Divide f(x) by d(x), and write a summary statement in the form indicated.f(x) = x^4 + 4x^3 + 6x^2 + 4x + 5: d(x) = x^2+1•f(x)=(x^2+1)(x^2+4x+5)+12x-15•f(x)=(x^2+1)(x^2+4x+5) •f(x)=(x^2+1)(x^2-4x+5) •f(x)=(x^2+1)(x^2-4x+5)+12x-15

Answer:The correct option is B)  [tex]f(x) =(x^2+1)(x^2+4x+5)[/tex]Step-by-step explanation:Consider the provided function.[tex]f(x) = x^4 + 4x^3 + 6x^2 + 4x + 5[/tex] and [tex]d(x) = x^2+1[/tex]We need to divide f(x) by d(x)As we know: Dividend = Divisor × Quotient + RemainderIn the above function f(x) is dividend and divisor is d(x)Divide the leading term of the dividend by the leading term of the divisor:[tex]\frac{x^4}{x^2}=x^2[/tex]Write the calculated result in upper part of the table.Multiply it by the divisor: [tex]x^2(x^2+1)=x^4+x^2[/tex]Now Subtract the dividend from the obtained result:[tex](x^4 + 4x^3 + 6x^2 + 4x + 5)-(x^4-x^2)=4x^3+5x^2+4x+5[/tex]Again divide the leading term of the obtained remainder by the leading term of the divisor: [tex]\frac{4x^3}{x^2}=4x[/tex]Write the calculated result in upper part of the table.Multiply it by the divisor: [tex]4x(x^2+1)=4x^3+4x[/tex]Subtract the dividend:[tex](4x^3+5x^2+4x+5)-(4x^3+4x)=5x^2+5[/tex]Divide the leading term of the obtained remainder by the leading term of the divisor: [tex]\frac{5x^2}{x^2}=5[/tex]Multiply it by the divisor: [tex]5(x^2+1)=5x^2+5[/tex]Subtract the dividend:[tex](5x^2+5)-(5x^2+5)=0[/tex]Therefore, Dividend = [tex]x^4 + 4x^3 + 6x^2 + 4x + 5[/tex]Divisor = [tex]x^2+1[/tex]Quotient = [tex]x^2+4x+5[/tex]Remainder = 0Dividend = Divisor × Quotient + Remainder[tex]f(x) = (x^2+1)(x^2+4x+5)[/tex]Hence, the correct option is B)  [tex]f(x) =(x^2+1)(x^2+4x+5)[/tex]