1Cademy - Finding the Quotient $$(x^2 + 9x + 20) \div (x + 5)$$

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Dividing a Polynomial by a Binomial

Example

Finding the Quotient $(x^2 + 9x + 20) \div (x + 5)$

Apply polynomial long division to divide a trinomial by a binomial with no remainder: $(x^2 + 9x + 20) \div (x + 5)$ .

Step 1 — Set up. Write the dividend $x^2 + 9x + 20$ under the division bracket and the divisor $x + 5$ outside. The dividend is already in standard form.

Step 2 — Divide $x^2$ by $x$ . Ask: "What must $x$ be multiplied by to produce $x^2$ ?" The answer is $x$ . Write $x$ in the quotient above the $x$ term of the dividend.

Step 3 — Multiply and subtract. Multiply $x(x + 5) = x^2 + 5x$ and write it beneath the first two terms of the dividend. Subtract $x^2 + 5x$ from $x^2 + 9x$ (change signs and add): $(x^2 + 9x) - (x^2 + 5x) = 4x$ . Bring down the constant term $20$ to form $4x + 20$ .

Step 4 — Divide $4x$ by $x$ . Ask: "What must $x$ be multiplied by to produce $4x$ ?" The answer is $4$ . Write $+4$ in the quotient above the constant term.