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Leya [2.2K]
2 years ago
10

X^2-x-12 factor completely

Mathematics
1 answer:
steposvetlana [31]2 years ago
5 0
Use the sum-product pattern

2
−

−
1
2
x
2
−
x
−
12
x2−x−12

2
+
3

−
4

−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12
2
Common factor from the two pairs

2
+
3

−
4

−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12

(

+
3
)
−
4
(

+
3
)
x
(
x
+
3
)
−
4
(
x
+
3
)
x(x+3)−4(x+3)
3
Rewrite in factored form

(

+
3
)
−
4(+3)x
(x+3)−4(x+3)
x(x+3)−4(x+3)
(−4)(+3)
(x−4)(x+3)
(x−4)(x+3)
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Answer:

1. 474

2. 397

Step-by-step explanation:

1. If the three-digit number is xyz, then y = z + 3.

When rounded to the nearest ten and reduced by 320, the result is 150.  150 + 320 = 470, so x = 4.  y = 6 if z ≥ 5, and y = 7 if z < 5.

So the number is either 463 or 474.  463 doesn't round to 470, so the answer is 474.

2. If the three-digit number is xyz, then z = x + 4.  y is the largest of the three digits; since all the digits are odd, y is either 5, 7, or 9.  So z is either 5 or 7, and x is either 1 or 3.

When rounded to the nearest hundred and reduced by 100, the result is 300.  100 + 300 = 400, and y > 5, so xyz is rounded up to 400, which means x = 3.  So z = 7 and y = 9.

The answer is 397.

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