Factor the following trinomials completely.y2−7y+12y^2-7y+12

(y−3)(y−4)\left(y-3\right)\left(y-4\right)(y−3)(y−4)

Factor the following trinomials completely. y 2 − 7 y + 12 y^2-7y+12

Since this polynomial has a leading term of just y squared, we're going to use the method that we learned recently to factor it where we ask ourselves what are two numbers that multiply to our c value and add to our b value. So let's start by listing some factor pairs for 12. We have one and twelve, as well as two and six, and three and four. Now do any of these sum to seven? Yes. Three plus four equal seven. But we're not looking for seven, we're actually looking for negative seven. So instead, we're gonna use the factor pairs of negative three and negative four, which still multiply to positive 12 but also sum to negative seven. So that means I can factor this polynomial as y minus three times y minus four. And this here is our final answer.

Factor the following trinomials completely.y2−$$7y+12y^2-7y+12$$

(y−3)(y−4)\left(y-3\right)\left(y-4\right)(y−3)(y−4)

(y+3)(y−4)\left(y+3\right)\left(y-4\right)(y+3)(y−4)

(y+7)(y−1)\left(y+7\right)\left(y-1\right)(y+7)(y−1)

(y−1)(y−12)\left(y-1\right)\left(y-12\right)(y−1)(y−12)

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1. Review of Real Numbers2h 39m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
40m

2. Linear Equations and Inequalities3h 38m

The Addition and Subtraction Properties of Equality
41m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Linear Inequalities in One Variable
1h 11m

3. Solving Word Problems2h 43m

Introduction to Problem Solving
37m

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21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

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The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

5. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

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15m

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45m

6. Exponents and Polynomials3h 25m

The Product Rule
10m

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13m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
33m

Quadratic Equations & Applications
41m

8. Rational Expressions and Equations3h 13m

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39m

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25m

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19m

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32m

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32m

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44m

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42m

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28m

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23m

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57m

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15m

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5m

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24m

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24m

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27m

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19m

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23m

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18m

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51m

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25m

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26m

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40m

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1h 28m

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25m

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13m

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26m

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32m

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15m

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10m

15. Sequences, Series, and the Binomial Theorem1h 46m

Introduction to Sequences
40m

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27m

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26m

Factorials
11m

7. Factoring

Factoring Trinomials of the Form x² + bx + c

Beginning & Intermediate Algebra

7. Factoring

Factoring Trinomials of the Form x² + bx + c

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Multiple Choice

Factor the following trinomials completely.
$y^{2} - 7 y + 12$

$$\left$(y+3$\right$)$\left$(y-4$\right$)$

$$\left$(y-3$\right$)$\left$(y-4$\right$)$

$$\left$(y+7$\right$)$\left$(y-1$\right$)$

$$\left$(y-1$\right$)$\left$(y-12$\right$)$

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Verified step by step guidance

Identify the trinomial to factor: $y^2 - 7y + 12$.

Look for two numbers that multiply to the constant term (12) and add up to the coefficient of the middle term (-7).

List the factor pairs of 12: (1, 12), (2, 6), (3, 4). Determine which pair sums to -7 when both numbers are negative, since the middle term is negative.

Write the factors as binomials using the numbers found: $(y - a)(y - b)$, where $a$ and $b$ are the numbers from the previous step.

Verify by expanding the binomials using the FOIL method to ensure the product equals the original trinomial.

2:03m

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Master Factoring Trinomials of the Form x² + bx + c Example 1 with a bite sized video explanation from Patrick Ford