Algebra Class Products and Factoring

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.