Factoring Polynomials by Grouping and Quadratic Form

The video tutorial covers two main methods of factoring polynomials: factoring by grouping and using quadratic form. It begins with an introduction to the concept of factoring, followed by a detailed explanation of factoring by grouping, including examples. The tutorial then shifts to factoring using quadratic form, providing examples and demonstrating how to rewrite expressions in a quadratic model. The video emphasizes the importance of recognizing patterns such as the difference of squares and perfect squares in the factoring process.

What is the first step in factoring by grouping?

• Factor out the greatest common divisor

• Expand the polynomial

• Group pairs that have a common monomial factor

• Combine all terms into one group

In the expression r(a + b) + s(a + b), what can be factored out?

• r + s

• r

• s

• a + b

What is the common factor in the terms x cubed and -3x squared?

• x

• x squared

• x cubed

• 3x

When factoring -16x + 48, what should be factored out?

• 16

• -16

• -48

• 48

What is the common factor in the terms 27t cubed and 45t squared?

• 3

• 9

• t

• t squared

What is the common factor in the terms -3t and -5?

• -1

• 3

• -3

• 1

What is the common factor in the terms x cubed and 7x squared?

• x squared

• 7

• x

• 7x

What is the common factor in the terms -9x and -63?

• 9

• -63

• -9

• 63

In the quadratic form a u squared + b u + c, what does u represent?

• Any expression of x

• Any constant

• Any polynomial

• Any variable

What is the quadratic form of x to the fourth - 14x squared + 45?

• x squared - 14x + 45

• x squared squared - 14x squared + 45

• x to the fourth - 14x + 45

• x squared - 14x squared + 45