Practice Objectives
  • Demonstrate the ability to factor out the GCF from a polynomial
  • Demonstrate the ability to factor a trinomial when the leading coefficient is 1
  • Demonstrate the ability to factor a trinomial when two variables are involved

Practice Factoring Trinomials When a = 1

Instructions:

Answer 7/10 questions correctly to pass.

Factor each trinomial and then enter the values for p, m, and n.

Formatting Rules:
  • If the GCF is 1, type 1 in the p-value input field
  • If the leading coefficient is negative, you must factor out the -GCF
    • The first position is fixed in each binomial (always "x"), you can only change m and n
  • The GCF might contain "x" but will never contain "y"
    • y is prohibited from entry in the p-value input field
    • Exponents are single-digit positive integers only (zero is not allowed)
    • Use "^" to raise "x" to a power
      • Ex: 3x or 3x^1
      • Ex: 17x^2
      • Ex: -5x^3
  • Since we can multiply polynomials in any order, the values of m and n can be entered in any order
  • Numbers allowed: (-99) to 99 (excluding 0)
    • The number 0 is prohibited from entry in all input fields
  • The m-value and n-value might contain "y" but will never contain "x"
    • "x" is prohibited from entry in the m and n input fields
    • "y" will never have an exponent ("y^" is prohibited from entry in the m and n input fields)

Problem:

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Factoring Trinomials (a = 1):

  1. Factor out the GCF (if it isn't 1)
  2. For the trinomial x2 + bx + c:
    • Find two integers whose sum is b and whose product is c
    • Both integers will be positive if b and c are positive
    • Both integers will be negative if b is negative and c is positive
    • One integer will be positive, and the other negative if c is negative
      • The larger integer in terms of absolute value will have the same sign as b
      • If b is negative, the larger integer in terms of absolute value will be negative
      • If b is positive, the larger integer in terms of absolute value will be positive
  3. Use the two integers and the GCF (when appropriate) to find the factored form
    • _(x + _)(x + _)
    • The GCF will go in the first blank
      • When the GCF is 1, this blank is removed
    • The two integers will go in the final two blanks
    • Note: The order in which we place the integers does not matter
  4. When there is a "y" in the middle term and a "y2" in the final term
    • For the trinomial x2 + bxy + cy2:
      • (x + _y)(x + _y)
      • The blanks are the two integers found using the steps from above

Step-by-Step:

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$$p\left(x + m\right)\left(x + n\right)$$
p =
m =
n =

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Correct Answers: 0 of 7

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Wrong Answers: 0 of 3

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