About Factoring Trinomials Using Trial & Error:
When we factor a trinomial into the product of two binomials, we encounter two very different scenarios. The harder scenario occurs when the leading coefficient is not one. When this happens, we generally have two methods available: factoring by grouping and reverse FOIL (trial and error). In order to use the reverse FOIL method, we reverse each step of the FOIL process.
Test Objectives
- Demonstrate the ability to factor out the GCF or -(GCF) from a group of terms
- Demonstrate the ability to factor a trinomial into the product of two binomials
- Demonstrate the ability to factor a trinomial when two variables are involved
#1:
Instructions: Factor each.
$$a)\hspace{.2em}14x^2 + 96x - 128$$
$$b)\hspace{.2em}15x^2 + 69x + 72$$
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#2:
Instructions: Factor each.
$$a)\hspace{.2em}35x^2 - 45x - 50$$
$$b)\hspace{.2em}5x^2 + 13x - 6$$
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#3:
Instructions: Factor each.
$$a)\hspace{.2em}3x^2 + 5x - 15$$
$$b)\hspace{.2em}30x^2 + 65x + 30$$
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#4:
Instructions: Factor each.
$$a)\hspace{.2em}{-}27x^2 - 177x - 90$$
$$b)\hspace{.2em}40x^2 - 108x - 324$$
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#5:
Instructions: Factor each.
$$a)\hspace{.2em}45x^2 - 260xy - 60y^2$$
$$b)\hspace{.2em}12x^2 - 57xy - 189y^2$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}2(7x - 8)(x + 8)$$
$$b)\hspace{.2em}3(5x + 8)(x + 3)$$
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#2:
Solutions:
$$a)\hspace{.2em}5(7x + 5)(x - 2)$$
$$b)\hspace{.2em}(5x - 2)(x + 3)$$
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#3:
Solutions:
$$a)\hspace{.2em}\text{Prime}$$
$$b)\hspace{.2em}5(3x + 2)(2x + 3)$$
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#4:
Solutions:
$$a)\hspace{.2em}{-}3(x + 6)(9x + 5)$$
$$b)\hspace{.2em}4(5x + 9)(2x - 9)$$
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#5:
Solutions:
$$a)\hspace{.2em}5(x - 6y)(9x + 2y)$$
$$b)\hspace{.2em}3(x - 7y)(4x + 9y)$$
