Question

Honestly if anyone could help be understand how to solve these by factoring, that would be great! Thank you!

Answer 1

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) $y = x^2 + 4x + 3$

Lets split the middle term.

$=> y = x^2 + 3x + x + 3$

$=> y = x(x+3) + 1(x + 3)$

$=> y = (x+1)(x+3)$

∴ $x = -3 , -1$

2) $y = 8x^2 - 22x + 5$

Lets split the middle term.

$=> y = 8x^2 - 20x - 2x + 5$

$=> y = 4x(2x - 5) - 1(2x - 5)$

$=> y = (2x - 5)(4x - 1)$

∴ $x =\frac{1}{4} , \frac{5}{2}$

3) $y = x^2 - 5x$

$=> y = x(x - 5)$

∴ $x = 0 , 5$

4) $y = 12x^2 + 18x$

$=> y = 6x(2x + 3)$

∴ $x = \frac{-3}{2} , 0$

5) $y = x^2 - 7x + 12$

Lets split the middle term.

$=> y = x^2 -3x - 4x + 12$

$=> y = x(x - 3) - 4(x - 3)$

$=> y = (x - 3)(x - 4)$

∴ $x = 3,4$

6) $y = 3x^2 + 10x + 8$

Lets split the middle term.

$=> y = 3x^2 + 6x + 4x + 8$

$=> y = 3x(x + 2) + 4(x + 2)$

$=> y = (x + 2)(3x + 4)$

∴ $x = -2 , \frac{-4}{3}$

7) $y = x^2 - 4x - 45$

Lets split the middle term.

$=> y = x^2 - 9x + 5x - 45$

$=> y = x(x - 9) + 5(x - 9)$

$=> y = (x - 9)(x + 5)$

∴ $x = -5 , 9$