Answer:
1) Option 3
2) Option 3
3) Option 3
4) Option 1
5) Option 2
6) Option 3
7) Option 1
Step-by-step explanation:
1) [tex]y = x^2 + 4x + 3[/tex]
Lets split the middle term.
[tex]=> y = x^2 + 3x + x + 3[/tex]
[tex]=> y = x(x+3) + 1(x + 3)[/tex]
[tex]=> y = (x+1)(x+3)[/tex]
∴ [tex]x = -3 , -1[/tex]
2) [tex]y = 8x^2 - 22x + 5[/tex]
Lets split the middle term.
[tex]=> y = 8x^2 - 20x - 2x + 5[/tex]
[tex]=> y = 4x(2x - 5) - 1(2x - 5)[/tex]
[tex]=> y = (2x - 5)(4x - 1)[/tex]
∴ [tex]x =\frac{1}{4} , \frac{5}{2}[/tex]
3) [tex]y = x^2 - 5x[/tex]
[tex]=> y = x(x - 5)[/tex]
∴ [tex]x = 0 , 5[/tex]
4) [tex]y = 12x^2 + 18x[/tex]
[tex]=> y = 6x(2x + 3)[/tex]
∴ [tex]x = \frac{-3}{2} , 0[/tex]
5) [tex]y = x^2 - 7x + 12[/tex]
Lets split the middle term.
[tex]=> y = x^2 -3x - 4x + 12[/tex]
[tex]=> y = x(x - 3) - 4(x - 3)[/tex]
[tex]=> y = (x - 3)(x - 4)[/tex]
∴ [tex]x = 3,4[/tex]
6) [tex]y = 3x^2 + 10x + 8[/tex]
Lets split the middle term.
[tex]=> y = 3x^2 + 6x + 4x + 8[/tex]
[tex]=> y = 3x(x + 2) + 4(x + 2)[/tex]
[tex]=> y = (x + 2)(3x + 4)[/tex]
∴ [tex]x = -2 , \frac{-4}{3}[/tex]
7) [tex]y = x^2 - 4x - 45[/tex]
Lets split the middle term.
[tex]=> y = x^2 - 9x + 5x - 45[/tex]
[tex]=> y = x(x - 9) + 5(x - 9)[/tex]
[tex]=> y = (x - 9)(x + 5)[/tex]
∴ [tex]x = -5 , 9[/tex]
