Answer:
The answer to your question is the letter a.
Step-by-step explanation:
Data
x² + 12x + c
If this trinomial is a perfect square trinomial, the third term must be half the second term divided by the square root of the first term, and to the second power.
-Get half the second term
12x/2 = 6x
-Divide by the square root of the first term
6x/x = 6
-Express the result to the second power
6² = 36
-Write the perfect square trinomial
(x² + 12x + 36) = (x + 6)²
Answer:
no
Step-by-step explanation:
Answer:
-3, 1, 4 are the x-intercepts
Step-by-step explanation:
The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).
In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.
__
For the given polynomial, we notice that the sum of the coefficients is zero:
1 -2 -11 +12 = 0
This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.
Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...
f(x) = (x -1)(x² -x -12)
We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...
f(x) = (x -1)(x -4)(x +3)
Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.
The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.
Answer:
x=62
Step-by-step explanation:
1. add + 25 to both sides because when you have a negative you have to add.
2. When you add 25 to 37 you get 62.
therefore 62 is the answer
Answer:
Since
x
is on the right side of the equation, switch the sides so it is on the left side of the equation.
x
2
−
2
x
+
3
=
G
(
x
)
Multiply
G
by
x
.
x
2
−
2
x
+
3
=
G
x
Subtract
G
x
from both sides of the equation.
x
2
−
2
x
+
3
−
G
x
=
0
Use the quadratic formula to find the solutions.
−
b
±
√
b
2
−
4
(
a
c
)
2
a
Substitute the values
a
=
1
,
b
=
−
2
−
G
, and
c
=
3
into the quadratic formula and solve for
x
.
−
(
−
2
−
G
)
±
√
(
−
2
−
G
)
2
−
4
⋅
(
1
⋅
3
)
2
⋅
1
Simplify.
Tap for more steps...
x
=
2
+
G
±
√
G
2
+
4
G
−
8
2
The final answer is the combination of both solutions.
x
=
2
+
G
+
√
G
2
+
4
G
−
8
2
x
=
2
+
G
−
√
G
2
+
4
G
−
8
2
Step-by-step explanation: