How do you factor #-x ^ { 2} + 10x + 7#?
2 Answers
Jul 5, 2018
Explanation:
This does not factor with integer coefficients: consider the quadratic determinant,
Solve the expression equal to zero to find the non-integer coefficients:
Quadratic formula:
So
Jul 5, 2018
Explanation:
#"using the method of "color(blue)"completing the square"#
#=-(x^2-10x-7)#
#=-(x^2+2(-5)x color(red)(+25)color(red)(-25)-7)#
#=-(x-5)^2+32#
#=32-(x-5)^2#
#"factor using "color(blue)"difference of squares"#
#•color(white)(x)a^2-b^2=(a-b)(a+b)#
#"with "a=4sqrt2" and "b=x-5#
#=(4sqrt2-(x-5))(4sqrt2+x-5)#
#=(4sqrt2-x+5)(4sqrt2+x-5)#