Question

LESSON: DIVISION OF POLYNOMIALS

Solve the following problems. Show your complete solutions and use long division method or synthetic division to find the quotient.

1. The total cost of (3a - 2b) units of cell phone is (6a² + 5ab - 6b²) pesos. What expression represents the cost of one cell phone?

2. If one ream of bond paper costs (3x - 4) pesos, how many reams can you buy for (6x⁴ - 17x³ + 24x² - 34x + 24) pesos?

3. If a car covers (15x² + 7x - 2) km in (3x + 2) hours, what is the average speed in km/hr?


GOOD FOR 80 PTS!!!​

Answer 1

`\textsf{1.} \quad (2a+3b)\; \sf pesos`

`\textsf{2.} \quad (2x^2-3x^2+4x-6)\; \sf reams`

`\textsf{3.} \quad (5x-1)\; \sf km/h`

Explanation:

Dividend : A number/expression that is divided by the divisor.

Divisor : The number/expression that divides the dividend.

Quotient : The result obtained by the division.

Remainder : The number/expression left behind.

Long division method

• Divide the first term of the dividend by the first term of the divisor, and put that in the answer.
• Multiply the divisor by that answer, put that below the dividend.
• Subtract to create a new dividend.
• Repeat.

The solution is the quotient plus the remainder divided by the divisor.

Question 1

Using long division:

`\large \begin{array}{r}2a+3b\phantom{))}\\3a-2b{\overline{\smash{\big)}\,6a^2+5ab-6b^2\phantom{)}}}\\{-~\phantom{(}\underline{(6a^2-4ab)\phantom{-b)..)}}\\9ab-6b^2\phantom{)}\\-~\phantom{()}\underline{(9ab-6b^2)\phantom{}}\\0\phantom{))}\end{array}`

Question 2

Using long division:

`\large \begin{array}{r}2x^3-3x^2+4x-6\phantom{)}\\3x-4{\overline{\smash{\big)}\,6x^4-17x^3+24x^2-34x+24\phantom{)}}}\\{-~\phantom{(}\underline{(6x^4-8x^3)\phantom{-bbbbbbbbbbbbbbbbb.)}}\\-9x^3+24x^2-34x+24\phantom{)}\\-~\phantom{()}\underline{(-9x^3+12x^2)\phantom{bbbbbbbbbbb.}}\\12x^2-34x+24\phantom{)}\\-~\phantom{()}\underline{(12x^2-16x)\phantom{bbbb..}}\\-18x+24\phantom{)}\\-~\phantom{()}\underline{(-18x+24)}\\0\phantom{)}\end{array}`

Question 3

Using long division:

`\large \begin{array}{r}5x-1\phantom{)}\\3x+2{\overline{\smash{\big)}\,15x^2+7x-2\phantom{)}}}\\{-~\phantom{(}\underline{(15x^2+10x)\phantom{-b)}}\\-3x-2\phantom{)}\\-~\phantom{()}\underline{(-3x-2)\phantom{}}\\0\phantom{)}\\\end{array}`