Factor Trinomials of the Form x2+bx+c Quiz
The question sheet
Reveal any answer as you study-
To factor a trinomial of the form x²+bx+c, the factors are written as two binomials with what first terms?
- x
- 2x
- b
- c
Reveal answer
Answer: x
Source evidence
PDF page 903: Step 1. Write the factors as two binomials with first terms x: (x )(x ) . Step 2. Find two numbers m and n that Multiply to c, m · n = c Add to b, m + n = b
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When factoring x²+bx+c, the two numbers m and n must multiply to what?
- x
- c
- bc
- b
Reveal answer
Answer: c
Source evidence
PDF page 903: Step 1. Write the factors as two binomials with first terms x: (x )(x ) . Step 2. Find two numbers m and n that Multiply to c, m · n = c Add to b, m + n = b
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After finding m and n, how are they used in factoring x²+bx+c?
- As the first terms
- As coefficients of x
- As the exponents
- As the last terms of the factors
Reveal answer
Answer: As the last terms of the factors
Source evidence
PDF page 904: Step 3. Use m and n as the last terms of the factors: (x + m)(x + n) . Step 4. Check by multiplying the factors.
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What is the final step when factoring a trinomial of the form x²+bx+c?
- Check by multiplying the factors
- Rewrite in standard form
- Split the middle term
- Find the GCF
Reveal answer
Answer: Check by multiplying the factors
Source evidence
PDF page 904: Step 3. Use m and n as the last terms of the factors: (x + m)(x + n) . Step 4. Check by multiplying the factors.
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In the step (x + m)(x + n), what do m and n represent?
- The first terms
- The exponents
- The coefficients
- The last terms of the factors
Reveal answer
Answer: The last terms of the factors
Source evidence
PDF page 904: Step 3. Use m and n as the last terms of the factors: (x + m)(x + n) . Step 4. Check by multiplying the factors.
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How many numbers must you find to factor x²+bx+c?
- Four
- One
- Three
- Two
Reveal answer
Answer: Two
Source evidence
PDF page 903: Step 1. Write the factors as two binomials with first terms x: (x )(x ) . Step 2. Find two numbers m and n that Multiply to c, m · n = c Add to b, m + n = b
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According to the strategy, if a polynomial is a trinomial of the form x²+bx+c, you should:
- Undo FOIL
- Factor the GCF only
- Use the grouping method
- Use difference of cubes
Reveal answer
Answer: Undo FOIL
Source evidence
PDF page 904: Step 1. Is there a greatest common factor? Factor it. Step 2. Is the polynomial a binomial, trinomial, or are there more than three terms? If it is a binomial, right now we have no method to factor it. 2 If it is a trinomial of the form x + bx + c Undo FOIL (x )(x ) . 2 If it is a trinomial of the form ax + bx + c Use Trial and Error or the “ac” method. If it has more than three terms Use the grouping method. Step 3. Check by multiplying the factors.
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The first step in choosing a strategy to factor a polynomial is:
- Write as two binomials
- Split the middle term
- Check by multiplying
- Is there a greatest common factor?
Reveal answer
Answer: Is there a greatest common factor?
Source evidence
PDF page 904: Step 1. Is there a greatest common factor? Factor it. Step 2. Is the polynomial a binomial, trinomial, or are there more than three terms? If it is a binomial, right now we have no method to factor it. 2 If it is a trinomial of the form x + bx + c Undo FOIL (x )(x ) . 2 If it is a trinomial of the form ax + bx + c Use Trial and Error or the “ac” method. If it has more than three terms Use the grouping method. Step 3. Check by multiplying the factors.
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A polynomial with more than three terms should be factored using which method?
- Undo FOIL
- Trial and error
- Difference of squares
- The grouping method
Reveal answer
Answer: The grouping method
Source evidence
PDF page 904: Step 1. Is there a greatest common factor? Factor it. Step 2. Is the polynomial a binomial, trinomial, or are there more than three terms? If it is a binomial, right now we have no method to factor it. 2 If it is a trinomial of the form x + bx + c Undo FOIL (x )(x ) . 2 If it is a trinomial of the form ax + bx + c Use Trial and Error or the “ac” method. If it has more than three terms Use the grouping method. Step 3. Check by multiplying the factors.
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In the ac method, what is the first step?
- Factor any GCF
- Split the middle term
- Check by multiplying
- Find the product ac
Reveal answer
Answer: Factor any GCF
Source evidence
PDF page 904: Step 1. Factor any GCF. Step 2. Find the product ac. Step 3. Find two numbers m and n that:
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In the ac method, the two numbers m and n must multiply to what?
- a
- ac
- b
- c
Reveal answer
Answer: ac
Source evidence
PDF page 904: Multiply to ac m · n = a · c Add to b m + n = b
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In the ac method, after splitting the middle term, the next step is to:
- Find the product ac
- Write in descending order
- Find the GCF
- Factor by grouping
Reveal answer
Answer: Factor by grouping
Source evidence
PDF page 904: Step 5. Factor by grouping. Step 6. Check by multiplying the factors.
Elementary Algebra 2e
Elementary Algebra 2e by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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