Answer :
The division yields [tex]\( \frac{{x(3x^2 - 25x - 7)}}{{2(4x + 1)}} \).[/tex]
To divide [tex]\(4(12x^4 - 25x^3 - 7x^2)\) by \(8x(4x + 1)\),[/tex]you can follow these steps:
1. First, factor out the common terms from [tex]\(4(12x^4 - 25x^3 - 7x^2)\) and \(8x(4x + 1)\).[/tex]
2. Then, divide the factored expression of[tex]\(12x^4 - 25x^3 - 7x^2\) by the factored expression of \(8x(4x + 1)\).[/tex]
Let's solve it step by step:
1. Factor out common terms:
[tex]\[ 4(12x^4 - 25x^3 - 7x^2) = 4x^2(3x^2 - 25x - 7) \] \[ 8x(4x + 1) = 8x(4x + 1) \][/tex]
[tex]Divide \(3x^2 - 25x - 7\) by \(8x\): \[ \begin{align*} \frac{{4x^2(3x^2 - 25x - 7)}}{{8x(4x + 1)}} &= \frac{{4x^2}}{{8x}} \cdot \frac{{3x^2 - 25x - 7}}{{4x + 1}} \\ &= \frac{{x(3x^2 - 25x - 7)}}{{2(4x + 1)}} \end{align*} \][/tex]
So, the division of [tex]\(4(12x^4 - 25x^3 - 7x^2)\) by \(8x(4x + 1)\) is:\[[/tex]
[tex]\frac{{x(3x^2 - 25x - 7)}}{{2(4x + 1)}}\][/tex]
Complete Question;
Divide [tex]\(4(12x^4 - 25x^3 - 7x^2)\) by \(8x(4x + 1)\).[/tex]
