factor the trinomial -5a^2 - ab + 6b^2?

Question

factor out all common monomials first (including -1 if the lead coefficient is negative)

Answer 1

first: find a number that is divisible by the coefficients: -5, -1, and 6; also find a common variable. In this case, there is no divisible number nor a common variable.

Second: the leading coefficient (-5) is negative, take out a -1 and bring it to the front. Multiply -1 by the remaining parts and signs:

= -1(5a^2 + ab - 6b^2)

Third: factor: take the first coeffcient (5) and multiply it by the last coefficient (-6) = -30. Find two numbers that give you -30 when multiplied and 1 (middle coefficient) when added/subtracted. We can use: 6, -5.

Fourth: rewrite the expression and group like terms:
= (5a^2 - 5ab) + (6ab - 6b^2)

Fifth: factor each set:

= 5a(a - b) + 6b(a - b)
= (a - b)(5a + 6b)

Answer 2

-5a^2 - ab + 6b^2
= -1(5a^2 + ab - 6b^2)
= -1(5a + 6b)(a - b)

Answer 3

-5a^2 - ab + 6b^2
-1(5a^2+ab-6b^2)
-1(5a+6b)(a-b)

Answer 4

-5a² - ab + 6b²
= -(5a² + ab - 6b²)
= -(a-b)(5a+6b)

Answer 5

-(5a^2+ab-6b^2)
-(5a+6b)(a-b)

Answer 6

-5a^2+5ab-6ab+6b^2=-5a(a-b)-6b(a-b)=(a-b)(-5a-6b)=-1(a-b)(5a+6b) OK???

Answer 7

do it urself