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Answer :
To factor the quadratic expression [tex]\(c^2 - 17c + 70\)[/tex], we want to rewrite it as a product of two binomials. The goal is to find two numbers that multiply to the constant term (70) and add to the coefficient of the linear term (-17).
1. Identify the necessary numbers: We need two numbers that multiply to 70 and add to -17.
2. List pairs of factors of 70:
- [tex]\(1 \times 70\)[/tex]
- [tex]\(2 \times 35\)[/tex]
- [tex]\(5 \times 14\)[/tex]
- [tex]\(7 \times 10\)[/tex]
3. Check the factor pairs for the correct sum:
- The pair (7, 10) stands out. If we take both as negative, [tex]\(-7\)[/tex] and [tex]\(-10\)[/tex], they still multiply to 70 because [tex]\((-7) \times (-10) = 70\)[/tex].
- Check the sum: [tex]\(-7 + (-10) = -17\)[/tex].
4. Rewrite the expression:
- We've found the numbers we need, [tex]\(-7\)[/tex] and [tex]\(-10\)[/tex], so the expression can be factored as:
[tex]\[
(c - 7)(c - 10)
\][/tex]
Therefore, the completely factored form of the expression [tex]\(c^2 - 17c + 70\)[/tex] is [tex]\((c - 7)(c - 10)\)[/tex].
So the correct choice is:
- A. The answer is [tex]\((c - 7)(c - 10)\)[/tex].
1. Identify the necessary numbers: We need two numbers that multiply to 70 and add to -17.
2. List pairs of factors of 70:
- [tex]\(1 \times 70\)[/tex]
- [tex]\(2 \times 35\)[/tex]
- [tex]\(5 \times 14\)[/tex]
- [tex]\(7 \times 10\)[/tex]
3. Check the factor pairs for the correct sum:
- The pair (7, 10) stands out. If we take both as negative, [tex]\(-7\)[/tex] and [tex]\(-10\)[/tex], they still multiply to 70 because [tex]\((-7) \times (-10) = 70\)[/tex].
- Check the sum: [tex]\(-7 + (-10) = -17\)[/tex].
4. Rewrite the expression:
- We've found the numbers we need, [tex]\(-7\)[/tex] and [tex]\(-10\)[/tex], so the expression can be factored as:
[tex]\[
(c - 7)(c - 10)
\][/tex]
Therefore, the completely factored form of the expression [tex]\(c^2 - 17c + 70\)[/tex] is [tex]\((c - 7)(c - 10)\)[/tex].
So the correct choice is:
- A. The answer is [tex]\((c - 7)(c - 10)\)[/tex].
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