Precalculus Examples

$f (x) = 3 x + 5$ $g (x) = 4 x^{2} - 2$ $h (x) = x^{2} - 3 x + 1$ Find $f (x) + g (x) - h (x)$

Step 1

Replace the function designators in $f (x) + g (x) - h x$ with the actual functions.

$3 x + 5 + 4 x^{2} - 2 - (x^{2} - 3 x + 1)$

Step 2

Simplify $3 x + 5 + 4 x^{2} - 2 - (x^{2} - 3 x + 1)$ .

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Step 2.1

Remove parentheses.

$3 x + 5 + 4 x^{2} - 2 - (x^{2} - 3 x + 1)$

Step 2.2

Simplify each term.

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Step 2.2.1

Apply the distributive property.

$3 x + 5 + 4 x^{2} - 2 - x^{2} - (- 3 x) - 1 \cdot 1$

Step 2.2.2

Simplify.

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Step 2.2.2.1

Multiply $- 3$ by $- 1$ .

$3 x + 5 + 4 x^{2} - 2 - x^{2} + 3 x - 1 \cdot 1$

Step 2.2.2.2

Multiply $- 1$ by $1$ .

$3 x + 5 + 4 x^{2} - 2 - x^{2} + 3 x - 1$

Step 2.3

Simplify by adding terms.

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Step 2.3.1

Add $3 x$ and $3 x$ .

$6 x + 5 + 4 x^{2} - 2 - x^{2} - 1$

Step 2.3.2

Subtract $2$ from $5$ .

$6 x + 4 x^{2} + 3 - x^{2} - 1$

Step 2.3.3

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

$6 x + 3 x^{2} + 3 - 1$

Step 2.3.4

Simplify the expression.

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Step 2.3.4.1

Subtract $1$ from $3$ .

$6 x + 3 x^{2} + 2$

Step 2.3.4.2

Reorder $6 x$ and $3 x^{2}$ .

$3 x^{2} + 6 x + 2$