Find expert answers and community support for all your questions on IDNLearn.com. Join our knowledgeable community and get detailed, reliable answers to all your questions.
Sagot :
To factor the trinomial [tex]\( x^2 - x - 20 \)[/tex], we need to express it as the product of two binomials of the form [tex]\((x + a)(x + b)\)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants.
1. Identify the coefficients:
The trinomial is given as [tex]\( x^2 - x - 20 \)[/tex], so:
- The coefficient of [tex]\( x^2 \)[/tex] is [tex]\( 1 \)[/tex].
- The coefficient of [tex]\( x \)[/tex] is [tex]\( -1 \)[/tex].
- The constant term is [tex]\( -20 \)[/tex].
2. Find two numbers that multiply to the constant term and add up to the coefficient of [tex]\( x \)[/tex]:
We need two numbers [tex]\( a \)[/tex] and [tex]\( b \)[/tex] such that:
- [tex]\( a \cdot b = -20 \)[/tex]
- [tex]\( a + b = -1 \)[/tex]
By examining the factor pairs of [tex]\(-20\)[/tex]:
- [tex]\((-1, 20)\)[/tex]
- [tex]\((1, -20)\)[/tex]
- [tex]\((-2, 10)\)[/tex]
- [tex]\((2, -10)\)[/tex]
- [tex]\((-4, 5)\)[/tex]
- [tex]\((4, -5)\)[/tex]
The pair that adds up to [tex]\(-1\)[/tex] is [tex]\((4, -5)\)[/tex].
3. Write the binomials:
Since [tex]\( a = 4 \)[/tex] and [tex]\( b = -5 \)[/tex], we can write the trinomial as the product of two binomials:
[tex]\[ (x + 4)(x - 5) \][/tex]
Therefore, the trinomial [tex]\( x^2 - x - 20 \)[/tex] factors to:
[tex]\[ (x - 5)(x + 4) \][/tex]
So, the correct choice is:
A. [tex]\( x^2 - x - 20 = (x - 5)(x + 4) \)[/tex]
1. Identify the coefficients:
The trinomial is given as [tex]\( x^2 - x - 20 \)[/tex], so:
- The coefficient of [tex]\( x^2 \)[/tex] is [tex]\( 1 \)[/tex].
- The coefficient of [tex]\( x \)[/tex] is [tex]\( -1 \)[/tex].
- The constant term is [tex]\( -20 \)[/tex].
2. Find two numbers that multiply to the constant term and add up to the coefficient of [tex]\( x \)[/tex]:
We need two numbers [tex]\( a \)[/tex] and [tex]\( b \)[/tex] such that:
- [tex]\( a \cdot b = -20 \)[/tex]
- [tex]\( a + b = -1 \)[/tex]
By examining the factor pairs of [tex]\(-20\)[/tex]:
- [tex]\((-1, 20)\)[/tex]
- [tex]\((1, -20)\)[/tex]
- [tex]\((-2, 10)\)[/tex]
- [tex]\((2, -10)\)[/tex]
- [tex]\((-4, 5)\)[/tex]
- [tex]\((4, -5)\)[/tex]
The pair that adds up to [tex]\(-1\)[/tex] is [tex]\((4, -5)\)[/tex].
3. Write the binomials:
Since [tex]\( a = 4 \)[/tex] and [tex]\( b = -5 \)[/tex], we can write the trinomial as the product of two binomials:
[tex]\[ (x + 4)(x - 5) \][/tex]
Therefore, the trinomial [tex]\( x^2 - x - 20 \)[/tex] factors to:
[tex]\[ (x - 5)(x + 4) \][/tex]
So, the correct choice is:
A. [tex]\( x^2 - x - 20 = (x - 5)(x + 4) \)[/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.