Algebra - Factoring Problems Flashcards

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Questions and Answers

What is the factored form of 15x^2 + 4x - 32?

(5x + 8) (3x - 4) (correct)

(5x - 8) (3x + 4)

(3x - 8) (5x + 4)

(3x + 8) (5x - 4)

What is the factored form of 4x^2 - 13x + 10?

(4x - 5) (x - 2) (correct)

(x + 5) (4x - 2)

(x - 5) (4x + 2)

(4x + 5) (x + 2)

What is the factored form of 9x^2 - 4?

(3x - 2) (3x + 2) (correct)

(9x - 4) (x + 1)

(3x - 4) (3x + 4)

(3x + 4) (3x - 2)

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

(8x - 4) (8x + 4) Signup and view all the answers

What is the factored form of -6x^2 - 6x + 36?

-6 (x + 3) (x - 2) Signup and view all the answers

What is the factored form of 56p^3 - 72p?

8p (7p^2 - 9) Signup and view all the answers

What is the factored form of 3x^2 + 6x - 144?

3 (x + 8) (x - 6) Signup and view all the answers

What is the factored form of 108s^2 + 54?

54 (2s^2 + 1) Signup and view all the answers

What is the factored form of 16x^2 - 36?

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

What is the factored form of -x^2 - 10x - 24?

<ul> <li>(x + 6) (x + 4)</li> </ul> Signup and view all the answers

What is the factored form of 81y^2 - 49/144?

(9y - 7/12) (9y + 7/12) Signup and view all the answers

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

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

What is the factored form of -12x^2 - 26x - 12?

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

What is the factored form of 6a^2 - 12a - 48?

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

What is the factored form of 9x^2 + 49?

prime Signup and view all the answers

What is the factored form of 25/49a^2 - b^2?

(5/7a - b) (5/7a + b) Signup and view all the answers

What is the factored form of 40x^2 + 150x + 135?

5 (4x + 9) (2x + 3) Signup and view all the answers

What is the factored form of 3a^2 + 24a + 48?

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

What is the factored form of 24x^3 - 26x^2 + 6x?

2x (4x - 3) (3x - 1) Signup and view all the answers

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

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

Study Notes

Factoring Algebraic Expressions

Factoring is the process of breaking down an expression into simpler components, known as factors.
Key strategies include finding common factors, using special products, and applying the quadratic formula when necessary.

Specific Factored Expressions

15x² + 4x - 32 factors into (5x + 8)(3x - 4).
4x² - 13x + 10 simplifies to (4x - 5)(x - 2).
9x² - 4 is factored as (3x - 2)(3x + 2), representing a difference of squares.
64x² - 16 can be broken down to (8x - 4)(8x + 4).
Expression -6x² - 6x + 36 simplifies to -6(x + 3)(x - 2).
For 56p³ - 72p, the greatest common factor (GCF) is 8p(7p² - 9).

GCF and Special Cases

3x² + 6x - 144 factors to 3(x + 8)(x - 6).
108s² + 54 can be factored to 54(2s² + 1).
16x² - 36 simplifies to (4x - 6)(4x + 6).
Expression -x² - 10x - 24 factors as -(x + 6)(x + 4).

Perfect Squares and Parabolic Functions

d² - 6d + 9 can be written as (d - 3)², indicating a perfect square trinomial.
-12x² - 26x - 12 can be factored into -2(3x + 2)(2x + 3).

More Complex Factoring

The expression 6a² - 12a - 48 breaks down to 6(a - 4)(a + 2).
9x² + 49 is classified as prime, meaning it cannot be factored further over the integers.
For the expression 25/49a² - b², it factors as (5/7a - b)(5/7a + b), indicating a difference of squares.
40x² + 150x + 135 simplifies to 5(4x + 9)(2x + 3).
3a² + 24a + 48 can be factored as 3(a + 4)², indicating a repeated root.
Finally, 24x³ - 26x² + 6x factors to 2x(4x - 3)(3x - 1), showcasing the procedure for cubic expressions.
The quadratic equation x² - 11x + 18 factors as (x - 9)(x - 2).

Conclusion

Understanding these factoring techniques is vital for solving quadratic equations and simplifying polynomial expressions effectively.

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Description

Test your skills in factoring algebraic expressions with these flashcards. Each card presents a polynomial to factor along with its solution. Perfect for students looking to reinforce their understanding of algebraic concepts.