Answer:
Activity 1: My Quotient (1 whole)
Direction: Find the quotient.
1) [tex]\frac{4x - 12}{4}[/tex] Answer: x - 3
2) [tex]\frac{6ab-2ab^2-8a^2b-14a^2b^2}{-2ab}[/tex] Answer: 7ab + 4a + b - 3
3) [tex]\frac{-10a+25a^2}{-5a}[/tex] Answer: 2 - 5a
4) [tex]x^{2}[/tex] + 8x + 15 + x + 5 Answer: [tex]x^{2}[/tex] + 9x + 20
5) - 5x - 36 + x + 4 Answer: - 4x - 32
Activity 2: Problem Solving
Direction: Answer the following.
1) A typist earns [tex]cd^{2}[/tex] + [tex]c^{2}d^{2}[/tex] + [tex]c^{3}d[/tex] for working cd hours. How much does she earn per hour?
Answer: She earns d + cd + [tex]c^{2}[/tex] per hour.
2) The area of a rectangular garden is [tex]x^{2}[/tex] + 3x - 54 square feet. If the length is x + 9 feet, find a binomial that represents the width.
Answer: Width = x - 6 feet
Step-by-step explanation:
Activity 1: My Quotient (1 whole)
Direction: Find the quotient.
1) [tex]\frac{4x - 12}{4}[/tex] Cancel out the common factor of 4x - 12 and 4, which is 4. Divide 4 from 4x, the 4 will be canceled out and x will be left. Then divide 4 from -12, since the terms have different signs, the quotient will be negative, therefore we have - 3. To simply say, just simplify the expression.
= x - 3
2) [tex]\frac{6ab-2ab^2-8a^2b-14a^2b^2}{-2ab}[/tex] Simplify the expression.
[tex]{-3+b+4a+7ab}[/tex] Arrange the terms.
= 7ab + 4a + b - 3
3) [tex]\frac{-10a+25a^2}{-5a}[/tex] Simplify the expression. Just like number one, divide the terms to find the quotient.
= 2 - 5a
4) [tex]x^{2}[/tex] + 8x + 15 + x + 5 Combline like terms. Combine 8x and x (which becomes positive(+) 9x), 15 and 5 (which becomes positive (+) 20). Then, simplify.
= [tex]x^{2}[/tex] + 9x + 20
5) [tex]x^{2}[/tex] - 5x - 36 + x + 4 Combline like terms. Combine -5x and x (which becomes negative(-) 4x), -36 and 4 (which becomes negative(-) 32).
= [tex]x^{2}[/tex] - 4x - 32
Activity 2: Problem Solving
Direction: Answer the following.
1) A typist earns [tex]cd^{2}[/tex] + [tex]c^{2}d^{2}[/tex] + [tex]c^{3}d[/tex] for working cd hours. How much does she earn per hour?
[tex]cd^{2}[/tex] + [tex]c^{2}d^{2}[/tex] + [tex]c^{3}d[/tex] Factor out common factor which is cd, in the expression.
cd ([tex]cd^{2}[/tex] + [tex]c^{2}d^{2}[/tex] + [tex]c^{3}d[/tex]) Cancel common factors.
= cd (d + cd + [tex]c^{2}[/tex]) So the typist earns d + cd + [tex]c^{2}[/tex] per hour.
2) The area of a rectangular garden is [tex]x^{2}[/tex] + 3x - 54 square feet. If the length is x + 9 feet, find a binomial that represents the width.
[tex]x^{2}[/tex] + 3x - 54 Factor the expression. Find the binomial that when multiplied to 9, equals to -54, and when added to 9, equals to 3.
= x + 6
To check if factors are right:
( x + 9 ) ( x + 6 ) Expand by using the FOIL method.
= [tex]x^{2}[/tex] + 3x - 54
Hope this helps.
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