2.1.4 Factorizing quadratic expressions

• What is the general form of a quadratic expression?

  ax² + bx + c
• What does writing a quadratic expression in factored form involve?

  Combining common factors
• The factored form of x² + 5x + 6 is (x + 2)(x + 3).


  True
• Steps to write a quadratic expression in factored form

  1️⃣ Identify the factors of the constant term

  2️⃣ Check if the sum of the factors equals the coefficient of x

  3️⃣ Combine the factors into two binomial expressions
• 2x + 3 is a linear expression.


  True
• What is the pattern for factoring the difference of squares?

  a^2 - b^2 = (a + b)(a - b)</latex>
• The number 9 is a perfect square


  True
• What is an example of a quadratic expression?

  3x² + 5x + 2
• Steps to factor out common terms in an algebraic expression

  1️⃣ Group the first two and last two terms

  2️⃣ Identify the common factor in each group

  3️⃣ Factor out the common factors

  4️⃣ Combine the factored terms
• After factoring out common terms in x(x + 2) + 3(x + 2), the combined factored form is (x + 3)(x + 2)


  True
• What are the dimensions of a rectangular plot with an area expressed as x² + 5x + 6?

  (x + 2) and (x + 3)
• When factoring x² - 16, a = x and b = 4

  True
• The coefficient of the middle term in a quadratic expression is added to find the required sum.


  True
• What is the original expression being rewritten in this example?

  x² + 5x + 6
• Steps to factorize a quadratic expression ax² + bx + c

  1️⃣ Identify the constant term (c) and the coefficient of the middle term (b)

  2️⃣ Find two numbers that multiply to c and add up to b

  3️⃣ Use these numbers to factorize the expression
• Splitting the middle term creates four terms that can be grouped and factored more easily.


  True
• The degree of a linear expression is 2.


  False
• What is the example of a difference of squares expression mentioned in the text?

  x² - 16
• How is the middle term 5x rewritten in the expression x² + 5x + 6?

  2x + 3x
• Factoring out common terms can help determine the dimensions of sections in a garden


  True
• What two operations are involved in factorizing a quadratic expression ax² + bx + c?

  Multiplication and addition
• What are the two types of expressions combined in factored form?

  Binomial expressions
• In the example x² + 5x + 6, what is the constant term (c)?

  6
• What does being able to spot the difference of squares pattern make factoring easier?

  It simplifies the process
• To factorize x² + 5x + 6, we need two numbers that multiply to 6 and add up to 5.


  True
• Which pair of factors of 6 add up to 5?

  2 and 3
• In (x² + 2x), the common factor is x

  True
• Steps to rewrite a quadratic expression by splitting the middle term:

  1️⃣ Find two numbers that multiply to the constant term and add up to the coefficient of the middle term

  2️⃣ Replace the middle term with two new terms using these numbers

  3️⃣ Group the four terms created

  4️⃣ Factor the expression by grouping
• The factored form of x² + 5x + 6 is (x + 1)(x + 6).

  False
• Why is factoring a quadratic expression useful in real-life scenarios?

  Determining dimensions of land
• What is the coefficient in the linear term of a quadratic expression?

  b