x^(2) - 13x + 36 Factors to
( x - 9)(x - 4)
x^(2) + 13x + 36 Factors to ( x + 9)(x + 4) When learning factoring. ;- #1 ; If the coefficient of x^(2) is '1' , as in this case. Then #2 ; Write down all the factors of 36, which are ,1,36 ' 2,18 ' 3,12 ' 4,9 ' 6,6 ; #3 ; Out of these pairs of factors, select a pair that add/subtract to '13'. #5, They are 4,9 ; 4 + 9 = 13 #6 ; Since the quadratic eq;m has positive (+) signs , then all the signs in the brackets are positive(+). When the coefficient of x^(2) is > 1, and/or the signs are different , then different techniques come into play.
(x + 4)(x + 9)
(x + 9)(x + 4)
x^2 - 13x + 36 = 0 Factor: (X-9)(X-4) = 0 X = 9 X = 4
To factor the expression (x^2 + 13x + 36), you need to find two numbers that multiply to 36 (the constant term) and add up to 13 (the coefficient of the linear term). The numbers 9 and 4 meet these criteria, as (9 \times 4 = 36) and (9 + 4 = 13). Therefore, you can factor the expression as ((x + 9)(x + 4)).
x2 + 13x + 36 = 0 so (x+4)(x+9) = 0 so that x = -4 or x = -9
(x + 12)(x - 3)
x2-13x+36=(x-9)(x-4)=0 x=9 or x=4
(x - 9)(x - 4)
2x^(2) + 72 Factors to 2( x^(2) + 36) s(x^(2) + 6^(2)) Does NOT factor. NB Remember . two squared terms with a positive(+) between them does NOT factor!!!! However, two squared terms with a negative(-) between DOES factor . e.g. x^(2) + 6^(2) Does NOT factor x^(2) - 6^(2) factors to ( x - 6)( x + 6 ) Note the different signs. Similarly 8^(2) + 6^(2) does NOT factor 8^(2) - 6^(2) factors to (8 - 6)(8 + 6) Or using the ~Pythagorean Equation. h^(2) = a^(2) + b^(2) Does NOT factors However, a^(2) = h^(2) - b^(2) factors to a^(2) = (h - b)(h + b) .
(x -3)(2x2 + 3x - 4)
(6x - 1)(6x - 1)