Q(3x)=12x+2 then what is Q(x-2)

Mathematics

1 answer:

Mandarinka [93]2 years ago

8 0

Answer:

it's ax+b form answer is Q(x-2)=4x-6

Step-by-step explanation:

ax+b=Q(x),Q(x-2)=a(x-2)+2

Q(3x)=a(3x)+b=12x+2, 3a=12 =>a=4,b=2

the original q of x is 4x+2

Q of x-2 =4(x-2)+2=4x-8+2=4x-6

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The quotient of (x^3+3x^2-4x-12)/(x^2+5x+6)

Elis [28]

Answer: The quotient is (x-2).

Step-by-step explanation:

Since we have given that

$f(x)=(x^3+3x^2-4x-12)\\\\and\\\\g(x)=x^2+5x+6\\\\So,\ \frac{\left(x^3+3x^2-4x-12\right)}{\left(x^2+5x+6\right)}$

Now, we have to find the quotient of the above expression.

So, here we go:

$Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)$

Now, we will divide the above simplest form with g(x):

$\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2$