Factor the following trinomials completely.z2−11z+30z^2-11z+30

(z−5)(z−6)\left(z-5\right)\left(z-6\right)(z−5)(z−6)

Factor the following trinomials completely. z 2 − 11 z + 30 z^2-11z+30

Since this polynomial has a leading term of just z 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 my c value and add to my b value. So let's start by listing some factor pairs of 30. We've got one and thirty, as well as two and fifteen, three and ten, and five and six. Now do any of these sum to 11? Yes. Five plus six equals 11. But we're not looking for positive 11, we're actually looking for negative 11. So instead we're going to use the factors negative five and negative six, which sum to negative 11 and still have a product of positive 30. So this means I can factor this polynomial as z minus five times z minus six, and this is our final answer.

Factor the following trinomials completely.z2−$$11z+30z^2-11z+30 $$

(z−5)(z−6)\left(z-5\right)\left(z-6\right)(z−5)(z−6)

(z+5)(z−6)\left(z+5\right)\left(z-6\right)(z+5)(z−6)

(z−3)(z−10)\left(z-3\right)\left(z-10\right)(z−3)(z−10)

(z+5)(z+6)\left(z+5\right)\left(z+6\right)(z+5)(z+6)

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1. Review of Real Numbers2h 43m

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
44m

2. Linear Equations and Inequalities5h 35m

Solving Linear Equations
2h 23m

Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
1h 7m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

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37m

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25m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphs and Functions5h 12m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

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38m

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22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
53m

Function Notation
15m

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17m

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Solving Systems of Linear Equations by Graphing
29m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

Systems of Linear Inequalities
23m

6. Exponents, Polynomials, and Polynomial Functions3h 17m

The Product Rule
9m

The Quotient Rule
10m

Intro to the Power Rules
17m

The Power of a Quotient Rule
13m

Negative Exponents
24m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

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38m

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34m

7. Factoring2h 49m

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
41m

Quadratic Equations & Applications
41m

8. Rational Expressions and Functions3h 44m

Simplifying Rational Expressions
42m

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25m

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19m

Least Common Denominators
32m

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32m

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27m

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11m

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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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32m

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40m

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27m

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29m

Factorials
13m

7. Factoring

Factoring Trinomials of the Form x² + bx + c

Intermediate Algebra

7. Factoring

Factoring Trinomials of the Form x² + bx + c

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Multiple Choice

Factor the following trinomials completely.
$z^{2} - 11 z + 30$

$$\left$(z+5$\right$)$\left$(z-6$\right$)$

$$\left$(z-3$\right$)$\left$(z-10$\right$)$

$$\left$(z+5$\right$)$\left$(z+6$\right$)$

$$\left$(z-5$\right$)$\left$(z-6$\right$)$

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Verified step by step guidance

Identify the trinomial to factor: $z^2 - 11z + 30$.

Look for two numbers that multiply to the constant term \$30$ and add up to the coefficient of the middle term, which is $-11$.

List the factor pairs of \$30$: $(1, 30)$, $(2, 15)$, $(3, 10)$, and $(5, 6)$, and consider their signs to sum to $-11$.

Determine that the pair $-5$ and $-6$ multiply to \$30$ and add to $-11$.

Write the factored form as $(z - 5)(z - 6)$.

7:23m

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