Factoring Polynomials: Real-Life Applications & Grouping

A farmer has a rectangular field with a length of 3x + 6 and a width of x + 2. How can he factor the area of the field by grouping?

• 3(x + 2)^2

• 3(x + 2)(x + 2)

• (3x + 6)(x + 2)

• (3x + 6)(x - 2)

A school is organizing a concert and sells tickets for 5x + 15 for adults and 3x + 9 for students. How can the school factor the total ticket sales by grouping?

• 7(x + 2)

• 9(x + 1)

• 8(x + 3)

• 6(x + 4)

A company produces two types of gadgets, with production costs represented by the expression 4x^2 + 8x + 12. How can the company factor this expression by grouping?

• 8(x^2 + x + 1)

• 2(2x^2 + 4x + 6)

• 4(x^2 + 2x + 3)

• 4(x^2 + 2x + 2)

A recipe requires 2x^2 + 6x ingredients for a cake. If the chef wants to double the recipe, how can he factor the new ingredient amount by grouping?

• 8x(x + 2)

• 4x(x + 3)

• 2x(x + 3)

• 4x^2 + 12x

A car rental service charges a base fee of 10x + 20 for a car and an additional fee of 5x + 15 for insurance. How can they factor the total cost by grouping?

• 5(4x + 5)

• 10(3x + 2)

• 5(2x + 4)

• 5(3x + 7)

A local gym has a membership fee represented by the expression 6x^2 + 9x. How can the gym factor this expression by grouping to find common membership costs?

• 2x(3x + 3)

• 6(x^2 + 1.5x)

• 9(2x + 1)

• 3x(2x + 3)

A bookstore sells novels for 7x + 14 and textbooks for 5x + 10. How can the bookstore factor the total sales by grouping?

• 12(x + 2)

• 6(x + 4)

• 8(x + 3)

• 10(x + 1)

A landscaping company charges for services represented by the expression 3x^2 + 12x. How can they factor this expression by grouping to find common service costs?

• 3x(x + 4)

• 6x(x + 2)

• x(3x + 12)

• 3(x^2 + 4)

A tech company has a profit represented by the expression 8x^2 + 16x + 24. How can they factor this expression by grouping to analyze their earnings?

• 4(2x^2 + 4x + 6)

• 8(x^2 + 4x + 6)

• 2(4x^2 + 8x + 12)

• 8(x^2 + 2x + 3)

A local bakery sells pastries for 4x + 8 and cakes for 6x + 12. How can the bakery factor the total sales by grouping?

• 12(x + 1)

• 8(x + 1)

• 10(x + 3)

• 10(x + 2)