Question

i) x³- 11x² + 30x;

j) 4x⁴- 21x²y² + y⁴
k) x³ + 4x²- 7x - 10;

l) (x² + x)²- (x² + x) + 15;

Answer 1

i) x³- 11x² + 30x

=\(x\left(x^2-11x+30\right)\)

=\(x\left(x-6\right)\left(x-5\right)\)

 

 

Answer 2

j) 4x⁴- 21x²y² + y⁴

=4x^4+4x^2y^2+y^4-25x^2y^2

=(2x^2+y^2)^2-(5xy)^2

=(2x^2+y^2-5xy)(2x^2+y^2+5xy)

Answer 3

              k,x³ + 4x²- 7x - 10

Answer 4

i: \(x^3-11x^2+30x\)

\(=x\left(x^2-11x+30\right)\)

\(=x\left(x-6\right)\left(x-5\right)\)

j: \(4x^4-21x^2y^2+y^4\)

\(=\left(2x^2+y^2\right)^2-25x^2y^2\)

\(=\left(2x^2-5xy+y^2\right)\left(2x^2+5xy+y^2\right)\)

k: \(x^3+4x^2-7x-10\)

\(=x^3+5x^2-x^2-5x-2x-10\)

\(=\left(x+5\right)\cdot\left(x^2-x-2\right)\)

\(=\left(x+5\right)\left(x-2\right)\left(x+1\right)\)

Answer 5

i) x³- 11x² + 30x
 =x( x2-11x+30)

=x(x2-5x-6x+30)

=x[x(x-5)-6(x-5)]

=x(x-5)(x-6)

${}^{}+4{}^{}-7x-10$

$={}^{}-2{}^{}+6{}^{}-12x+5x-10$

$={}^{}\left(x-2\right)+6x\left(x-2\right)+5\left(x-2\right)$

$=\left(x-2\right)\left({}^{}+6x+5\right)$

$=\left(x-2\right)\left({}^{}+x+5x+5\right)$

Answer 6

 

${}^{}-2\left({}^{}+x\right)-15$

$={}^{}-2\left({}^{}+x\right)+1-16$

$={}^{}-{}^{}$

$=\left({}^{}+x-1+4\right)\left({}^{}+x-1-4\right)$

$=\left({}^{}+x+3\right)({}^{}$

Answer 7

l: Ta có: \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)

\(=\left(x^2+x\right)^2-5\left(x^2+x\right)+3\left(x^2+x\right)-15\)

\(=\left(x^2+x-5\right)\left(x^2+x+3\right)\)