Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
e ko bt phân tích đa thức thành nhân tử nên a tham khảo linh này nha
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwim29i-oIzyAhVSNKYKHZBdCJ4QFjAAegQIBRAD&url=https%3A%2F%2Fh7.net%2Fhoi-dap%2Ftoan-8%2Fphan-h-da-thuc-5x-2-2x-2-2x-5x-2-6-thanh-nhan-tu-faq341450.html&usg=AOvVaw2Kkix8idzI43uM1i2Mitp4
#)Giải :
\(x^3-2x-4\)
\(=x^3+2x^2-2x^2+2x-4x-4\)
\(=x^3+2x^2+2x-2x^2-4x-4\)
\(=x\left(x^2+2x+2\right)-2\left(x^2+2x+2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
\(x^4+2x^3+5x^2+4x-12\)
\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)
\(=x^2\left(x^2+x+6\right)+x\left(x^2+x+6\right)-2\left(x^2+x+6\right)\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)
Câu 1.
Đoán được nghiệm là 2.Ta giải như sau:
\(x^3-2x-4\)
\(=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+2\right)\)
\(2x^3-x^2+5x+3=2x^3+x^2-2x^2-x+6x+3\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
a, x^2 + 2x - 8
= x^2 -2x + 4x - 8
= x(x - 2) + 4(x - 2)
= (x + 4)(x - 2)
b, x^2 + 5x + 6
= x^2 + 2x + 3x + 6
= x(x + 2) + 3(x + 2)
= (x + 3)(x + 2)
a/ \(x^2+2x-8\)
\(=x^2+4x-2x-8\)
\(=\left(x^2+4x\right)-\left(2x+8\right)\)
\(=x\left(x+4\right)-2\left(x+4\right)\)
\(=\left(x-2\right)\left(x+4\right)\)
b/ \(x^2+5x+6\)
\(=x^2+2x+3x+6\)
\(=\left(x^2+2x\right)+\left(3x+6\right)\)
\(=x\left(x+2\right)+3\left(x+2\right)\)
\(=\left(x+2\right)\left(x+3\right)\)
\(\left(5x^2-2x\right)^2+2x-5x^2-6=25x^4-2.5x^2.2x+4x^2+2x-5x^2-6.\)
\(=25x^4-20x^3-x^2+2x-6\)
\(=25x^4-25x^3+5x^3-5x^2+4x^2-4x+6x-6.\)
\(=\left(25x^4-25x^3\right)+\left(5x^3-5x^2\right)+\left(4x^2-4x\right)+\left(6x-6\right).\)
\(=25x^3\left(x-1\right)+5x^2\left(x-1\right)+4x\left(x-1\right)+6\left(x-1\right).\)
\(=\left(x-1\right)\left(25x^3+5x^2+4x+6\right)\)
\(=\left(x-1\right)\left[25x^3+15x^2-10x^2-6x+10x+6\right]\)
\(=\left(x-1\right)\left[5x^2\left(5x+3\right)-2x\left(5x+3\right)+2\left(5x+3\right)\right]\)
\(=\left(x-1\right)\left(5x+3\right)\left(5x^2-2x+2\right)\)
a) \(\left(x-7\right)\left(x+2\right)\)
b) \(\left(2x-3\right)\left(x+2\right)\)
Lời giải:
$2x^2-5x-6=2(x^2-\frac{5}{2}x+\frac{5^2}{4^2})-\frac{73}{8}$
$=2(x-\frac{5}{4})^2-\frac{73}{8}$
$=2(x-\frac{5}{4}-\frac{\sqrt{73}}{4})(x-\frac{5}{4}+\frac{\sqrt{73}}{4})$