4. Solve the factored quadratic equation (19x−3)(9+x)=0

Question

. Enter the lesser number first.(2 points)
The solution set is {
,
}
Question 2
5. Which of the following quadratic equations is not solvable by grouping?(1 point)
Responses

2x2−2x−10=0
2 x squared minus 2 x minus 10 is equal to 0

x2−12x+35=0
x squared minus 12 x plus 35 is equal to 0

2x2+14x+12=0
2 x squared plus 14 x plus 12 is equal to 0

x2−2x+1=0
x squared minus 2 x plus 1 is equal to 0
Question 3
6. Factor the expression 49x4−4y6
by typing into the blank spaces. (4 points)
(7
+
) (
-2
)

Answer 1

Question 1: Solve the factored quadratic equation (19x−3)(9+x)=0

To solve the equation, we can set each factor equal to zero:

1. \(19x - 3 = 0\)

   • \(19x = 3\)
   • \(x = \frac{3}{19}\)

2. \(9 + x = 0\)

   • \(x = -9\)

Thus, the solution set is: \[ { -9, \frac{3}{19} } \]

Question 2: Which of the following quadratic equations is not solvable by grouping?

We can analyze how to factor each equation:

1. \(2x^2 - 2x - 10 = 0\)

   • Can be factored as \(2(x^2 - x - 5) = 0\).

2. \(x^2 - 12x + 35 = 0\)

   • Can be factored as \((x - 5)(x - 7) = 0\).

3. \(2x^2 + 14x + 12 = 0\)

   • Can be factored as \(2(x^2 + 7x + 6) = 0\) and further as \(2(x + 6)(x + 1) = 0\).

4. \(x^2 - 2x + 1 = 0\)

   • Can be factored as \((x - 1)(x - 1) = 0\) or \((x - 1)^2 = 0\).

The equation that is not solvable by grouping is: \[ 2x^2 - 2x - 10 = 0 \] as it requires a different factoring approach.

Question 3: Factor the expression \(49x^4 - 4y^6\)

This expression is a difference of squares, which can be factored using the formula \(a^2 - b^2 = (a - b)(a + b)\).

1. \(a^2 = (7x^2)^2\) and \(b^2 = (2y^3)^2\)

Thus, we can rewrite it as: \[ 49x^4 - 4y^6 = (7x^2 - 2y^3)(7x^2 + 2y^3) \]

So the factored expression is: \[ (7x^2 - 2y^3)(7x^2 + 2y^3) \]

To fill in the blank spaces:

1. First blank: \(x^2\)
2. Second blank: \(y^3\)

Final factorization: \[ (7 , x^2 - 2y^3)(7 , x^2 + 2y^3) \]