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Factor Linear Expressions

Grade 7 · Algebra · Worksheet 2

  1. Factor: 105x + 63 = ? Answer: ______________
  2. Factor: 91x + 26 = ? Answer: ______________
  3. A community center is planning a mural project that requires rectangular panels. The total area needed for the panels can be expressed as 42x + 56 square feet, where x represents the length of each panel in feet. The project manager needs to factor this expression to determine the standard width that will work for all panels. What is the factored form of the expression 42x + 56 using the greatest common factor? Answer: ______________
  4. A community center is planning to create identical care packages for senior citizens. They have collected 144 boxes of tea and 96 packets of biscuits to distribute equally among the packages with no items left over. What is the greatest number of identical care packages they can create? Answer: ______________
  5. Aroha is helping to organize a large community hāngī. The total cost for the food can be expressed as 84x + 126 dollars, where x represents the number of food baskets. The organizing committee wants to factor this expression using the greatest common factor to find out how much each basket costs before additional fixed costs. What is the factored form of 84x + 126? Answer: ______________
  6. Factor the expression: 54x + 72y = ? Answer: ______________
  7. Noah is organizing a school fundraiser where he sells tickets for a raffle. The total profit from ticket sales can be expressed as 84x + 126 dollars, where x represents the number of ticket bundles sold. To determine how much profit comes from each bundle and the fixed costs, Noah needs to factor this expression using the greatest common factor. What is the factored form of 84x + 126? Answer: ______________
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Answer Key & Explanations

Factor Linear Expressions · Grade 7 · Worksheet 2

  1. Factor: 105x + 63 = ? Answer: 21(5x + 3) Solution: Identify the terms: 105x and 63. Find the GCF of 105 and 63. Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105 Factors of 63: 1, 3, 7, 9, 21, 63 The greatest common factor is 21.
    Full step-by-step solution

    Step 1: Identify the terms: 105x and 63. Step 2: Find the GCF of 105 and 63. Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105 Factors of 63: 1, 3, 7, 9, 21, 63 The greatest common factor is 21. Step 3: Divide each term by the GCF. 105x ÷ 21 = 5x 63 ÷ 21 = 3 Step 4: Write the factored form: 21(5x + 3). The answer is 21(5x + 3).

  2. Factor: 91x + 26 = ? Answer: 13(7x + 2) Solution: Identify the coefficients: 91 and 26. Find the GCF of 91 and 26. - Factors of 91: 1, 7, 13, 91 - Factors of 26: 1, 2, 13, 26 - The GCF is 13.
    Full step-by-step solution

    Step 1: Identify the coefficients: 91 and 26. Step 2: Find the GCF of 91 and 26. - Factors of 91: 1, 7, 13, 91 - Factors of 26: 1, 2, 13, 26 - The GCF is 13. Step 3: Divide each term by 13. - 91x ÷ 13 = 7x - 26 ÷ 13 = 2 Step 4: Write the factored form: 13(7x + 2) The answer is 13(7x + 2).

  3. A community center is planning a mural project that requires rectangular panels. The total area needed for the panels can be expressed as 42x + 56 square feet, where x represents the length of each panel in feet. The project manager needs to factor this expression to determine the standard width that will work for all panels. What is the factored form of the expression 42x + 56 using the greatest common factor? Answer: 14(3x + 4) Solution: Identify the terms in the expression: 42x and 56 Find the greatest common factor of 42 and 56 The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42 The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56 The common factors are: 1, 2, 7, 14 The greatest common factor is 14 Divide each term by 14: 42x ÷ 14 =…
    Full step-by-step solution

    Step 1: Identify the terms in the expression: 42x and 56 Step 2: Find the greatest common factor of 42 and 56 Step 3: The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42 Step 4: The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56 Step 5: The common factors are: 1, 2, 7, 14 Step 6: The greatest common factor is 14 Step 7: Divide each term by 14: 42x ÷ 14 = 3x, 56 ÷ 14 = 4 Step 8: Write the factored form: 14(3x + 4) The factored form is 14(3x + 4).

  4. A community center is planning to create identical care packages for senior citizens. They have collected 144 boxes of tea and 96 packets of biscuits to distribute equally among the packages with no items left over. What is the greatest number of identical care packages they can create? Answer: 48 Solution: Identify the two quantities: 144 boxes of tea and 96 packets of biscuits Find the greatest common factor (GCF) of 144 and 96 List the factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 List the factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 Identify the common factors:…
    Full step-by-step solution

    Step 1: Identify the two quantities: 144 boxes of tea and 96 packets of biscuits Step 2: Find the greatest common factor (GCF) of 144 and 96 Step 3: List the factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Step 4: List the factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 Step 5: Identify the common factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Step 6: The greatest common factor is 48 Step 7: Therefore, they can create 48 identical care packages Step 8: Check: 144 ÷ 48 = 3 boxes of tea per package, 96 ÷ 48 = 2 packets of biscuits per package The answer is 48.

  5. Aroha is helping to organize a large community hāngī. The total cost for the food can be expressed as 84x + 126 dollars, where x represents the number of food baskets. The organizing committee wants to factor this expression using the greatest common factor to find out how much each basket costs before additional fixed costs. What is the factored form of 84x + 126? Answer: 42(2x + 3) Solution: Find the GCF of 84 and 126. Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 The greatest common factor is 42. Divide each term by the GCF.
    Full step-by-step solution

    Step 1: Find the GCF of 84 and 126. Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 The greatest common factor is 42. Step 2: Divide each term by the GCF. 84x divided by 42 = 2x 126 divided by 42 = 3 Step 3: Write the factored form. 84x + 126 = 42(2x + 3) The answer is 42(2x + 3).

  6. Factor the expression: 54x + 72y = ? Answer: 18(3x + 4y) Solution: Find the greatest common factor (GCF) of 54 and 72. List the factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 List the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 The largest common factor is 18.
    Full step-by-step solution

    Step 1: Find the greatest common factor (GCF) of 54 and 72. Step 2: List the factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 Step 3: List the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Step 4: The largest common factor is 18. Step 5: Divide each term by 18: 54x ÷ 18 = 3x, 72y ÷ 18 = 4y Step 6: Write the factored expression: 18(3x + 4y) The answer is 18(3x + 4y).

  7. Noah is organizing a school fundraiser where he sells tickets for a raffle. The total profit from ticket sales can be expressed as 84x + 126 dollars, where x represents the number of ticket bundles sold. To determine how much profit comes from each bundle and the fixed costs, Noah needs to factor this expression using the greatest common factor. What is the factored form of 84x + 126? Answer: 42(2x + 3) Solution: Identify the coefficients in the expression 84x + 126. The coefficients are 84 and 126. Find the greatest common factor (GCF) of 84 and 126.
    Full step-by-step solution

    Step 1: Identify the coefficients in the expression 84x + 126. The coefficients are 84 and 126. Step 2: Find the greatest common factor (GCF) of 84 and 126. List the factors: Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 Common factors: 1, 2, 3, 6, 7, 14, 21, 42 The greatest common factor is 42. Step 3: Factor out 42 from each term. 84x divided by 42 equals 2x. 126 divided by 42 equals 3. Step 4: Write the factored form: 42(2x + 3). The answer is 42(2x + 3).