From personal advice to professional guidance, IDNLearn.com has the answers you seek. Get accurate and detailed answers to your questions from our knowledgeable and dedicated community members.
Sagot :
Sure, let's break down the process of factoring the trinomial [tex]\( 12v^2 + 11v - 15 \)[/tex].
First, identify the coefficients in the trinomial [tex]\( 12v^2 + 11v - 15 \)[/tex]:
- The coefficient of [tex]\( v^2 \)[/tex] term (a) is 12.
- The coefficient of [tex]\( v \)[/tex] term (b) is 11.
- The constant term (c) is -15.
We want to factor this into the form [tex]\( (pv + q)(rv + s) \)[/tex]. To do this, we need to find numbers p, q, r, and s such that:
1. [tex]\( pr = 12 \)[/tex]
2. [tex]\( qs = -15 \)[/tex]
3. [tex]\( ps + qr = 11 \)[/tex]
From the calculations, we obtain the solution as follows:
1. The factors of 12 are 1, 2, 3, 4, and 6.
2. The factors of -15 are 1, -1, 3, -3, 5, and -5.
By trial and error (which might involve several steps if solving manually):
- We noticed that the correct pairs are [tex]\( p = 3 \)[/tex], [tex]\( q = 5 \)[/tex], [tex]\( r = 4 \)[/tex], and [tex]\( s = -3 \)[/tex].
Putting these together, the factored form of [tex]\( 12v^2 + 11v - 15 \)[/tex] is:
[tex]\[ (3v + 5)(4v - 3). \][/tex]
Therefore, the correct numbers to fill in the blanks are:
[tex]\[ (3v + 5)(4v - 3). \][/tex]
First, identify the coefficients in the trinomial [tex]\( 12v^2 + 11v - 15 \)[/tex]:
- The coefficient of [tex]\( v^2 \)[/tex] term (a) is 12.
- The coefficient of [tex]\( v \)[/tex] term (b) is 11.
- The constant term (c) is -15.
We want to factor this into the form [tex]\( (pv + q)(rv + s) \)[/tex]. To do this, we need to find numbers p, q, r, and s such that:
1. [tex]\( pr = 12 \)[/tex]
2. [tex]\( qs = -15 \)[/tex]
3. [tex]\( ps + qr = 11 \)[/tex]
From the calculations, we obtain the solution as follows:
1. The factors of 12 are 1, 2, 3, 4, and 6.
2. The factors of -15 are 1, -1, 3, -3, 5, and -5.
By trial and error (which might involve several steps if solving manually):
- We noticed that the correct pairs are [tex]\( p = 3 \)[/tex], [tex]\( q = 5 \)[/tex], [tex]\( r = 4 \)[/tex], and [tex]\( s = -3 \)[/tex].
Putting these together, the factored form of [tex]\( 12v^2 + 11v - 15 \)[/tex] is:
[tex]\[ (3v + 5)(4v - 3). \][/tex]
Therefore, the correct numbers to fill in the blanks are:
[tex]\[ (3v + 5)(4v - 3). \][/tex]
To factor the trinomial 12v + 11v - 15, we need to find two binomials (av + b) (cu + d) such that their product is the given trinomial.
1. First, consider the product of the leading coefficient (12) and the constant term (-15), which is -180.
2. We need to find two numbers that multiply to —180 and add up to the middle coefficient (11).
3. The numbers that satisfy these conditions are 20 and -9, since 20 × (-9) = -180
and 20 + (-9) = 11
4. Rewrite the middle term using these numbers:
1202 + 20v - 90 - 15
5. Factor by grouping:
• Group the first two terms and the last two terms:
(1202+200)+(-90-15).
• Factor out the greatest common factor from each group:
40(30 + 5) - 3(30 + 5)
6. Notice that (3v + 5) is a common factor:
(40=3)(30+5)
Thus, the factors of 1202 + 11v - 15 are (40 - 3) (30 + 5).
1. First, consider the product of the leading coefficient (12) and the constant term (-15), which is -180.
2. We need to find two numbers that multiply to —180 and add up to the middle coefficient (11).
3. The numbers that satisfy these conditions are 20 and -9, since 20 × (-9) = -180
and 20 + (-9) = 11
4. Rewrite the middle term using these numbers:
1202 + 20v - 90 - 15
5. Factor by grouping:
• Group the first two terms and the last two terms:
(1202+200)+(-90-15).
• Factor out the greatest common factor from each group:
40(30 + 5) - 3(30 + 5)
6. Notice that (3v + 5) is a common factor:
(40=3)(30+5)
Thus, the factors of 1202 + 11v - 15 are (40 - 3) (30 + 5).
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. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.