Factoring Polynomials and Perfect Squares

The video tutorial guides viewers through the process of factoring a polynomial completely. It begins by identifying common terms that can be factored out, specifically the variable X. The tutorial then focuses on recognizing perfect squares within the polynomial and applies the perfect square formula to simplify the expression. The final section concludes the factoring process and highlights the key realizations, such as identifying common factors and recognizing patterns of perfect squares.

What is the first step in factoring the polynomial 16x^3 + 24x^2 + 99x?

• Divide by 2

• Multiply by 3

• Factor out an x

• Add 5 to each term

After factoring out an x, what is the resulting expression?

• 16x^2 + 24x + 99

• 16x^3 + 24x + 9

• 16x^2 + 24x + 9

• 16x^3 + 24x^2 + 9

Tags

CCSS.HSA.APR.C.4

Which term in the expression 16x^2 + 24x + 9 is a perfect square?

• None of the above

• 99

• 24x

• 16x^2

Tags

CCSS.HSA.APR.C.4

How can the term 24x be expressed to fit the perfect square pattern?

• As 3 * 8x

• As 2 * 4 * 3x

• As 4 * 6x

• As 12 * 2x

Tags

CCSS.HSA.APR.C.4

What is the value of 'a' in the perfect square trinomial pattern (ax + b)^2?

• 5

• 4

• 2

• 3

Tags

CCSS.HSA.APR.C.4

What is the value of 'b' in the perfect square trinomial pattern (ax + b)^2?

• 5

• 4

• 3

• 2

What is the final factored form of the polynomial?

• x(4x + 3)(4x + 3)

• x(4x + 9)(4x + 9)

• x(4x + 3)^2

• x(4x + 9)^2

Tags

CCSS.HSA.APR.C.4

What is the key realization in the final step of factorization?

• Recognizing a perfect square trinomial

• Identifying a common factor

• Adding terms

• Subtracting terms

Tags

CCSS.HSA.APR.C.4

Which pattern is used to identify the perfect square trinomial?

• (ax + b)^2 = ax^2 + 2bx + b^2

• (ax + b)^2 = ax^2 + 2abx + b^2

• (ax + b)^2 = ax^2 + abx + b^2

• (ax + b)^2 = ax^2 + 2ax + b^2

Tags

CCSS.HSA.APR.C.4

What is the importance of recognizing the perfect square pattern?

• It aids in complete factorization

• It helps in adding terms

• It simplifies the polynomial

• It allows for easier multiplication

Tags

CCSS.HSA.APR.C.4