Consider the equation ?2−13?+36=0 x 2 − 13 x + 36 = 0 , which sets a quadratic expression equal to zero. Part A Which, if any, special factoring pattern could be used in finding the factorization of the expression? Perfect Square Trinomial of a sum: ?2+2??+?2=(?+?)2 a 2 + 2 a b + b 2 = ( a + b ) 2 Perfect Square Trinomial of a difference: ?2−2??+?2=(?−?)2 a 2 − 2 a b + b 2 = ( a − b ) 2 Difference of Squares: ?2−?2=(?+?)(?−?) a 2 − b 2 = ( a + b ) ( a − b ) Sum of Squares: ?2+?2=(?+??)(?−??) a 2 + b 2 = ( a + b i ) ( a − b i ) None of these Enter the Letter of your choice here (just the letter, as a capital, no periods or spaces): Part B If the expression matches one of the patterns, what are the values for the ? a and the ? b used in that pattern? (For ? a , enter both the coefficient and variable
Consider the equation ?2−13?+36=0 x 2 − 13 x + 36 = 0 , which sets a quadratic expression equal to zero. Part A Which, if any, special factoring pattern could be used in finding the factorization of the expression? Perfect Square Trinomial of a sum: ?2+2??+?2=(?+?)2 a 2 + 2 a b + b 2 = ( a + b ) 2 Perfect Square Trinomial of a difference: ?2−2??+?2=(?−?)2 a 2 − 2 a b + b 2 = ( a − b ) 2 Difference of Squares: ?2−?2=(?+?)(?−?) a 2 − b 2 = ( a + b ) ( a − b ) Sum of Squares: ?2+?2=(?+??)(?−??) a 2 + b 2 = ( a + b i ) ( a − b i ) None of these Enter the Letter of your choice here (just the letter, as a capital, no periods or spaces): Part B If the expression matches one of the patterns, what are the values for the ? a and the ? b used in that pattern? (For ? a , enter both the coefficient and variable
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter5: Factoring Polynomials
Section5.4: Multiplying Binomials Mentally
Problem 14OE
Related questions
Question
Consider the equation
?2−13?+36=0
x
2
−
13
x
+
36
=
0
, which sets a quadratic expression equal to zero.
Part A
Which, if any, special factoring pattern could be used in finding the factorization of the expression?
Perfect Square Trinomial of a sum:
?2+2??+?2=(?+?)2
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
Perfect Square Trinomial of a difference:
?2−2??+?2=(?−?)2
a
2
−
2
a
b
+
b
2
=
(
a
−
b
)
2
Difference of Squares:
?2−?2=(?+?)(?−?)
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
Sum of Squares:
?2+?2=(?+??)(?−??)
a
2
+
b
2
=
(
a
+
b
i
)
(
a
−
b
i
)
None of these
Enter the Letter of your choice here (just the letter, as a capital, no periods or spaces):
Part B
If the expression matches one of the patterns, what are the values for the
?
a
and the
?
b
used in that pattern?
(For
?
a
, enter both the coefficient and variable; for
?
b
, enter the constant; if no pattern applies (answer E, above), enter "n/a" with no quotes)
The value for
?
a
is given by the expression .
The value for
?
b
is given by the constant .
Part C
What is the factored form of the expression? (enter without spaces)
The factored form of the expression is given by
Type the same factored expression again:
Part D
What is the solution to the equation?
(Enter as either a single number or as two numbers separated by a comma and with no spaces. Solutions with imaginary numbers should be entered as integer
?
i
or (fraction)
?
i
; e.g. a solution of
?=−2?
x
=
−
2
i
or
?=2?
x
=
2
i
would be entered as
?={
x
=
{
-2i,2i
}
}
, while an answer of
?=−12?
x
=
−
1
2
i
or
?=12
x
=
1
2
i would be entered as
?={
x
=
{
-(1/2)i,(1/2)i
}
}
. Note the use of parentheses, that the sign is outside of and in front of them, and that the i is outside of and after them and that there are no spaces.)
The solution to the equation is
?={
x
=
{
}
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