Answer:
x² – x – 12 = (x – 4)(x + 3)
Step-by-step explanation:
Identify two numbers that add to -1 and multiply to -12, let's call them p and q.
So ax² + bx + c = (x + p)(x + q)
pq = c
p + q = b.
It is easier to find these numbers by finding factors of -12.
This can be done by splitting the number up until all the numbers are prime.
-12 → 6 × -2 or -6 × 2 → -(3 × 2 × 2)
There can only be two numbers so the only options we have are 6 and -2, -6 and 2, 3, and -4, or -3 and 4.
We can eliminate them by adding them up.
6 + -2 = 4 ≠ -1 so that can't be it.
-6 + 2 = -4 ≠ -1 so that can't be it either.
-3 + 4 = 1 ≠ -1
therefore p and q are 3 and -4 because 3 + -4 = -1.
so x² – x – 12 = (x – 4)(x + 3)
p = -4, and q = 3.
(x – 4)(x + 3) = x(x + 3) – 4(x + 3) = x² + 3x – 4x + 12 = x² – x – 12
Answer: ._.
Step-by-step explanation:
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Answer:
a) QT = 8
b) QN = 24
c) QP = 23
d) MP = 46
e) RT = 6
f) TP = 12
Step-by-step explanation:
Find the diagram attached
If T is the centroid of<MNP, then the following are true;
TN = 2QT
Given TN = 16
16 = 2QT
QT = 16/2
QT = 8
QN = QT + TN
QN = 8 + 16
QN = 24
MQ + QP = MP and MQ = QP
If MQ = 23
QP = 23
Recall that MP = MQ + QP
MP = MQ + MQ
MP = 2MQ
MP = 2(23)
MP = 46
Similarly, TP = 2RT
RT = TP/2
Also RP = RT + TP
RP = RT + 2 RT
RP = 3RT
18 = 3RT
RT = 18/3
RT = 6
Recall that TP = 2RT
TP = 2(6)
TP = 12
