Question

Factor 1-3

Answer 1

1. $x^2 - 14x + 45$

You need two numbers that multiply to 45 and add to -14.
Since the numbers must multiply to a positive number, 45, they must both be positive or both be negative. Since they must add to -14, they must both be negative.

$-9 \times (-5) = 45$
$-9 + (-5) = -14$

The numbers are -9 and -5.

$x^2 - 14x + 45 = (x - 9)(x - 5)$

2. $x^2 - 15x + 36$

You need two numbers that multiply to 36 and add to -15.
Since the numbers must multiply to a positive number, 36, they must both be positive or both be negative. Since they must add to -15, they must both be negative.

$-12 \times (-3) = 36$
$-12 + (-3) = -15$

The numbers are -12 and -3.

$x^2 - 15x + 36 = (x - 12)(x - 3)$

3. $x^2 - 7x - 44$

You need two numbers that multiply to -44 and add to -7.
Since the numbers must multiply to a negative number, -44, one number is positive, and one number is negative.

$-11 \times 4 = -44$
$-11 + 4 = -7$

The numbers are -11 and 4.

$x^2 - 7x - 44 = (x - 11)(x + 4)$

Solve by factoring:
1. $x^2 - 15x + 50 = 0$

$(x - 10)(x - 5) = 0$

$x - 10 = 0$   or   $x - 5 = 0$

$x = 10$   or   $x = 5$

2. $x^2 = -2x + 15$

$x^2 + 2x - 15 = 0$

$(x - 3)(x + 5) = 0$

$x - 3 = 0$   or   $x + 5 = 0$

$x = 3$   or   $x + 5 = 0$

$x = 3$   or   $x = -5$