a ) \(x^2-13x+36\)
\(=x^2-4x-9x+36\)
\(=x\left(x-4\right)-9\left(x-4\right)\)
\(=\left(x-9\right)\left(x-4\right)\)
b ) \(x^2+5x-14\)
\(=x^2-2x+7x-14\)
\(=x\left(x-2\right)+7\left(x-2\right)\)
\(=\left(x+7\right)\left(x-2\right)\)
c ) \(2x^2-5x-12\)
\(=2x^2-8x+3x-12\)
\(=2x\left(x-4\right)+3\left(x-4\right)\)
\(=\left(2x+3\right)\left(x-4\right)\)
d ) \(x^2-4xy-12y^2\)
\(=x^2-4xy+4y^2-16y^2\)
\(=\left(x-2y\right)^2-\left(4y\right)^2\)
\(=\left(x-2y-4y\right)\left(x-2y+4y\right)\)
\(=\left(x-6y\right)\left(x+2y\right)\)
a) x2-13x+36
=x2-4x-9x+36
=(x2-4x)-(9x-36)
=x(x-4)-9(x-4)
=(x-4)(x-9)
b) x2+5x-14
=x2+7x-2x-14
=(x2+7x)-(2x+14)
=x(x+7)-2(x+7)
=(x+7)(x-2)
c) 2x2-5x-12
=2x2+3x-8x-12
=(2x2+3x)-(8x+12)
=x(2x+3)-4(2x+3)
=(2x+3)(x-4)
d) x2-4xy-12y2
=x2-4xy+4y2-16y2
=(x2-4xy+4y2)-16y2
=(x-2y)2-16y2
=(x-2y-4y)(x-2y+4y)
=(x-6y)(x+2y)
a)\(x^2-13x+36=x^2-4x-9x+36=x\left(x-4\right)-9\left(x-4\right)=\left(x-9\right)\left(x-4\right)\)b)\(x^2+5x-14=x^2-2x+7x-14=x\left(x-2\right)+7.\left(x-2\right)=\left(7+x\right)\left(x-2\right)\)c)\(2x^2-5x-12=2x^2+3x-8x-12=x\left(2x+3\right)-4\left(2x+3\right)=\left(x-4\right)\left(2x+3\right)\)d)\(x^2-4xy-12y^2=x^2+2xy-6xy-12y^2=x\left(x+2y\right)-6y\left(x+2y\right)=\left(x-6y\right)\left(x+2y\right)\)
