We are asked to factor the following quadratic expressions: 7. $3x^2 - 5x - 2$ 8. $2x^2 - x - 15$ 10. $3x^2 - 17x - 28$ 11. $6x^2 + 7x + 2$ 13. $3x^2 - 11x + 6$ 14. $3y^2 - 11y + 10$

1. Problem Description

We are asked to factor the following quadratic expressions:

7. $3x^2 - 5x - 2$

8. $2x^2 - x - 15$

1

0. $3x^2 - 17x - 28$

1

1. $6x^2 + 7x + 2$

1

3. $3x^2 - 11x + 6$

1

4. $3y^2 - 11y + 10$

2. Solution Steps

7. Factor $3x^2 - 5x - 2$.

We are looking for two numbers that multiply to $3*(-2) = -6$ and add up to $-5$. Those two numbers are $-6$ and $1$.

$3x^2 - 6x + x - 2 = 3x(x - 2) + 1(x - 2) = (3x + 1)(x - 2)$

8. Factor $2x^2 - x - 15$.

We are looking for two numbers that multiply to $2*(-15) = -30$ and add up to $-1$. Those two numbers are $-6$ and $5$.

$2x^2 - 6x + 5x - 15 = 2x(x - 3) + 5(x - 3) = (2x + 5)(x - 3)$

1

0. Factor $3x^2 - 17x - 28$.

We are looking for two numbers that multiply to $3*(-28) = -84$ and add up to $-17$. Those two numbers are $-21$ and $4$.

$3x^2 - 21x + 4x - 28 = 3x(x - 7) + 4(x - 7) = (3x + 4)(x - 7)$

1

1. Factor $6x^2 + 7x + 2$.

We are looking for two numbers that multiply to $6*2 = 12$ and add up to $7$. Those two numbers are $3$ and $4$.

$6x^2 + 3x + 4x + 2 = 3x(2x + 1) + 2(2x + 1) = (3x + 2)(2x + 1)$

1

3. Factor $3x^2 - 11x + 6$.

We are looking for two numbers that multiply to $3*6 = 18$ and add up to $-11$. Those two numbers are $-2$ and $-9$.

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

1

4. Factor $3y^2 - 11y + 10$.

We are looking for two numbers that multiply to $3*10 = 30$ and add up to $-11$. Those two numbers are $-5$ and $-6$.

$3y^2 - 6y - 5y + 10 = 3y(y - 2) - 5(y - 2) = (3y - 5)(y - 2)$

3. Final Answer

7. $(3x + 1)(x - 2)$

8. $(2x + 5)(x - 3)$

1

0. $(3x + 4)(x - 7)$

1

1. $(3x + 2)(2x + 1)$

1

3. $(3x - 2)(x - 3)$

1

4. $(3y - 5)(y - 2)$