Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To factor the given trinomial [tex]\(x^2 - 14x + 45\)[/tex], let's follow a systematic approach:
1. Identify the coefficients: For the quadratic trinomial [tex]\(ax^2 + bx + c\)[/tex], we have:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = -14 \)[/tex]
- [tex]\( c = 45 \)[/tex]
2. Find two numbers that multiply to [tex]\(ac\)[/tex] and add to [tex]\(b\)[/tex]:
- We need two numbers that multiply to [tex]\(a \cdot c = 1 \cdot 45 = 45\)[/tex] and add to [tex]\(b = -14\)[/tex].
3. List pairs of factors of 45:
- [tex]\(1 \times 45\)[/tex]
- [tex]\(3 \times 15\)[/tex]
- [tex]\(5 \times 9\)[/tex]
4. Determine which pair sums to -14:
- Check if [tex]\(1 + 45 = 46\)[/tex]
- Check if [tex]\(3 + 15 = 18\)[/tex]
- Check if [tex]\(5 + 9 = 14\)[/tex], and we find that [tex]\(9 + 5 = 14\)[/tex]. Now, since [tex]\(b\)[/tex] is negative, we will consider [tex]\(-9\)[/tex] and [tex]\(-5\)[/tex].
5. Write the factors:
- The numbers that match our requirements are [tex]\(-9\)[/tex] and [tex]\(-5\)[/tex].
6. Factor the trinomial:
- Thus, [tex]\(x^2 - 14x + 45\)[/tex] can be written as [tex]\((x - 9)(x - 5)\)[/tex].
Therefore, the trinomial [tex]\(x^2 - 14x + 45\)[/tex] factors to:
[tex]\[ (x - 9)(x - 5) \][/tex]
Let's identify the correct multiple-choice answer:
A. [tex]\((x - 5)(x - 9)\)[/tex]
B. [tex]\((x - 5)(x + 9)\)[/tex]
C. [tex]\((x - 3)(x + 15)\)[/tex]
D. [tex]\((x - 3)(x - 15)\)[/tex]
Given that multiplication is commutative, [tex]\( (x - 9)(x - 5) \)[/tex] is the same as [tex]\( (x - 5)(x - 9) \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{A} \][/tex]
1. Identify the coefficients: For the quadratic trinomial [tex]\(ax^2 + bx + c\)[/tex], we have:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = -14 \)[/tex]
- [tex]\( c = 45 \)[/tex]
2. Find two numbers that multiply to [tex]\(ac\)[/tex] and add to [tex]\(b\)[/tex]:
- We need two numbers that multiply to [tex]\(a \cdot c = 1 \cdot 45 = 45\)[/tex] and add to [tex]\(b = -14\)[/tex].
3. List pairs of factors of 45:
- [tex]\(1 \times 45\)[/tex]
- [tex]\(3 \times 15\)[/tex]
- [tex]\(5 \times 9\)[/tex]
4. Determine which pair sums to -14:
- Check if [tex]\(1 + 45 = 46\)[/tex]
- Check if [tex]\(3 + 15 = 18\)[/tex]
- Check if [tex]\(5 + 9 = 14\)[/tex], and we find that [tex]\(9 + 5 = 14\)[/tex]. Now, since [tex]\(b\)[/tex] is negative, we will consider [tex]\(-9\)[/tex] and [tex]\(-5\)[/tex].
5. Write the factors:
- The numbers that match our requirements are [tex]\(-9\)[/tex] and [tex]\(-5\)[/tex].
6. Factor the trinomial:
- Thus, [tex]\(x^2 - 14x + 45\)[/tex] can be written as [tex]\((x - 9)(x - 5)\)[/tex].
Therefore, the trinomial [tex]\(x^2 - 14x + 45\)[/tex] factors to:
[tex]\[ (x - 9)(x - 5) \][/tex]
Let's identify the correct multiple-choice answer:
A. [tex]\((x - 5)(x - 9)\)[/tex]
B. [tex]\((x - 5)(x + 9)\)[/tex]
C. [tex]\((x - 3)(x + 15)\)[/tex]
D. [tex]\((x - 3)(x - 15)\)[/tex]
Given that multiplication is commutative, [tex]\( (x - 9)(x - 5) \)[/tex] is the same as [tex]\( (x - 5)(x - 9) \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{A} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.