Question

If (x+2) is a factor of x^3+ax^2 +4bx +12 and a+b=-4 find the values of and b

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Concept:

An algebraic expression is factorized when it is written as the product of its factors. These variables, factors, or algebraic expressions could be present.

A number is broken down for the factor into components that can be multiplied to produce the original number.

Using factors in algebra:

The division of 12 by the integers 1, 2, 6, and 12 leaves no residue, making them all factors of 12. It is a crucial algebraic procedure that is used to solve equations, simplify fractions, and simplify expressions. Factorization in algebra is another name for it.

Given:

$(x+2)$ is a factor of $x^3+ax^2 +4bx +12$ and $a+b=-4$

Find:

To find the values of $a$ and $b$

Solution:

Given $(x+2)$ is a factor  of $x^3+ax^2 +4bx +12$

substituting $x = -2$ in the above equation then we get

$(-2)^{3} + a (-2)^{2} + 4b(-2) + 12 = 0$

$-8 + 4a -8b + 12 = 0$

$4a - 8b = 4$

$a - 2b = -1$ let it be equation 1

Given $a+b=-4$  let it be equation 2

so subtracting equation 1 with equation 2 then we will get

                            $a - 2b = -1$

                            $a + b = -4$

                            $-3b = 3$ ⇒ $b = -1$

Now substituting $b = -1$ in equation 1 then

                           $a - 2 *- 1 = -1$ ⇒$a = -3$

Hence the values of$a$ and $b$ are $-3$ and $-1$

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