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Prove that if f(x) = akx^k +ak−1x^k+1 +ak−2x^k+2+...+a1x+a0 is a polynomial in Q[x] and ak ̸=...

Prove that if f(x) = akx^k +ak−1x^k+1 +ak−2x^k+2+...+a1x+a0 is a polynomial in Q[x] and ak ̸= 0, and f (x) factors as f (x) = g(x)h(x), where g(x) and h(x) are polynomials in Q[x], then deg f = deg g+ deg h.

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