Question

factorise (x square - 5 x ) square - 36

Answer 1

Answer:

x2+5x−36=(x+9)(x−4)

Explanation:

Find a pair of factors of 36 which differ by 5.

The pair 9,4 works in that 9×4=36 and 9−4=5

Hence we find:

x2+5x−36=(x+9)(x−4)


Alternative method

Alternatively, we can complete the square and use the difference of squares identity:

a2−b2=(a−b)(a+b)

with a=(2x+5) and b=13 as follows.

First multiply by 22=4 to cut down on arithmetic involving fractions. Remember to divide by it at the end...

4(x2+5x−36)

=4x2+20x−144

=(2x)2+2(2x)(5)−144

=(2x+5)2−25−144

=(2x+5)2−169

=(2x+5)2−132

=((2x+5)−13)((2x+5)+13)

=(2x−8)(2x+18)

=(2(x−4))(2(x+9))

=4(x−4)(x+9)

Dividing both ends by 4 we find:

x2+5x−36=(x−4)(x+9)

Answer 2

Answer:

Step-by-step explanation:

(x^2 - 5x - 36)

=x^2 - 9x + 4x - 36

=x(x - 9) + 4(x - 9)

=(x - 9)(x + 4)