Question

cum se descompune in factori?
a) 4x²-4xy-8y² =?
b)40x²+42x-49=?

Answer 1

[tex]a)4x^2-4xy-8y^2=4(x^2-xy-2y^2)=4(x^2-2xy+xy-2y^2)=\\ =4[x(x-2y)+y(x-2y)]=4(x-2y)(x +y)\\ \\ b)Vom\ folosi\ formula:ax^2+bx+c=a(x-x_1)(x-x_2)\ unde\ x_1\\ si\ x_2\ sunt\ solutiile\ ecuatiei\\ 40x^2+42x-49=0\\ \Delta=42^2+4\cdot40\cdot 49\\ \Delta=1764+7840\\ \Delta=9604\Rightarrow \sqrt{\Delta}=98\\ x_1=\frac{-42-98}{80}=-\frac{140}{80}=-\frac{7}{4}\\ \\ x_2=\frac{-42+98}{80}=\frac{56}{80}=\frac{7}{10}\\ Asadar:40x^2+42x-49=40(x+\frac{7}{4})(x-\frac{7}{10})=\\ =\boxed{(4x+7)(10x-7)} [/tex]