - 4)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Step 1.4

Simplify terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

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

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Step 1.4.1.1.1

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

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Step 1.4.1.1.1.1

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

$x^{2} x^{1} + x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Step 1.4.1.1.1.2

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

$x^{2 + 1} + x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Step 1.4.1.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Step 1.4.1.2

Move $- 4$ to the left of $x^{2}$ .

$x^{3} - 4 \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Step 1.4.1.3

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

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Step 1.4.1.3.1

Move $x$ .

$x^{3} - 4 x^{2} - 2 (x \cdot x) - 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Step 1.4.1.3.2

Multiply $x$ by $x$ .

$x^{3} - 4 x^{2} - 2 x^{2} - 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Step 1.4.1.4

Multiply $- 4$ by $- 2$ .

$x^{3} - 4 x^{2} - 2 x^{2} + 8 x - 3 x - 3 \cdot - 4$

Step 1.4.1.5

Multiply $- 3$ by $- 4$ .

$x^{3} - 4 x^{2} - 2 x^{2} + 8 x - 3 x + 12$

Step 1.4.2

Simplify by adding terms.

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Step 1.4.2.1

Subtract $2 x^{2}$ from $- 4 x^{2}$ .

$x^{3} - 6 x^{2} + 8 x - 3 x + 12$

Step 1.4.2.2

Subtract $3 x$ from $8 x$ .

$x^{3} - 6 x^{2} + 5 x + 12$

Step 2

The largest exponent is the degree of the polynomial.

$3$