476,293 views
44 votes
44 votes
What is the quotient when (x+3) is divided into the polynomial 2x2 + 3x-9?

O A. 2x-5 with no remainder
B. X+ 3 with a remainder of -2
O c. 2x+ 1 with no remainder
D. 2x-3 with no remainder

User Shreyangi Saxena
by
2.9k points

1 Answer

14 votes
14 votes

Problem: 2x^2+3x-9

For a polynomial of the form, ax^2+bx+c rewrite the middle term as the sum of two terms whose product a·c=2·-9=-18 and whose sum is b=3.

Factor 3 out of 3x

2x^2+3(x)-9

Rewrite 3 as -3 plus 6.

2x^2+(-3+6)x-9

Apply the distributive property

2x^2(-3x+6x)-9

Remove the parentheses

2x^2-3x+6x-9

Factor out the greatest common factor from each group

Group the first two terms and the last two terms

(2x^2-3x) (6x-9)

Factor out the greatest common factor in each group.

x(2x-3)+3(2x-3)

Factor the polynomial by factoring out the greatest common factor, 2x-3

(x+3) (2x-3). So, the quotient is 2x-3

Thus, the correct answer is Option D 2x-3 with no remainder

User Shawnynicole
by
2.3k points