Question

Factor Completely:

2x^2−21x+49


2x^2+11x+15


2x^2−24x+64

Answer 1

(2x - 7)(x - 7)

(2x + 5)(x + 3)

(2x - 8)(x - 8)

These problems require you to deduce which numbers, when multiplied will equal the last number. Then, which of those two numbers should be eventually multiplied by 2. These problems are sort of intuitive once you done a couple, so do some!

Answer 2

1.
`2x^(2) - 21x + 49`

`2x^(2) - 14x - 7x + 49`

`2x(x) - 2x(7) - 7(x) + 7(7)`

`2x(x - 7) - 7(x - 7)`

`(2x - 7)(x - 7)`

2.
`2x^(2) + 11x + 15`

`2x^(2) + 6x + 5x + 15`

`2x(x) + 2x(3) + 5(x) + 5(3)`

`2x(x + 3) + 5(x + 3)`

`(2x + 5)(x + 3)`

3.
`2x^(2) - 24x + 64`

`2(x^(2)) - 2(12x) + 2(32)`

`2(x^(2) - 12x + 32)`

`2(x^(2) - 8x - 4x + 32)`

`2(x(x) - x(8) - 4(x) + 4(8)`

`2(x(x - 8) - 4(x - 8))`

`2(x - 4)(x - 8)`