a) \(x^2+7x+12\)
\(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
b) \(3x^2-5x+2\)
\(=3x^2-3x-2x+2\)
\(=3x\left(x-1\right)-2\left(x-1\right)\)
\(=\left(x-1\right)\left(3x-2\right)\)
a) x2 + 7x + 12 = x2 + 3x + 4x + 12 = x(x + 3) + 4(x + 3) = (x + 4)(x + 3)
b) 3x2 - 5x + 2 = 3x2 - 3x - 2x + 2 = 3x(x - 1) - 2(x - 1) = (3x - 2)(x - 1)
c) x2 + 9x - 10 = x2 + 10x - x - 10 = x(x + 10) - (x + 10) = (x - 1)(x + 10)
d) x2 - 7x - 8 = x2 - 8x + x - 8 = x(x - 8) + (x - 8) = (x + 1)(x - 8)
e) 2x2 + 3x - 5 = 2x2 + 5x - 2x - 5 = x(2x + 5) - (2x + 5) = (x - 1)(2x + 5)
c) \(x^2+9x-10\)
\(=x^2-x+10x-10\)
\(=x\left(x-1\right)+10\left(x-1\right)\)
\(=\left(x-1\right)\left(x+10\right)\)