1) The document discusses factoring quadratic equations of the form ax^2 + bx + c = 0. 2) It provides three examples of factoring and solving quadratic equations: 2x^2 - x - 6 = 0, 10x^2 + 3x - 1 = 0, and 3x^2 - x - 2 = 0. 3) The method involves writing the equation in standard form, factoring the left side into two binomials, setting each binomial equal to zero using the zero product property, and solving for the roots.

1. FACTORING

2. Factoring Quadratic Equation ax2
+ bx + c = 0, where a>1.

3. Example 1. Solve 2x2 – x – 6 = 0
Steps Solution
1. Write in standard form. 2x2 – x – 6 = 0
2. Factor the quadratic expression on the
left side of the equation using the
following process.
a. Multiply (a) (c)
b. Find the factors of -12 that gives you
the sum of the value of b which is -1.
c. Copy the expression and replace the
middle term as the value obtain in step b.
d. Factor using the groupings
(2).(-6) = -12
-12 = (-4).(3)
2x2 – x – 6 = 0
2x2 – 4x + 3x - 6 = 0
(2x2 – 4x) + (3x – 6) = 0
2x (x – 2) + 3 (x – 2) = 0
(2x + 3) (x – 2) = 0

4. 3. Use the Zero Product Property. (2x + 3) (x – 2) = 0
So, (2x + 3 ) = 0 and (x – 2) = 0
4. Solve for the roots 2x + 3 = 0 and x – 2 = 0
2x = -3 and x = 2
𝟐𝒙
𝟐
=
−𝟑
𝟐
x = -
𝟑
𝟐
Therefore, the roots of x2 + 3x + 2 = 0 are x = -1 and x = -2.

5. Example 2. Solve for the roots of 10x2 + 3x - 1 = 0
Steps Solution
1.Write in standard form 10x2 + 3x – 1 = 0
2. Factor the expression on the left side.
a. Multiply (a). (c)
b. Factors of -10 that gives the sum of b
which is 3.
c. Copy the expression and replace the
middle term.
d. Factor using groupings.
(10) . (-1) = -10
(3)= (5) . (-2)
10x2 + 3x – 1 = 0
10x2 + 5x – 2x – 1 = 0
(10x2 + 5x) – (2x – 1) = 0
5x(2x + 1) – 1(2x + 1) = 0
(5x – 1) (2x + 1) = 0

6. 3. Use the Zero Product Property
.
(5x - 1) (2x + 1) = 0
So, 5x – 1 = 0 and 2x + 1 = 0
4. Solve for the roots. 5x – 1 = 0 and 2x + 1 = 0
5x = 1 and 2x = -1
x =
𝟏
𝟓
and x = -
𝟏
𝟐
So, the roots of 10x2 + 3x – 1 = 0 are x =
𝟏
𝟓
and x = -
𝟏
𝟐

7. Example 3. Find the roots of 3x2 = x + 2
Steps Solution
1.Write in standard form 3x2 – x – 2 = 0
2. Factor the left side of the expression.
a. Multiply (a) . (c) (3). (-2) = -6
b. Find the factors of 6 that gives you
the sum of the value of b which is -1.
c. Copy the expression and replace the
middle term by the value obtain in step
b.
d. Factor using the method of
groupings.
(-1) = (-3) . (2)
3x2 – x – 2 = 0
3x2 – 3x + 2x – 2 = 0
(3x2 – 3x) + (2x – 2) = 0
3x(x – 1) + 2(x – 1) = 0
(3x + 2) (x – 1) = 0

8. 3. Use the Zero Product Property (3x + 2) (x – 1) = 0
(3x + 2) = 0 and (x – 1) = 0
4. Solve for the roots. 3x + 2 = 0 and (x – 1) = 0
3x = -2 and x = 1
3𝑥
3
=
−2
3
x = -
𝟐
𝟑
Therefore, the roots of 3x2 = x + 2 are -
𝟐
𝟑
and 1.

9. ThankYou!