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Giải bài 54 trang 55 sách bài tập toán 7 - Cánh diều

Viết đa thức biến x trong mỗi trường hợp sau:

ꦏTổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Viết đa thức biến x trong mỗi trường hợp sau:

a) Đa thức bậc nhất có hệ số của biến bằng - 7 và hệ số tự do bằng 0 b) Đa thức bậc ba có hệ số của luỹ thừa bậc hai và bậc nhất của biến đều bằng 5 c) Đa thức bậc bốn có tổng hệ số của luỹ thừa bậc ba và bậc hai của biến bằng 6 và hệ số tự do bằng − 1 d) Đa thức bậc tám trong đó tất cả các hệ số của luỹ thửa bậc lẻ của biến đều bằng 0

Phương pháp giải - Xem chi tiết

Bước 1: Xác định dạng của các đa thức + Bậc nhất: \(ax + b\) + Bậc hai: \(a{x^3} + b{x^2} + cx + d\) + Bậc bốn: \(a{x^4} + b{x^3} + c{x^2} + dx + e\) + Bậc tám: \(a{x^8} + b{x^7} + c{x^6} + d{x^5} + e{x^4} + m{x^3} + n{x^2} + px + q\) Bước 2: Tìm các hệ số tương ứng của từng đa thức theo giả thiết (hệ số nào không có điều kiện thì giữ nguyên dạng biến)

Lời giải chi tiết

a) Đa thức bậc nhất có hệ số của biến bằng -7 và hệ số tự do bằng 0 có dạng: \( - 7x\)b) Đa thức bậc ba có hệ số của luỹ thừa bậc hai và bậc nhất của biến đều bằng 5 có dạng:

\(a{x^3} + 5{x^2} + 5x + d\) (với a, d là các số cho trước và a ≠ 0)

c) Đa thức bậc bốn có tổng hệ số của luỹ thừa bậc ba và bậc hai của biến bằng 6 và hệ số tự do bằng – 1có dạng: \(a{x^4} + b{x^3} + c{x^2} + dx + e\)Khi đó: \(b + c = 6 \Rightarrow c = 6 - b\)

Vậy đa thức cần tìm là: \(a{x^4} + b{x^3} + (6 - b){x^2} + dx - 1\) (với a, b, d là các số cho trước và a ≠ 0)

d) Đa thức bậc tám trong đó tất cả các hệ số của luỹ thửa bậc lẻ của biến đều bằng 0 có dạng:

\(a{x^8} + b{x^6} + c{x^4} + d{x^2} + e\) (với a, b, c, d, e là các số cho trước và a ≠ 0)

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