About Factoring Out the GCF:
In some cases, we will need to reverse our distributive property and change a sum into a product. This process is known as factoring. When we factor out the GCF from a polynomial, we are basically pulling out the largest factor that each term of the polynomial is divisible by.
Test Objectives
- Demonstrate the ability to find the GCF of a group of monomial terms
- Demonstrate the ability to factor out the GCF from a polynomial
#1:
Instructions: Find the GCF.
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$$a)\hspace{.2em}{-}3x^2y^4, 9xy^2, 12x^3y^3$$
$$b)\hspace{.2em}20x^4y^2z, -15x^3y^2, 30x^3yz^2$$
$$c)\hspace{.2em}165x^6y^2z^3, 231x^4y^2z^2, 165x^3y^2z$$
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#2:
Instructions: Factor out the GCF.
$$a)\hspace{.2em}6x^3y^2 + 8x^2y - 4xy + 12y$$
$$b)\hspace{.2em}16x^2y^3z + 32x^4y^3 - 48x^2y^4$$
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#3:
Instructions: Factor out the GCF.
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$$a)\hspace{.2em}65x^2y^2z^2 - 260x^3y^3z^3 + 91x^4y^4z^4$$
$$b)\hspace{.2em}68x^9y^{15}z - 153x^3y^5 + 357x^2z^2$$
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#4:
Instructions: Factor out the GCF.
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$$a)\hspace{.2em}2(x + y) + 4z(x + y)$$
$$b)\hspace{.2em}(5x - 6)(x + 3) - (2x - 1)(x + 3)$$
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#5:
Instructions: Factor out the GCF.
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$$a)\hspace{.2em}5y(x + 3)^3 + (x + 3)^2 - 2(x + 3)$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}3xy^2$$
$$b)\hspace{.2em}5x^3y$$
$$c)\hspace{.2em}33x^3y^2z$$
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#2:
Solutions:
$$a)\hspace{.2em}2y(3x^3y + 4x^2 - 2x + 6)$$
$$b)\hspace{.2em}16x^2y^3(2x^2 - 3y + z)$$
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#3:
Solutions:
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$$a)\hspace{.2em}13x^2y^2z^2(7x^2y^2z^2 - 20xyz + 5)$$
$$b)\hspace{.2em}17x^2(4x^7y^{15}z - 9xy^5 + 21z^2)$$
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#4:
Solutions:
$$a)\hspace{.2em}2(x + y)(2z + 1)$$
$$b)\hspace{.2em}(x + 3)(3x - 5)$$
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#5:
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Solutions:
$$a)\hspace{.2em}(x + 3)(5x^2y + 30xy + 45y + x + 1)$$
