Answer:
- (a - 2)(a - 7)
Explanation:
given the expression
9a - a² - 14
express in standard form , that is ax² + bx + c ( a ≠ 0 )
= - a² + 9a - 14 ( factor out - 1 from each term )
= - 1 (a² - 9a + 14) ← factorise the quadratic
Consider the factors of the constant term (+ 14) which sum to give the coefficient of the a- term (- 9)
the factors are - 2 and - 7 , since
- 2 × - 7 = + 14 and - 2 - 7 = - 9
use these factors to split the a- term
a² - 2a - 7a + 14 ( factor the first/second and third/fourth terms )
= a(a - 2) - 7(a - 2) ← factor out (a - 2) from each term
= (a - 2)(a - 7)
Then
9a - a² - 14 = - (a - 2)(a - 7)