Question

Brandy is trying to factor the quadratic $3x^2 - x - 10.$ She starts by assuming that the quadratic factors as \[3x^2 - x - 10 = (x + B)(3x + D),\]for some integers $B$ and $D.$ After some work, Brandy successfully factors the quadratic. Find the ordered pair $(B,D).$

Answer 1

(B , D) = (-2,5)

Explanation:

The given quadratic expression is

`3x^(2) -x-10`

compare the given expression with
`ax^(2) +bx+c`

so we have
`a = 3 , b = -1 ,c = -10`

now
`ac=3 (-10)=- 30` and
`b= -1`

we need to find two numbers such that their product is -30 and sum is -1

-6 and 5 are such numbers

so we have

`3x^(2) -6x+5x-10`

grouping first two terms and last two terms

`(3x^(2) -6x)+(5x-10)`

factor out 3x from first two terms and 5 from last two terms

`3x(x-2) +5(x-2)`

`(x-2)(3x+5)` ( factor out (x-2))

`(x+(-2))(3x+5)`

hence B =-2 and D= 5

(B,D)= (-2,5)