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

Answer:

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

Step-by-step 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)