Factoring Quadratic Polynomials

The video tutorial covers various methods of factoring polynomials, including U substitution, difference of squares, and difference of cubes. It explains how to factor trinomials and identify patterns, as well as using the greatest common factor. The tutorial provides examples to illustrate each method, helping students understand the concepts and apply them to different polynomial expressions.

What is the purpose of U substitution in polynomial factoring?

• To graph the polynomial

• To eliminate all variables

• To introduce new variables for complexity

• To simplify the polynomial to a basic form

Which pair of numbers multiplies to -36 and adds up to 5?

• 5 and -7

• 1 and -36

• 6 and -6

• 9 and -4

What does x^2 - 4 factor into?

• x + 2 * x - 2

• x^2 + 4

• x - 2 * x + 2

• x^2 - 2x + 2

What does the expression x^2 - 4 factor into?

• (x - 2)(x - 2)

• (x + 4)(x - 4)

• (x + 2)(x - 2)

• x^2 + 4

What is a characteristic of the difference of squares?

• Sum instead of difference

• Always contains a variable

• No middle term in the expression

• Coefficients are always positive

Which method is used to factor the expression 9x^4 - 25?

• Factoring by grouping

• Sum of squares

• Difference of squares

• U substitution

What is factored out when dealing with 16x^4 - 1?

• 4

• 8

• 2

• 16

What does the expression 16x^4 - 1 factor into after factoring out a common factor?

• 4x^2 + 1 and 4x^2 - 1

• None of the above

• 8x^2 + 1 and 8x^2 - 1

• 2x^2 + 1 and 2x^2 - 1

What is the result of factoring x^6 - x^3 - 56 using U substitution?

• x^3(x - 2)(x^2 + 2x + 4) + x^3 + 7

• x^3(x - 2)(x^2 + 2x + 4) + x^3 - 7

• x^3(x + 2)(x^2 - 2x + 4) + x^3 - 7

• x^3(x + 2)(x^2 - 2x + 4) + x^3 + 7

What is the factored form of x^6 - x^3 - 56?

• x^3(x + 2)(x^2 - 2x + 4) + x^3 - 7

• x^3(x - 2)(x^2 + 2x + 4) + x^3 + 7

• x^3(x - 2)(x^2 + 2x + 4) + x^3 - 7

• x^3(x + 2)(x^2 - 2x + 4) + x^3 + 7