Algebra 1 Factoring Practice Flashcards

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Questions and Answers

What is the factored form of $x^2 + 8x + 7$?

(x+7)(x+1) (correct)

(x-10)(x-1)

(x-2)(x+6)

(x-9)(x+10)

What is the factored form of $x^2 - 11x + 10$?

(x-10)(x-1) (correct)

(x-3)(x-4)

(x+8)(x+8)

(x-9)(x+10)

What is the factored form of $x^2 + x - 90$?

(x-6)(x+15)

(x-9)(x+10) (correct)

(x+5)(x-18)

(x+8)(x-10)

What is the factored form of $x^2 + 4x - 12$?

(x-2)(x+6) Signup and view all the answers

What is the factored form of $x^2 - 10x + 9$?

(x-1)(x-9) Signup and view all the answers

What is the factored form of $x^2 + 16x + 64$?

(x+8)^2 Signup and view all the answers

What is the factored form of the polynomial $x^2+2x-24$?

(x+6)(x-4) Signup and view all the answers

What is the factored form of $x^2 - 4x + 24$?

Not Factorable Signup and view all the answers

What is the factored form of $x^2 - 13x + 40$?

(x-5)(x-8) Signup and view all the answers

What is the factored form of the polynomial $x^2 + 11x + 18$?

(x+2)(x+9) Signup and view all the answers

What is the factored form of the polynomial $x^2 - x - 56$?

(x+7)(x-8) Signup and view all the answers

What is the factored form of the polynomial $x^2 - 5x + 6$?

(x-2)(x-3) Signup and view all the answers

What is the factored form of the polynomial $x^2 - 6x + 8$?

(x-4)(x-2) Signup and view all the answers

What is the factored form of the polynomial $x^2 + 6x + 8$?

(x+2)(x+4) Signup and view all the answers

What is the factored form of the polynomial $x^2 + 2x - 8$?

(x+4)(x-2) Signup and view all the answers

What is the factored form of $2x^2 + 22x + 60$?

2(x+5)(x+6) Signup and view all the answers

What is the factored form of $2x^2 + 6x - 108$?

2(x+9)(x-6) Signup and view all the answers

What is the factored form of $x^2 - x - 90$?

(x-10)(x+9) Signup and view all the answers

What is the factored form of $x^2 + 11x + 10$?

(x+10)(x+1) Signup and view all the answers

What is the factored form of $2x^2 + 2x - 4$?

2(x-1)(x+2) Signup and view all the answers

What is the factored form of $2x^2 - 2x - 4$?

2(x+1)(x-2) Signup and view all the answers

What is the factored form of $x^2 - 15x + 50$?

(x-10)(x-5) Signup and view all the answers

What is the factored form of $x^2 - 7x + 10$?

(x-5)(x-2) Signup and view all the answers

What is the factored form of $x^2 + 3x - 18$?

(x-3)(x+6) Signup and view all the answers

What is the factored form of $2x^2 + 22x + 20$?

2(x+10)(x+1) Signup and view all the answers

What is the factored form of $x^2 + 6x - 7$?

(x+7)(x-1) Signup and view all the answers

What is the factored form of $x^2 - 6x - 7$?

(x-7)(x+1) Signup and view all the answers

What is the factored form of $x^2 - 8x + 7$?

(x-7)(x-1) Signup and view all the answers

What is the factored form of $x^2 + 9x - 10$?

(x+10)(x-1) Signup and view all the answers

What is the factored form of $x^2 - 9x - 10$?

(x-10)(x+1) Signup and view all the answers

What is the factored form of $2x^2 - 6x - 108$?

2(x-9)(x+6) Signup and view all the answers

What is the factored form of $x^2 - 9$?

(x+3)(x-3) Signup and view all the answers

What is the factored form of $x^2 - 25$?

(x-5)(x+5) Signup and view all the answers

What is the factored form of $x^2 - 36$?

