Final answer to the problem
$16\left(4x+1\right)\left(\left(x+\frac{1}{4}\right)^2-\frac{25}{16}\right)^4$
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Step-by-step Solution
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1
Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($2$) to all terms
$\left(4x+1\right)\left(2\left(x^2+\frac{1}{2}x-\frac{3}{2}\right)\right)^4$
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$\left(4x+1\right)\left(2\left(x^2+\frac{1}{2}x-\frac{3}{2}\right)\right)^4$
Learn how to solve polynomial factorization problems step by step online. Factor by completing the square (4x+1)(2x^2+x+-3)^4. Use the complete the square method to factor the trinomial of the form ax^2+bx+c. Take common factor a (2) to all terms. Add and subtract \displaystyle\left(\frac{b}{2a}\right)^2. Factor the perfect square trinomial x^2+\frac{1}{2}x+\frac{1}{16}. Subtract the values -\frac{3}{2} and -\frac{1}{16}.
Final answer to the problem
$16\left(4x+1\right)\left(\left(x+\frac{1}{4}\right)^2-\frac{25}{16}\right)^4$