a: \(2x^2+7x-15\)
\(=2\left(x^2+\frac72x-\frac{15}{2}\right)\)
\(=2\left(x^2+2\cdot x\cdot\frac74+\frac{49}{16}-\frac{169}{16}\right)\)
\(=2\left\lbrack\left(x+\frac74\right)^2-\left(\frac{13}{4}\right)^2\right\rbrack\)
\(=2\left(x+\frac74-\frac{13}{4}\right)\left(x+\frac74+\frac{13}{4}\right)=2\left(x-\frac32\right)\left(x+5\right)\)
b: \(3x^2-2x-8\)
\(=3\left(x^2-\frac23x-\frac83\right)\)
\(=3\left(x^2-2\cdot x\cdot\frac13+\frac19-\frac{25}{9}\right)\)
\(=3\left\lbrack\left(x-\frac13\right)^2-\left(\frac53\right)^2\right\rbrack\)
\(=3\left(x-\frac13-\frac53\right)\left(x-\frac13+\frac53\right)=3\left(x-2\right)\left(x+\frac43\right)\)
c: \(10x^2+17x+3\)
\(=10\left(x^2+\frac{17}{10}x+\frac{3}{10}\right)\)
\(=10\left(x^2+2\cdot x\cdot\frac{17}{20}+\frac{289}{400}-\frac{169}{400}\right)\)
\(=10\left\lbrack\left(x+\frac{17}{20}\right)^2-\left(\frac{13}{20}\right)^2\right\rbrack\)
\(=10\left(x+\frac{17}{20}-\frac{13}{20}\right)\left(x+\frac{17}{20}+\frac{13}{20}\right)=10\left(x+\frac{4}{20}\right)\left(x+\frac{30}{20}\right)\)
\(=10\left(x+\frac15\right)\left(x+\frac32\right)\)
d: \(7x^2+3x-4\)
\(=7\left(x^2+\frac37x-\frac47\right)\)
\(=7\left(x^2+2\cdot x\cdot\frac{3}{14}+\frac{9}{196}-\frac{121}{196}\right)\)
\(=7\left\lbrack\left(x+\frac{3}{14}\right)^2-\left(\frac{11}{14}\right)^2\right\rbrack=7\left(x+\frac{3}{14}-\frac{11}{14}\right)\left(x+\frac{3}{14}+\frac{11}{14}\right)\)
\(=7\left(x-\frac{8}{14}\right)\left(x+\frac{14}{14}\right)=7\left(x+1\right)\left(x-\frac47\right)\)
\(a,2x^2+7x-15=2x^2+10x-3x-15\)
\(=2x\left(x+5\right)-3\left(x+5\right)=\left(2x-3\right)\left(x+5\right)\)
\(b,3x^2-2x-8=3x^2-6x+4-8\)
\(=3x\left(x-2\right)+4\left(x-2\right)=\left(3x+4\right)\left(x-2\right)\)
\(c,10x^2+17x+3=10x^2+15x+2x+3\)
\(=5x\left(2x+3\right)+\left(2x+3\right)=\left(5x+1\right)\left(2x+3\right)\)
\(d,7x^2+3x-4=7x^2+7x-4x-4\)
\(=7x\left(x+1\right)-4\cdot x+1)=\left(7x-4\right)\left(x+1\right)\)
Giúp e bài 2 thôi ạ bài 1 e làm r ạ! Mong mn giúp e, e cần gấp ạ!
