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Fully factorise the quadratic expression 9a - a² – 14

User Atmelino
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1 Answer

2 votes

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)

User Femi Oni
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