Factoring and Simplifying Expressions

The video tutorial covers solving algebraic problems, including factorization, adding fractions, simplifying expressions, and dividing fractions. It begins with the complete factorization of 12x^2 - 147, followed by adding algebraic fractions by finding a common denominator. The tutorial then moves on to simplifying expressions with exponents and concludes with dividing fractions and simplifying the result.

What is the first step in completely factoring the expression 12x squared minus 147?

• Use the quadratic formula

• Check divisibility by 3

• Divide by 12

• Apply the difference of squares

Which expression represents the complete factorization of 12x squared minus 147?

• 12(x^2 - 12.25)

• 3(2x + 7)(2x - 7)

• 4(3x^2 - 36.75)

• 3(4x^2 - 49)

When adding algebraic fractions, what is the first step?

• Add the exponents

• Multiply the numerators

• Find a common denominator

• Subtract the denominators

What is the least common multiple of the denominators x+5 and x^2+3x-10?

• x-2

• x+5

• (x+5)(x-2)

• x^2+3x-10

How do you simplify an expression with a negative exponent?

• Add the exponent to the base

• Multiply the exponent by -1

• Subtract the exponent from the base

• Take the reciprocal of the base

What is the simplified form of 3a^2b^3c^-2 divided by a^-1b^2c, all raised to the third power?

• 3a^5b^3/c^5

• 3a^5/b^3c^5

• 3a^5c^5/b^3

• 3b^3c^5/a^5

What operation is equivalent to dividing by a fraction?

• Subtracting the fraction

• Multiplying by the inverse

• Squaring the fraction

• Adding the fraction

What is the result of dividing 20x^-4 by 27y^2 and then multiplying by the inverse of 15y^-5 over 8x^-3?

• 25/18xy^7

• 25/18x^2y^5

• 25/18x^3y^7

• 25/18x^5y^3

In the expression 20x^-4 over 27y^2, what is the result of simplifying the exponents when multiplied by 15y^-5 over 8x^-3?

• x^1y^7

• x^-1y^-7

• x^-3y^-5

• x^3y^5

What is the final simplified form of the expression 20x^-4 over 27y^2 times 15y^-5 over 8x^-3?

• 25/18x^3y^7

• 25/18x^2y^5

• 25/18xy^7

• 25/18x^5y^3