Chapter 3 - 3.2 - Polynomial Functions of Higher Degree - 3.2 Exercises - Page 261: 70

$f(x)=x^5-17x^4+79x^3-11x^2-332x-224$

Finding a polynomial with degree of $5$: $$f(x)=[x-(-1)]^2(x-4)(x-7)(x-8)$$ $$f(x)=(x+1)^2(x^2-11x+28)(x-8)$$ $$f(x)=(x^2+2x+1)(x^2-11x+28)(x-8)$$ $$f(x)=(x^4-9x^3+7x^2+45x+28)(x-8)$$ $$f(x)=x^5-8x^4-9x^4+72x^3+7x^3-56x^2+45x^2-360x+28x-224$$ $$f(x)=x^5-17x^4+79x^3-11x^2-332x-224$$