About Solving Quadratic Equations by Factoring:
In some cases, quadratic equations can be solved using factoring. To solve this type of equation using factoring, we move all terms to the left side and write the resulting equation in standard form. The right side will simply be zero. At this point, we can factor the left side and set each factor with a variable equal to zero. Solving the resulting equations will give us our solution(s).
Test Objectives
- Demonstrate the ability to write a quadratic equation in standard form
- Demonstrate the ability to factor a polynomial
- Demonstrate the ability to use the zero factor property to solve an equation
#1:
Instructions: solve each equation.
$$a)\hspace{.2em}75x^2 + 133x - 101=4 + 5x^2$$
$$b)\hspace{.2em}107x^2 - 258x - 56=2x^2 + x$$
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#2:
Instructions: solve each equation.
$$a)\hspace{.2em}10x^2 - 66x + 110=x^2 + 5$$
$$b)\hspace{.2em}67x^2 - 150x + 67=-5 - 8x^2$$
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#3:
Instructions: solve each equation.
$$a)\hspace{.2em}35x^2 -112=266x$$
$$b)\hspace{.2em}14x^2 - 80x + 76=-4 - x^2$$
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#4:
Instructions: solve each equation.
$$a)\hspace{.2em}15x^2 - 16=-21x + 2$$
$$b)\hspace{.2em}42x^2 - 174x + 140=-4$$
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#5:
Instructions: solve each equation.
$$a)\hspace{.2em}174 + 162x=6 - 30x^2$$
$$b)\hspace{.2em}14x^2 - 35x=-7x^2 + 56$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}x=-\frac{5}{2}, \frac{3}{5}$$
$$b)\hspace{.2em}x=-\frac{1}{5}, \frac{8}{3}$$
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#2:
Solutions:
$$a)\hspace{.2em}x=\frac{7}{3}, 5$$
$$b)\hspace{.2em}x=\frac{6}{5}, \frac{4}{5}$$
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#3:
Solutions:
$$a)\hspace{.2em}x=-\frac{2}{5}, 8$$
$$b)\hspace{.2em}x=\frac{4}{3}, 4$$
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#4:
Solutions:
$$a)\hspace{.2em}x=-2, \frac{3}{5}$$
$$b)\hspace{.2em}x=\frac{8}{7}, 3$$
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#5:
Solutions:
$$a)\hspace{.2em}x=-4, -\frac{7}{5}$$
$$b)\hspace{.2em}x=-1, \frac{8}{3}$$
