Answer:
a = p * q
b = p * s + q * r
c = r * s
Step-by-step explanation:
In the trinomial ax² + bx + c
a is the coefficient of x²
b is the coefficient of x
c is the numerical term
∵ The trinomial is ax² + bx + c
∵ Its factors are (px + r) and (qx + s)
∴ ax² + bx + c = (px + r)(qx + s)
∵ (px + r)(qx + s) = (px)(qx) + (px)(s) + r(qx) + (r)(s)
∴ (px + r)(qx + s) = pqx² + (psx + qrx) + rs
∴ ax² + bx + c = pqx² + (ps + qr)x + rs
→ By comparing the two sides
∵ ax² = pqx² ⇒ divide both sides by x²
∴ a = pq
∵ bx = (ps + qr)x ⇒ Divide both sides by x
∴ b = ps + qr
∴ c = rs
∴ a = p * q
∴ b = p * s + q * r
∴ c = r * s
Ron now has a 6 by 13 chocolate bar and his goal is to split it into a 1 by 1 square for his family. This means that
<em />we need to look for the area!Although we don't stop there. We might be tempted to assume that the product of 6 and 13 is the answer, but we need to consider that, for the last two remaining squares, Ron will only need to break the bar once, therefore only having to break the chocolate bar one less than its area.
With that in mind, the answer will simply be
.
Answer: 77 times!If you still don't get it, think small! Notice that, for a chocolate bar 2 squares high and 2 squares long, you will only need to break it 3 times in order to have individual squares. The same thing applies for the problem.
Answer:
8a + 2b + c
Step-by-step explanation:
For subtracting polynomials we just need to operate subtracting the terms with same unknown. In our case we sum/subtract the terms that include a between them, the terms that have b between them and the therms with c between them. So we have:
(13a−4b+8c) - (5a−6b+7c) =?
13a−4b+8c - 5a+6b-7c = ?
Lets operate putting together terms with same unknown:
(13a - 5a) + (-4b +6b) + (8c-7c) =
8a + 2b + c
So, if we subtract 5a−6b+7c from 13a−4b+8c we get 8a + 2b + c
I hope it is clear!
Answer:
4(x - 3) and x + 3(x-2) - 6 are equivalent.
Step-by-step explanation:
4(x - 3) = 4x - 12
6x - 2(x - 3) = 6x - 2x + 6 = 4x + 6
x + 3(x - 2) - 6 = x + 3x - 6 - 6 = 4x - 12
Answer:
The set A ∩ B contain {6, 12}
Step-by-step explanation:
Given : set A = {3, 6, 9, 12} and set B = {2, 4, 6, 8, 10, 12}
We have to find A ∩ B
Consider the given sets
Set A = {3, 6, 9, 12}
and set B = {2, 4, 6, 8, 10, 12}
Since, A ∩ B includes those elements that are both in set A and set B.
Thus, the common elements of A and B are 6 and 12
So , the set A ∩ B contain {6, 12}