Discover how IDNLearn.com can help you learn and grow with its extensive Q&A platform. Discover detailed and accurate answers to your questions from our knowledgeable and dedicated community members.
Sagot :
To factor the quadratic expression [tex]\(2x^2 - 16x + 30\)[/tex] completely, we will proceed through the following steps:
1. Identify a common factor if possible:
The given expression is [tex]\(2x^2 - 16x + 30\)[/tex].
- Here, we notice that each term in the quadratic expression contains a factor of 2. So, we can start by factoring out 2 from the entire expression.
[tex]\[ 2(x^2 - 8x + 15) \][/tex]
2. Factor the quadratic expression inside the parentheses:
Now, we need to focus on factoring [tex]\(x^2 - 8x + 15\)[/tex]. We look for two numbers that multiply to give the constant term (15) and add to give the coefficient of the middle term (-8).
- List down the pair of factors of 15 and find the pair that adds up to -8:
- [tex]\(1 \times 15 = 15\)[/tex] and [tex]\(1 + 15 = 16\)[/tex]
- [tex]\(3 \times 5 = 15\)[/tex] and [tex]\(3 + 5 = 8\)[/tex]
- Since we need the sum to be negative, consider the factors with negative signs: [tex]\((-3) \times (-5) = 15\)[/tex] and [tex]\((-3) + (-5) = -8\)[/tex].
Hence, the two numbers are -3 and -5.
3. Write the factored form:
Utilizing the numbers we found, we can now factor the quadratic expression:
[tex]\[ x^2 - 8x + 15 = (x - 3)(x - 5) \][/tex]
4. Combine with the factor we initially factored out:
Now, we multiply back the factor of 2 that we had factored out earlier:
[tex]\[ 2(x - 3)(x - 5) \][/tex]
Thus, the completely factored form of the given quadratic expression [tex]\(2x^2 - 16x + 30\)[/tex] is:
[tex]\[ 2(x - 3)(x - 5) \][/tex]
Therefore, the correct answer is:
[tex]\[ 2(x - 5)(x - 3) \][/tex]
1. Identify a common factor if possible:
The given expression is [tex]\(2x^2 - 16x + 30\)[/tex].
- Here, we notice that each term in the quadratic expression contains a factor of 2. So, we can start by factoring out 2 from the entire expression.
[tex]\[ 2(x^2 - 8x + 15) \][/tex]
2. Factor the quadratic expression inside the parentheses:
Now, we need to focus on factoring [tex]\(x^2 - 8x + 15\)[/tex]. We look for two numbers that multiply to give the constant term (15) and add to give the coefficient of the middle term (-8).
- List down the pair of factors of 15 and find the pair that adds up to -8:
- [tex]\(1 \times 15 = 15\)[/tex] and [tex]\(1 + 15 = 16\)[/tex]
- [tex]\(3 \times 5 = 15\)[/tex] and [tex]\(3 + 5 = 8\)[/tex]
- Since we need the sum to be negative, consider the factors with negative signs: [tex]\((-3) \times (-5) = 15\)[/tex] and [tex]\((-3) + (-5) = -8\)[/tex].
Hence, the two numbers are -3 and -5.
3. Write the factored form:
Utilizing the numbers we found, we can now factor the quadratic expression:
[tex]\[ x^2 - 8x + 15 = (x - 3)(x - 5) \][/tex]
4. Combine with the factor we initially factored out:
Now, we multiply back the factor of 2 that we had factored out earlier:
[tex]\[ 2(x - 3)(x - 5) \][/tex]
Thus, the completely factored form of the given quadratic expression [tex]\(2x^2 - 16x + 30\)[/tex] is:
[tex]\[ 2(x - 3)(x - 5) \][/tex]
Therefore, the correct answer is:
[tex]\[ 2(x - 5)(x - 3) \][/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.