Question

Factoring polynomials
-12n2-11n=-15

Answer 1

• (3n + 5)(4n - 3) = 0

Explanation:

• -12 n² - 11n = -15
• 12n² + 11n - 15 = 0
• 12n² + 20n - 9n - 15 = 0
• 4n(3n + 5) - 3(3n + 5) = 0
• (3n + 5)(4n - 3) = 0

Answer 2

`(4n-3)(3n+5)=0`

Explanation:

Given polynomial:

`-12n^2-11n=-15`

Add 15 to both sides:

`\implies -12n^2-11n+15=0`

Divide both sides by -1:

`\implies 12n^2+11n-15=0`

To factor a quadratic in the form
`ax^2+bx+c` find two numbers that multiply to ac and sum to b.

`\implies ac=12(-15)=-180`

`\implies b=11`

Therefore, the two numbers are: 20 and -9

Rewrite b as the sum of these two numbers:

`\implies 12n^2+20n-9n-15=0`

Factorize the first two terms and the last two terms separately:

`\implies 4n(3n+5)-3(3n+5)=0`

Factor out the common term (3n+5):

`\implies (4n-3)(3n+5)=0`