Question

a polynomial has the following solutions -3,4,10, -12. Write in factored form. The multiply it out to write in standard form

Answer 1

`\begin{cases} x=-3\implies &x+3=0\\ x=4\implies &x-4=0\\ x=10\implies &x-10=0\\ x=-12\implies &x+12=0 \end{cases}\implies (x+3)(x-4)(x-10)(x+12)=\stackrel{0}{y} \\\\\\ \stackrel{F~O~I~L}{(x^2-x-12)}(x-10)(x+12)=y\implies (x^2-x-12)\stackrel{F~O~I~L}{(x^2+2x-120)}=y \\\\\\ x^4+2x^3-120x^2-x^3-2x^2+120x-12x^2-24x+1440=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x^4+x^3-134x^2+96x+1440=y~\hfill`