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Giải mục 2 trang 38, 39 SGK Toán 7 tập 2 - Chân trời sáng tạo

Thực hiện phép nhân

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HĐ 2

Thực hiện phép nhân \((3x + 1)({x^2} - 2x + 1)\), rồi đoán xem \((3{x^3} - 5{x^2} + x + 1):(3x + 1)\) bằng đa thức nào.

Phương pháp giải:

  • Nhân chia đa thức bằng phương pháp phân phối

Lời giải chi tiết:

\(\begin{array}{l}(3x + 1)({x^2} - 2x + 1)\\ = 3x({x^2} - 2x + 1) + 1({x^2} - 2x + 1)\\ = 3{x^3} - 6{x^2} + 3x + {x^2} - 2x + 1\\ = 3{x^3} - 5{x^2} + x + 1\end{array}\) Vì \((3x + 1)({x^2} - 2x + 1) = 3{x^3} - 5{x^2} + x + 1\) \( \Rightarrow (3{x^3} - 5{x^2} + x + 1):(3x + 1) = {x^2} - 2x + 1\) 

Thực hành 2

Thực hiện phép chia P(x) = \((6{x^2} + 4x)\) cho Q(x) = 2x

Phương pháp giải:

  • Sử dụng công thức chia đa thức một biến

Lời giải chi tiết:

\((6{x^2} + 4x):2x = (6{x^2}:2x) + (4x:2x)\) \( = 3x + 2\)

Vận dụng 2

Thực hiện các phép chia sau \(\frac{{9{x^2} + 5x + x}}{{3x}}\) và \(\frac{{(2{x^2} - 4x) + (x - 2)}}{{2 - x}}\)

Phương pháp giải:

  • Ta chia lần lượt theo công thức đã cho, phải thu gọn các đa thức trong phép chia và xếp thứ tự lũy thừa giảm dần của biến

Lời giải chi tiết:

\(\frac{{9{x^2} + 5x + x}}{{3x}} = \frac{{9{x^2} + 6x}}{{3x}} = \frac{{9{x^2}}}{{3x}} + \frac{{6x}}{{3x}} = 3x + 2\) \(\frac{{2{x^2} - 3x - 2}}{{2 - x}} = \frac{{2{x^2} - 3x - 2}}{{ - x + 2}} =  - 2x - 1\)

Thực hành 3

Thực hiện phép chia \(({x^2} + 5x + 9):(x + 2)\)

Phương pháp giải:

Ta sử dụng qui tắc chia 2 đa thức

Lời giải chi tiết:

\(({x^2} + 2x + 9):(x + 2) = \frac{{{x^2} + 5x + 9}}{{3x + 6}} = x + 3 + \frac{3}{{x + 2}}\) ta có :

Vậy \( = x + 3 + \frac{3}{{x + 2}}\)

Vận dụng 3

Tính diện tích đáy của một hình hộp chữ nhật (Hình 3) có chiều cao bằng (x + 3) cm và có thể tích bằng \(({x^3} + 8{x^2} + 19x + 12)\)\(c{m^3}\)

Phương pháp giải:

  • Ta tính diện tích đáy của hình hộp chữ nhật có chiều cao là (x+3) cm
  • Ta sử dụng công thức V = S.h để tìm ra diện tích đáy

Lời giải chi tiết:

\( \Rightarrow ({x^3} + 8{x^2} + 19x + 12):(x + 3) =\) diện tích đáy  Ta có :

 

Vậy diện tích đáy là : \({x^2} + 5x + 4\) \(c{m^2}\)

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