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Giải bài 13 trang 12 sách bài tập toán 8 - Cánh diều

Cho hai đơn thức: \(A = - 123{x^{n + 1}}{y^{10}}{z^{n + 2}};B = 1,2{x^5}{y^n}{z^{n + 1}}\) với \(n\) là số tự nhiên.

♚Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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Đề bài

Cho hai đơn thức: \(A =  - 123{x^{n + 1}}{y^{10}}{z^{n + 2}};B = 1,2{x^5}{y^n}{z^{n + 1}}\) với \(n\) là số tự nhiên.

Phương pháp giải - Xem chi tiết

Đơn thức \(A\) chia hết cho đơn thức \(B\) \(\left( {B \ne 0} \right)\) khi mỗi biến của \(B\) đều là biến của \(A\) với số mũ không lớn hơn số mũ của nó trong \(A\).

Lời giải chi tiết

a) Đơn thức \(A\) chia hết cho đơn thức \(B\) khi mỗi biến của \(B\) đều là biến của \(A\) với số mũ không lớn hơn số mũ của nó trong \(A\).Suy ra \(5 \le n + 1;n \le 10;n + 1 \le n + 2\) hay \(4 \le n \le 10\).Vậy \(n \in \left\{ {4;5;6;7;8;9;10} \right\}\) thì đơn thức \(A\) chia hết cho đơn thức \(B\).b) \(P = A:B = \left( { - 123{x^{n + 1}}{y^{10}}{z^{n + 2}}} \right):\left( {1,2{x^5}{y^n}{z^{n + 1}}} \right) =  - 110{x^{n - 4}}{y^{10 - n}}z\)c) Giá trị của đa thức \(P\) tại \(n = 9;x = 2;y =  - 1;z = 5,8\) là:\( - {110.2^{9 - 4}}.{\left( { - 1} \right)^{10}}.5,8 = 20416\)

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