Mrs campbell gave her algebra 1 students a list of trinomials to factor for homework. which of these can be factored into two binomials A. x^2+3x+2B. x^2+4x+5C. x^2+5x+7D. x^2+6x+10

Accepted Solution

Answer:AStep-by-step explanation:A trinomial can be factored into two binomials, when the discriminant of the trinomial is greater than or equal to 0. The discriminant for trinomial [tex]ax^2+bx+c[/tex] is he expression [tex]D=b^2-4ac.[/tex]Check all options:A. [tex]D=3^2-4\cdot 1\cdot 2=9-8=1,[/tex]then[tex]x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}=\dfrac{-3\pm\sqrt{1}}{2}=-2,\ -1.[/tex]Thus,[tex]x^2+3x+2=(x-x_1)(x-x_2)=(x-(-2))(x-(-1))=(x+2)(x+1).[/tex]B.[tex]D=4^2-4\cdot 1\cdot 5=16-20=-4<0,[/tex]so this trinomial cannot be factored.C.[tex]D=5^2-4\cdot 1\cdot 7=25-28=-3<0,[/tex]so this trinomial cannot be factored.D.[tex]D=6^2-4\cdot 1\cdot 10=36-40=-4<0,[/tex]so this trinomial cannot be factored.