FACTORING TRINOMIAL - FACTORING QUADRATIC EXPRESSIONS, EXAMPLES, EXERCISE

Please study

Method of Factoring Trinomial

if you have not already done so.

There, we explained a Five Step Method,
with each step explained in detail.

That knowledge is a prerequisite here.

Example 1 :

Factorize 4 + x - 14x²

Solution to Example 1 :

Let P = 4 + x - 14x² = -14x² + x + 4

In Factoring of Trinomials (Quadratics) , follow the five steps listed above.

Step 1: Coefficient of x² x constant term
= -14 x 4 = -56

Step 2: We have to express -56 as two factors whose sum
= coefficient of x = 1;
-56 = 8 x (-7); [8 + (-7) = 1]

Step 3: P = -14x² + x + 4 = -14x² + 8x - 7x + 4

Step 4: P = 2x(-7x + 4) + 1(-7x + 4)

Step 5: P = (-7x + 4)(2x + 1)

Thus, Applying the Method of Algebra Factoring of Quadratic Polynomial to 4 + x - 14x²,we get the Factors as (-7x + 4)(2x + 1) Ans.

Example 2 of Factoring Trinomial

Factorize x² + 7x - 78

Solution to Example 2 of Factoring Trinomial :

Let P = x² + 7x - 78

In Factoring of Trinomials (Quadratics), follow the five steps listed above.

Step 1: Coefficient of x² x constant term
= 1 x -78 = -78

Step 2: We have to express -78 as two factors whose sum
= coefficient of x = 7 ;
-78 = -2 x 39 = -2 x 3 x 13 = -6 x 13; (-6 + 13 = 7)

Step 3: P = x² + 7x - 78 = x² - 6x + 13x - 78

Step 4: P = x(x - 6) + 13(x - 6)

Step 5: P = (x - 6)(x + 13)

Thus, Applying the Method of Algebra Factoring of Quadratic Polynomial to x² + 7x - 78,we get the Factors as (x - 6)(x + 13) Ans.

Example 3 of Factoring Trinomial

Factorize x² + x - 42

Solution to Example 3 of Factoring Trinomial :

Let P = x² + x - 42

In Factoring of Trinomials (Quadratics), follow the five steps listed above.

Step 1: Coefficient of x² x constant term
= 1 x -42 = -42

Step 2: We have to express -42 as two factors whose sum
= coefficient of x = 1 ;
-42 = -6 x 7; (- 6 + 7 = 1)

Step 3: P = x² + x - 42 = x² + 7x - 6x - 42

Step 4: P = x(x + 7) - 6(x + 7)

Step 5: P = (x + 7)(x - 6)

Thus, Applying the Method of Algebra Factoring of Quadratic Polynomial to x² + x - 42,we get the Factors as (x + 7)(x - 6) Ans.

Exercise on Factoring Trinomial

1. Factorize 2 + x - 15x²
2. Factorize x² + 9x - 136
3. Factorize x² + x - 30

Answers to Exercise on Factoring Trinomial

1. (-5x + 2)(3x + 1)
2. (x + 17)(x - 8)
3. (x + 6)(x - 5)