### About Factoring Trinomials (a = 1):

When we are asked to factor a trinomial into the product of two binomials, the easiest scenario occurs when our trinomial has a leading coefficient of 1. When this happens, we will automatically know the first term for each binomial. We only need to find the last term for each binomial. This can be found by determining which two integers sum to the middle coefficient and multiply to the final term (constant term). We often hear this as: find two integers whose sum is b (coefficient of the variable raised to the first power) and whose product is c (constant term).

Test Objectives

- Demonstrate an understanding of how to factor a whole number
- Demonstrate the ability to factor out the GCF
- Demonstrate the ability to factor a trinomial into the product of two binomials
- Demonstrate the ability to factor a trinomial with two variables

#1:

Instructions: Factor each.

$$a)\hspace{.2em}x^2 + 11x + 24$$

$$b)\hspace{.2em}x^2 + 6x - 16$$

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#2:

Instructions: Factor each.

$$a)\hspace{.2em}x^2 - 3x - 18$$

$$b)\hspace{.2em}x^2 + 18x + 80$$

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#3:

Instructions: Factor each.

$$a)\hspace{.2em}x^2 - 17x + 72$$

$$b)\hspace{.2em}6x^2 - 18x - 324$$

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#4:

Instructions: Factor each.

$$a)\hspace{.2em}3x^2 + 9xy - 54y^2$$

$$b)\hspace{.2em}5x^2y^2 + 45xy^3 + 100y^4$$

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#5:

Instructions: Factor each.

$$a)\hspace{.2em}3x^2 - 33xy + 90y^2$$

$$b)\hspace{.2em}6x^2 + 30xy - 36y^2$$

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}(x + 3)(x + 8)$$

$$b)\hspace{.2em}(x + 8)(x - 2)$$

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#2:

Solutions:

$$a)\hspace{.2em}(x - 6)(x + 3)$$

$$b)\hspace{.2em}(x + 8)(x + 10)$$

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#3:

Solutions:

$$a)\hspace{.2em}(x - 8)(x - 9)$$

$$b)\hspace{.2em}6(x - 9)(x + 6)$$

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#4:

Solutions:

$$a)\hspace{.2em}3(x - 3y)(x + 6y)$$

$$b)\hspace{.2em}5y^2(x + 4y)(x + 5y)$$

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#5:

Solutions:

$$a)\hspace{.2em}3(x - 5y)(x - 6y)$$

$$b)\hspace{.2em}6(x - y)(x + 6y)$$