Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(d^{2} + 4 d + 3) \frac{1}{d + 1}$

Step 3

Multiply $d^{2} + 4 d + 3$ by $\frac{1}{d + 1}$ .

$\frac{d^{2} + 4 d + 3}{d + 1}$

Step 4

Factor $d^{2} + 4 d + 3$ using the AC method.

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Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $3$ and whose sum is $4$ .

$1, 3$

Step 4.2

Write the factored form using these integers.

$\frac{(d + 1) (d + 3)}{d + 1}$

Step 5

Cancel the common factor of $d + 1$ .

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Step 5.1

Cancel the common factor.

$\frac{(d + 1) (d + 3)}{d + 1}$

Step 5.2

Divide $d + 3$ by $1$ .

$d + 3$