Come valuti # 2x ^ 2 + 5x-3 #?

The standard form of the #color(blue)"quadratic function"# is.

#y=ax^2+bx+c#

To factorise the function.

• consider the factors of the product ac which sum to give b

#"for "2x^2+5x-3#

#a=2, b=5" and "c=-3#

#rArrac=2xx-3=-6#

#"the required factors of -6 are "+6" and "-1#

#"Since " 6xx-1=-6" and " +6-1=+5#

#"now express " 2x^2+5x-3" as"#

#2x^2color(red)(+6x-x)-3#

Factorise by 'grouping'

#rArr2x(x+3)-1(x+3)#

Take out #color(blue)"common factor " "of " (x+3)#

#rArr(x+3)(2x-1)larr" in factorised form"#