Solve by Factoring

Solve Quadratic Equation by Factoring

By Henry Phan

​How to solve for x by factoring: ax² + bx + c =0

• ​Exist two numbers (m and n) such that the product of m and n is equal the product of a and c {m × n = (a)(c)}, and the sum of m and n is equal to b {m + n = b}

• ​Then the factor form by rewriting as:

• (x - m/a)(x - n/a) = 0". Then factor them out.

​x² – 3x – 10 = 0

​x² – 3x – 10 = 0

​(x + m/a)(x + n/a)

​{x₁ = _____, x₂ = _____}

​m/a = ___

​n/a = ___

​(x + ______)(x + ______)

​a =

b =

c =​

​x² + x – 30 = 0

​x² – 3x – 10 = 0

​(x + m/a)(x + n/a)

​{x₁ = _____, x₂ = _____}

​m/a = ___

​n/a = ___

​(x + ______)(x + ______)

​a =

b =

c =​

​3x² + 7x – 6 = 0

​x² – 3x – 10 = 0

​(x + m/a)(x + n/a)

​{x₁ = _____, x₂ = _____}

​m/a = ___

​n/a = ___

​(x + ______)(x + ______)

​a =

b =

c =​

​2x² - x – 6 = 0

​x² – 3x – 10 = 0

​(x + m/a)(x + n/a)

​{x₁ = _____, x₂ = _____}

​m/a = ___

​n/a = ___

​(x + ______)(x + ______)

​a =

b =

c =​

Multiple Choice

Solve x by factoring: x² + 4x - 21

• (x - 7)(x -3)

  then

  x = 7

  x = 3

• (x + 7)(x + 3)

  then

  x = -7

  x = -3

• (x -7)(x +3)

  then

  x = 7

  x = -3

• (x + 7)(x -3)

  then

  x = -7

  x = 3

Multiple Choice

Solve x by factoring: x² - 2x - 63

• (x - 3)(x + 21)

  then

  x = 3

  x = -21

• (x + 3)(x - 21)

  then

  x = -3

  x = 21

• (x -7)(x +9)

  then

  x = 7

  x = -3

• (x + 7)(x -9)

  then

  x = -7

  x = 3

Multiple Choice

Solve x by factoring: 12x² - 11x +2

• (x - 2/12)(x - 12/12)

  then

  x = 1/6

  x = 1

• (x - 3/12)(x - 8/12)

  then

  x = 1/4

  x = 2/3

• (x - 4/12)(x - 6/12)

  then

  x = 1/3

  x = 1/2

• (x - 1/12)(x -2)

  then

  x = 1/12

  x = 2

Multiple Choice

Solve x by factoring: 6x² + 13x + 5

• (x - 2/6)(x + 15/6)

  then

  x = 1/3

  x = -5/2

• (x + 3/6)(x + 10/6)

  then

  x = -1/2

  x = -5/3

• (x - 3/6)(x - 10/6)

  then

  x = 1/2

  x = 5/3

• (x + 5/6)(x + 6/6)

  then

  x = -5/6

  x = -1