1Cademy - Factoring $$u^2

Learn Before

Factoring Trinomials of the Form $x^2 + bx + c$

Example

Factoring $u^2 - 9u + 18$

To factor the trinomial $u^2 - 9u + 18$ , find two numbers that multiply to $18$ and add to $-9$ . Because the constant term ( $18$ ) is positive and the middle term ( $-9u$ ) is negative, both factors must be negative.

List the negative factor pairs of $18$ :

$-1$ and $-18$ : sum is $-19$
$-2$ and $-9$ : sum is $-11$
$-3$ and $-6$ : sum is $-9$ The pair $-3$ and $-6$ adds to $-9$ .

Use these numbers to write the binomial factors: $(u - 3)(u - 6)$ .

Check the result by multiplying: $(u - 3)(u - 6) = u^2 - 6u - 3u + 18 = u^2 - 9u + 18$ .

The factored form is $(u - 3)(u - 6)$ .

Updated 2026-06-03

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.6 Factoring - Intermediate Algebra @ OpenStax

Algebra

Factoring $u^2 + 11u + 24$
Factoring $y^2 + 17y + 60$
Factoring $x^2 + bx + c$ When $b$ Is Negative and $c$ Is Positive
Factoring $x^2 + bx + c$ When $c$ Is Negative
Factoring Trinomials of the Form $x^2 + bxy + cy^2$
Factoring $x^2 + 12xy + 36y^2$
Factoring Trinomials of the Form $ax^2 + bx + c$ Using the ac Method
A logistics coordinator is using a software tool to optimize warehouse space. The tool represents the area of a new storage unit with the algebraic expression x^2 + 15x + 54. To find the dimensions of the unit, the coordinator needs to factor this expression into the form (x + m)(x + n). Which rule must be followed to find the correct factors m and n?
A logistics coordinator is using a software tool to optimize warehouse space. The tool represents the area of a new storage unit with the algebraic expression x^2 + 15x + 54. To find the dimensions of the unit, the coordinator needs to factor this expression into the form (x + m)(x + n). Which rule must be followed to find the correct factors m and n?
A logistics coordinator is designing the layout for a new storage zone in a warehouse. The floor area is represented by the expression $x^2 + bx + c$ . To find the specific side lengths of the zone, the coordinator needs to factor this expression into the form $(x + m)(x + n)$ . Arrange the following steps of the factoring strategy in the correct sequence according to the standard method.
A logistics coordinator is designing a floor plan for a new storage facility where the area is represented by the expression $x^2 + bx + c$ . To find the dimensions $(x + m)$ and $(x + n)$ , the coordinator must identify two numbers, $m$ and $n$ . Match each part of the expression to the mathematical requirement those numbers must satisfy.
A facilities manager is analyzing the floor plan for a new office suite where the area is represented by the expression $x^2 + bx + c$ . To factor this into the dimensions $(x + m)$ and $(x + n)$ , the manager knows that the sum of the numbers $m$ and $n$ must be equal to the constant term $c$ .
Logic Documentation for Dimension Optimization Tools
Logistics Optimization Logic
In a corporate facility management system, the floor area of a modular office unit is represented by the trinomial $x^2 + bx + c$ . To factor this expression into the dimensions $(x + m)$ and $(x + n)$ , the system must identify two numbers, $m$ and $n$ , whose ____ is equal to the constant term $c$ .
Technical Documentation for Area Decomposition Logic
Factoring $x^2 + 11x + 24$
Factoring $q^2 + 10q + 24$
Factoring $t^2 + 14t + 24$
Factoring $u^2 - 9u + 18$
Factoring $2x + x^2 - 48$
Factoring $9m + m^2 + 18$
Factoring $-7n + 12 + n^2$
Factoring $4x^3 + 16x^2 - 20x$
Factoring $5x^3 + 15x^2 - 20x$
Factoring by Substitution
Factoring $4p^2q - 16pq + 12q$
Factoring $x^2 + bx + c$ : how must $m$ and $n$ relate to $b$ ?

Learn After

As a quality assurance analyst reviewing architectural software, you are verifying a module that calculates floor plan dimensions. The area of a particular layout is modeled by the expression $u^2 - 9u + 18$ . To verify the length and width parameters, you must recall the correct factored form of this expression. Which of the following represents the correctly factored form?
A facilities manager is using the expression $u^2 - 9u + 18$ to represent the area of a new storage unit. To determine the unit's dimensions by factoring, the manager must identify two integers based on the values in the trinomial. Match each factoring requirement with the correct value from the expression.
A CAD designer is using the area formula $u^2 - 9u + 18$ to specify the footprint of a modular office unit. To simplify the formula for construction teams, the designer must factor it into two binomials. Arrange the following steps in the correct chronological order to complete the factoring process.
Inventory Space Planning
A facilities manager is reviewing a floor plan where the area of a storage unit is represented by the expression $u^2 - 9u + 18$ . The manager concludes that the dimensions of the unit are represented by the factored form $(u - 2)(u - 9)$ because the product of -2 and -9 is 18.

True or False: The factored form of $u^2 - 9u + 18$ is $(u - 2)(u - 9)$ .
A logistics coordinator is analyzing the floor plan of a new distribution hub where the area of a designated storage zone is represented by the expression $u^2 - 9u + 18$ . To install modular partitions, the coordinator factors the area expression into two binomial dimensions. If one of the binomial dimensions is $u - 3$ , then the other binomial dimension must be ____.
Factoring Modular Workstation Floor Area

Learn Before

Related

Learn After