Question

x²+3x+2=
x²+5x+6=
x²+7x+12=
x²+7x+10=
x²+9x+20=
x²+8x+15=
x²+12x+35=
x²-3x+2=
x²-6x+8=
x²-5x+6=
x²-4x-5=
2x²-7=
x²-36=
4x²-25=

Answer 1

$a)x^2+3x+2=x^2+x+2x+2=x(x+1)+2(x+1)=(x+1)(x+2) \\ b)x^2+5x+6=x^2+2x+3x+6=x(x+2)+3(x+2)= \\ =(x+2)(x+3) \\ c)x^2+7x+12=x^2+4x+3x+12= x(x+4)+3(x+4)= \\ =(x+4)(x+3) \\ d)x^2+7x+10=x^2+5x+2x+10=x(x+5)+2(x+5)= \\ =(x+5)(x+2) \\ e)x^2+9x+20=x^2+4x+5x+20=x(x+4)+5(x+4)= \\ =(x+4)(x+5)$
$f)x^2+8x+15=x^2+5x+3x+15=x(x+5)+3(x+5)= \\ =(x+5)(x+3) \\ g)x^2+12x+35=x^2+5x+7x+35=x(x+5)+7(x+5)= \\ =(x+5)(x+7) \\ h)x^2-3x+2=x^2-2x-x+2=x(x-2)-(x-2)=(x-2)(x-1) \\ i)x^2-6x+8=x^2-4x-2x+8=x(x-4)-2(x-4)= \\ =(x-4)(x-2) \\ j)x^2-5x+6=x^2-3x-2x+6=x(x-3)-2(x-3)= \\ =(x-3)(x-2)$
$k)x^2-4x-5=x^2-5x+x-5=x(x-5)+(x-5)= \\ =(x-5)(x+1) \\ l)2x^2-7=( \sqrt{2} x- \sqrt{7} )( \sqrt{2} x+ \sqrt{7} ) \\ m)x^2-36=(x-6)(x+6) \\ n)4x^2-25=(2x-5)(2x+5)$

Answer 2

1. X²+3x+2=x²+x+2x+2=x(x+1)+2(x+1)=(x+1)(x+2)

 2. x²+5x+6=x²+2x+3x+6=x(x+2)+3(x+2)=(x+2)(x+3)

3.  x²+7x+12=x²+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)

4. x²+7x+10=x²+5x+2x+10=x(x+5)+2(x+5)=(x+2)(x+5)

5. x²+9x+20=x²+4x+5x+20=x(x+4)+5(x+4)=(x+4)(x+5)

6. x²+8x+15=x²+5x+3x+15=x(x+5)+3(x+5)=(x+3)(x+5)

7. x²+12x+35=x²+5x+7x+10=x(x+5)(7(x+5)=(x+7)(x+5)

8. x²-3x+2=x²-2x-x+2=x(x-2)+7(x-2)=(x+7)(x-2)

9. x²-6x+8=x²-4x-2x+8=x(x-4)-2(x-4)=(x-2)(x-4)

10.x²-5x+6=x²-3x-3x+6=x(x-3)-2(x-3)=(x-2)(x-3)

11. x²-4x-5=x²-5x+x-5=x(x-5)+(x-5)=(x-5)(x+1)

12. 2x²-7=(x√2-√7)(x√2+√7)

13. x²-36=(x-6)(x+6)

14. 4x²-25= (2x-5)(2x+5)