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Giải bài 56 trang 55 sách bài tập toán 7 - Cánh diều

Cho đa thức \(A(x) = - 11{x^5} + 4{x^3} - 12{x^2} + 11{x^5} + 13{x^2} - 7x + 2\)

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Đề bài

Cho đa thức \(A(x) =  - 11{x^5} + 4{x^3} - 12{x^2} + 11{x^5} + 13{x^2} - 7x + 2\)

a) Thu gọn và sắp xếp đa thức A(x) theo số mũ giảm dần của biến

b) Tìm bậc của đa thức A(x)

c) Tính giá trị của đa thức A(x) tại x = −1; x = 0; x = 2

Phương pháp giải - Xem chi tiết

Bước 1: Cộng, trừ các đơn thức có cùng số mũ của biến để rút gọn và sắp xếp đa thức rút gọn theo số mũ giảm dần của biến Bước 2: Tìm bậc của đa thức là số mũ cao nhất của biến

Bước 3: Thay x = -1, x = 0, x = 2 vào đa thức rút gọn để tính giá trị A(−1), A(0), A(2)

Lời giải chi tiết

a) \(A(x) =  - 11{x^5} + 4{x^3} - 12{x^2} + 11{x^5} + 13{x^2} - 7x + 2 = 4{x^3} + {x^2} - 7x + 2\)

b) Bậc của đa thức A(x) là 3

c) Ta có:\(A( - 1) = 4.{( - 1)^3} + {( - 1)^2} - 7.( - 1) + 2 =  - 4 + 1 + 7 + 2 = 6\)\(A(0) = {4.0^3} + {0^2} - 7.0 + 2 = 2\)\(A(2) = {4.2^3} + {2^2} - 7.2 + 2 = 32 + 4 - 14 + 2 = 24\)

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