(x+6)(x-6) Signup and view all the answers

What is the factored form of $2x^2 - 32$?

2(x-4)(x+4) Signup and view all the answers

What is the factored form of $x^2 - 100$?

(x-10)(x+10) Signup and view all the answers

What is the factored form of $x^2 - 1$?

(x+1)(x-1) Signup and view all the answers

What is the factored form of $2x^2 - 18$?

2(x+3)(x-3) Signup and view all the answers

What is the factored form of $x^2 - 4$?

(x+2)(x-2) Signup and view all the answers

What is the factored form of $x^2 + 4x + 4$?

(x+2)^2 Signup and view all the answers

What is the factored form of $x^2 - 4x + 4$?

(x-2)^2 Signup and view all the answers

What is the factored form of $x^2 + 6x + 9$?

(x+3)^2 Signup and view all the answers

What is the factored form of $x^2 - 6x + 9$?

(x-3)^2 Signup and view all the answers

What is the factored form of $x^2 + 8x + 16$?

(x+4)^2 Signup and view all the answers

What is the factored form of $x^2 - 8x + 16$?

(x-4)^2 Signup and view all the answers

What is the factored form of $x^2 + 10x + 25$?

(x+5)^2 Signup and view all the answers

What is the factored form of $x^2 - 10x + 25$?

(x-5)^2 Signup and view all the answers

Study Notes

Factoring Basics

Factoring involves rewriting a polynomial as a product of simpler polynomials.
Quadratic expressions typically take the form ( ax^2 + bx + c ).

Common Factoring Techniques

Two Binomials: Products like ( (x+a)(x+b) ) can be used to factor expressions.
Perfect Square: Forms such as ( (x+a)^2 ) indicate ( x^2 + 2ax + a^2 ).
Difference of Squares: ( (x-a)(x+a) = x^2 - a^2 ).

Examples of Factored Forms

( (x+7)(x+1) ) represents ( x^2 + 8x + 7 ).
( (x-10)(x-1) ) factors to ( x^2 - 11x + 10 ).
( (x-9)(x+10) ) leads to ( x^2 + x - 90 ).

Special Cases

Not Factorable: ( x^2 - 4x + 24 ) cannot be factored over the integers.
Double Roots: Forms like ( (x-2)^2 ) represent perfect squares, e.g., ( x^2 - 4x + 4 ).

Specific Factoring Examples

( 2(x+5)(x+6) ) represents ( 2x^2 + 22x + 60 ).
Conjugates: ( (x+3)(x-3) ) expands to ( x^2 - 9 ).

Factoring Quadratics with Leading Coefficient

When the leading coefficient is greater than 1, such as in ( 2x^2 + 22x + 60 ), multiple terms must be considered.
For instance, ( 2(x+1)(x-2) ) applies to ( 2x^2 - 2x - 4 ).

Factoring Rational Expressions

Recognizing standard forms helps in identifying how to simplify or factor rational expressions quickly.

Summary of Quadratic Factor Examples

( (x-5)(x-2) ) factors to ( x^2 - 7x + 10 ).
( (x+10)(x-1) ) provides ( x^2 + 9x - 10 ).

Perfect Square Trinomials

Recognizing patterns such as:
- ( (x+5)^2 = x^2 + 10x + 25 )
- ( (x-4)^2 = x^2 - 8x + 16 )

Practice and Application

Regular practice with various forms reinforces understanding and recognition of factors.
Exploring non-linear forms and higher-degree polynomials can expand learning.

Additional Notes

Not every polynomial can be factored in simple integer forms, and identifying these instances is part of mastering algebra.
Dedicating time to each form solidifies the knowledge necessary for factoring in future coursework.

Studying That Suits You

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Description

Test your skills in factoring polynomials with these flashcards designed for Algebra 1. Each card presents a quadratic expression to factor, helping you reinforce your understanding of the topic. Perfect for students looking to practice and improve their factoring techniques.