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Algebra 1 : Quadratic Equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #19 : How To Factor The Quadratic Equation

Factor the following quadratic expression:

$x^{2}+12x + 32$

Possible Answers:

(x+8)(x+4)

(x-8)(x+4)

(x+16)(x+2)

(x-32)(x-1)

(x+2)(x+8)

Correct answer:

(x+8)(x+4)

Explanation:

Given the following expression:

$x^{2}+12x + 32$

We need to find factors of that add up to .

can be broken down into the following factors:

32 , 1

16, 2

8,4

Of these choices, only 8 + 4 adds up to . Additionally, the coefficient in front of the variable is , so we do not need to worry about that when finding these values. There are no negatives in the quadratic expression, so the signs in the factored form are all positive. This gives us the final answer of

(x+8)(x+4)

You can use the FOIL method to re-expand the expression and check your work!

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Example Question #233 : Equations / Inequalities

Solve the following equation by factoring.

$x^{2}+14x+45=0$

Possible Answers:

(-11,-4)

(-15,-3)

(9,5)

None of the other answers.

(-9,-5)

Correct answer:

(-9,-5)

Explanation:

To factor a quadratic equation in the form

$ax^{2}+bx+c$ , where a=1 , find two integers that have a sum of and a product of .

For this equation, that would be 9 and 5.

9+5=14

$9\cdot 5=45$

Therefore, the solutions to this equation are and .

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Example Question #21 : How To Factor The Quadratic Equation

Solve the following equation by factoring.

$x^{2}+3x=88$

Possible Answers:

(4,-22)

(-44,41)

(-11,8)

(8,-11)

None of the other answers.

Correct answer:

(-11,8)

Explanation:

$x^{2}+3x=88$

Begin by setting the equation equal to 0 by subtracting 88 from both sides.

$x^{2}+3x-88=0$

Now that the equation is in the form $ax^{2}+bx+c=0$ , find two integers that sum to and have a product of .

For this equation, those integers are and .

11-8=3

$11\cdot -8=-88$

Therefore, the solutions to this equation are (-11,8)

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Example Question #22 : How To Factor The Quadratic Equation

Solve the following equation by factoring.

$n^{2}+17n-30=-102$

Possible Answers:

(17,-6)

(17,6)

(-8,-9)

(8,9)

(-13,-4)

Correct answer:

(-8,-9)

Explanation:

$n^{2}+17n-30=-102$

Begin by setting the equation equal to zero by adding 105 to each side.

$n^{2}+17n+72=0$

For an equation in the form $ax^{2}+bx+c=0$ , where a=1 , find two integers that have a sum of and a product of .

For this equation, that would be 8 and 9.

8+9=17

$8\cdot 9=72$

Therefore, the solutions to this equation are (-8,-9)

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Algebra 1 : Quadratic Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #19 : How To Factor The Quadratic Equation

Example Question #233 : Equations / Inequalities

Example Question #21 : How To Factor The Quadratic Equation

Example Question #22 : How To Factor The Quadratic Equation

All Algebra 1 Resources

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