Question

using factor method, divide the following polynomials by a bibomial p2-p-42 by p+6​

Answer 1

using factor method, divide the following polynomials by a bibomial p2-p-42 by p+6

Answer 2

Answer:

p=7

p=−6

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "p2" was replaced by "p^2".

Step by step solution :

STEP

1

:

Trying to factor by splitting the middle term

1.1 Factoring p2-p-42

The first term is, p2 its coefficient is 1 .

The middle term is, -p its coefficient is -1 .

The last term, "the constant", is -42

Step-1 : Multiply the coefficient of the first term by the constant 1 • -42 = -42

Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is -1 .

-42 + 1 = -41

-21 + 2 = -19

-14 + 3 = -11

-7 + 6 = -1 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and 6

p2 - 7p + 6p - 42

Step-4 : Add up the first 2 terms, pulling out like factors :

p • (p-7)

Add up the last 2 terms, pulling out common factors :

6 • (p-7)

Step-5 : Add up the four terms of step 4 :

(p+6) • (p-7)

Which is the desired factorization

Equation at the end of step

1

:

(p + 6) • (p - 7) = 0

STEP

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : p+6 = 0

Subtract 6 from both sides of the equation :

p = -6

Solving a Single Variable Equation:

2.3 Solve : p-7 = 0

Add 7 to both sides of the equation :

p = 7