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
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Chapter5: Factoring Polynomials
Section5.4: Multiplying Binomials Mentally
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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 = { }
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 integeri or (fraction)i; e.g.
2i would be entered as x
a solution of x =
-2i or x =
{-2i,2i}, while an answer of
%3D
x = -i or x = i would be entered as a = {-(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.)
%3D
The solution to the equation is a = {
}
Transcribed Image Text: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 integeri or (fraction)i; e.g. 2i would be entered as x a solution of x = -2i or x = {-2i,2i}, while an answer of %3D x = -i or x = i would be entered as a = {-(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.) %3D The solution to the equation is a = { }
Consider the equation r-13x+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?
A. Perfect Square Trinomial of a sum: a? + 2ab +b² = (a +b)²2
B. Perfect Square Trinomial of a difference: a? – 2ab+ b = (a – b)²
C. Difference of Squares: a2 - b = (a + b)(a – b)
D. Sum of Squares: a? + b? = (a + bi)(a – bi)
%3D
-
E. 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
Transcribed Image Text:Consider the equation r-13x+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? A. Perfect Square Trinomial of a sum: a? + 2ab +b² = (a +b)²2 B. Perfect Square Trinomial of a difference: a? – 2ab+ b = (a – b)² C. Difference of Squares: a2 - b = (a + b)(a – b) D. Sum of Squares: a? + b? = (a + bi)(a – bi) %3D - E. 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
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