Page 135 - Math Course 2 (Book 1)

Factoring: Trinomials

Solve a Real World Problem by
MO. 4 - L4b
Factoring
Solve Equations of the Form

x + bx + c ARCHITECTURE
2
Marion wants to build a new art studio that has
three times the area of the old studio by increasing
the length and width by the same amount. What will
Let’s Begin be the dimensions of the new studio?
Explore
Begin by making a diagram like the one shown to
the right, labeling the appropriate dimensions.
Solve an Equation by Factoring
x 12ft
Example

Existing 10 ft
2
Solve x + 2x – 15 = 0. Check your solution. Studio
2
x + 2x – 15 = 0 Original equation.
x
(x + 5)(x – 3) = 0 Factor.

x + 5 = 0 or x – 3 = 0 Zero Product Property.
Plan
x = –5 x = 3 Solve each equation. Let x = the amount added to each dimension of the
studio.

Answer The solution set is {–5, 3}. The new length times the new width equals the new area.

x + 12 • x + 10 = x(12)(10)

Check old area
Substitute –5 and 3 for x in the original equation. Solve
(x + 12)(x + 10) = 3(12)(10) Write the equation.
2
2
x + 2x – 15 = 0 x + 2x – 15 = 0
2
?
?
2
2
(–5) + 2(–5) – 15 = 0 3 + 2(3) – 15 = 0 x + 22x + 120 = 360 Multiply.
2
? ? x + 22x – 240 = 0 Rewrite the
25 + (–10) – 15 = 0 9 + 6 – 15 = 0 equation so that
one side equals 0.
0 = 0 0 = 0
(x + 30)(x – 8) = 0 Factor.
x + 30 = 0 or x – 8 = 0 Zero Product
Property.

x = –30 x = 8 Solve each equation.
Check
The solution set is {–30, 8}. Only 8 is a valid solution,
since dimensions cannot be negative.

The length of the new studio
should be 8 + 12 or 20 feet,
Answer
and the new width should be
8 + 10 or 18 feet.

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