Algebra Class Products and Factoring

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Questions and Answers

What is the product of (-x-4)(5x-5)?

-5x²-15x+20

What is the product of (-4x+3)(-2x+5)?

8x²-26x+15

What is the product of (7x+4)(-3x+3)?

-21x²+9x+12

What is the product of (-3x-5)(6x+5)?

-18x²-45x-25 Signup and view all the answers

What is the factored form of -2x²-4x+2?

-2(x²+2x-1) Signup and view all the answers

What is the factored form of -45x⁵+63x³-81x²?

-9x²(5x³-7x+9) Signup and view all the answers

What is the factored form of 12x³+20x+10?

2(6x³+10x+5) Signup and view all the answers

What is the factored form of -2x⁴+8x²-14x?

-2x(x³-4x+7) Signup and view all the answers

What is the completely factored form of 3x²+24x-27?

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

What is the completely factored form of x²-5x+4?

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

What is the completely factored form of x²+5x-24?

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

What is the completely factored form of 4x²-12x-216?

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

What is the completely factored form of 42x²-228x+216?

6(7x-6)(x-6) Signup and view all the answers

What is the completely factored form of 3x²+2x-21?

(3x-7)(x+3) Signup and view all the answers

What is the completely factored form of 24x²-28x-80?

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

What are the solutions to the equation 4x²-4x=48?

4, -3 Signup and view all the answers

What are the solutions to the equation 7x²=42-7x?

2, -3 Signup and view all the answers

What are the solutions to the equation 6x²+6x=0?

-1, 0 Signup and view all the answers

What are the solutions to the equation x²+6=-7x?

-1, -6 Signup and view all the answers

What is the simplified form of √150?

5√6 Signup and view all the answers

What is the simplified form of √27?

3√3 Signup and view all the answers

What is the simplified form of √28?

2√7 Signup and view all the answers

What is the simplified form of √320?

8√5 Signup and view all the answers

Study Notes

Algebraic Products

The product of (-x-4)(5x-5) is -5x²-15x+20.
The product of (-4x+3)(-2x+5) simplifies to 8x²-26x+15.
For (7x+4)(-3x+3), the result is -21x²+9x+12.
The multiplication of (-3x-5)(6x+5) yields -18x²-45x-25.

Factoring Out GCF (Greatest Common Factor)

The expression -2x²-4x+2 factors to -2(x²+2x-1).
Factor out the GCF from -45x⁵+63x³-81x², resulting in -9x²(5x³-7x+9).
The expression 12x³+20x+10 can be factored to 2(6x³+10x+5).
From -2x⁴+8x²-14x, the GCF is -2x(x³-4x+7).

Complete Factoring

The expression 3x²+24x-27 can be factored completely as 3(x+9)(x-1).
Factoring x²-5x+4 results in (x-4)(x-1).
The expression x²+5x-24 completely factors to (x+8)(x-3).
The expression 4x²-12x-216 simplifies to 4(x-9)(x+6).
From 42x²-228x+216, complete factoring gives 6(7x-6)(x-6).
The expression 3x²+2x-21 factors completely into (3x-7)(x+3).
24x²-28x-80 can be completely factored to 4(3x+4)(2x-5).
The expression 12x²+84x+135 factors to 3(2x+9)(2x+5).

Solving Quadratic Equations

The equation 4x²-4x=48 has solutions x=4 and x=-3.
Solving 7x²=42-7x yields x=2 and x=-3.
For 6x²+6x=0, solutions are x=-1 and x=0.
The equation x²+6=-7x results in x=-1 and x=-6.

Simplifying Square Roots

√150 simplifies to 5√6.
√27 simplifies to 3√3.
√28 simplifies to 2√7.
√320 simplifies to 8√5.

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Description

This quiz covers essential concepts of algebra, focusing on algebraic products and factoring techniques. Students will learn how to multiply polynomials and factor expressions utilizing the greatest common factor. Get ready to enhance your understanding of expressions and their simplification.