Question

6. Factorise the following
(i) a² + 5a –36
​

Answer 1

Answer:

Simplifying

a2 + 5a = 36

Reorder the terms:

5a + a2 = 36

Solving

5a + a2 = 36

Solving for variable 'a'.

Reorder the terms:

-36 + 5a + a2 = 36 + -36

Combine like terms: 36 + -36 = 0

-36 + 5a + a2 = 0

Factor a trinomial.

(-9 + -1a)(4 + -1a) = 0

Subproblem 1

Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying

-9 + -1a = 0

Solving

-9 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '9' to each side of the equation.

-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0

0 + -1a = 0 + 9

-1a = 0 + 9

Combine like terms: 0 + 9 = 9

-1a = 9

Divide each side by '-1'.

a = -9

Simplifying

a = -9

Subproblem 2

Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying

4 + -1a = 0

Solving

4 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-4' to each side of the equation.

4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0

0 + -1a = 0 + -4

-1a = 0 + -4

Combine like terms: 0 + -4 = -4

-1a = -4

Divide each side by '-1'.

a = 4

Simplifying

a = 4

Solution

a = {-9, 4}

Answer 2

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➡ ${a}^2 + {5a} - {36}$

= ${a}^2 + {(9-4)}a - {36}$

= ${a}^2 + {9a} - {4a} - {36}$

= ${a} ( a + 9 ) - {4} ( a + 9 )$

= ${(a - 4)} {(a + 9)}$ ✔✔

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THANKS :) ❤