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Giải Bài 3 trang 27 sách bài tập toán 7 - Chân trời sáng tạo

Cho đa thức \(P\left( x \right) = 4{x^2} + 2{x^3} - 15x + 7{x^3} - 9{x^2} + 6 + 5x\). Hãy nêu bậc, hệ số cao nhất và hệ số tự do của đa thức \(P\left( x \right)\).

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Đề bài

Cho đa thức \(P\left( x \right) = 4{x^2} + 2{x^3} - 15x + 7{x^3} - 9{x^2} + 6 + 5x\). Hãy nêu bậc, hệ số cao nhất và hệ số tự do của đa thức \(P\left( x \right)\).

Phương pháp giải - Xem chi tiết

Bước 1: Rút gọn đa thức. Bước 2: Dựa vào các khái niệm bậc, hệ số cao nhất, hệ số tự do của đa thức để trả lời. Bậc của đa thức một biến (khác đa thức không) là số mũ lớn nhất của biến trong đa thức đó khi ở dạng thu gọn. Hệ số cao nhất là hệ số của đơn thức có bậc cao nhất trong đa thức. Hệ số tự do là hệ số không chứa biến x.

Lời giải chi tiết

Ta có \(P\left( x \right) = 4{x^2} + 2{x^3} - 15x + 7{x^3} - 9{x^2} + 6 + 5x = 9{x^3} - 5{x^2} - 10x + 6\)Bậc của đa thức \(P\left( x \right)\) là 3.Hệ số cao nhất là 9.Hệ số tự do là 6.

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