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actoring $3x^2-6x-4x+8$3, x, start superscript, 2, end superscript, minus, 6, x, minus, 4, x, plus, 8

Extra care should be taken when using the grouping method to factor a polynomial with negative coefficients.

For example, the steps below can be used to factor $3x^2-6x-4x+8$3, x, start superscript, 2, end superscript, minus, 6, x, minus, 4, x, plus, 8.

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$\begin{aligned}\phantom{0}&&&\phantom{=}3x^2-6x-4x+8\\\\ \small{\blueD{(1)}}&&&=(3x^2-6x)+(-4x+8)&&\small{\gray{\text{Group terms}}}\\\\ \small{\blueD{(2)}}&&&=3x(x-2)+(-4)(x-2)&&\small{\gray{\text{Factor out GCFs}}}\\\\ \small{\blueD{(3)}}&&&=3x(x-2)-4(x-2)&&\small{\gray{\text{Simplify}}}\\\\ \small{\blueD{(4)}}&&&=3x(\goldD{x-2})-4(\goldD{x-2})&&\small{\gray{\text{Common factor!}}}\\\\ \small{\blueD{(5)}}&&&=(\goldD{x-2})(3x-4)&&\small{\gray{\text{Factor out $x-2$}}}\\\\ \end{aligned}$

The factored form of the polynomial is $(x-2)(3x-4)$left parenthesis, x, minus, 2, right parenthesis, left parenthesis, 3, x, minus, 4, right parenthesis. We can multiply the binomials to check our work.

[I'd like to see this, please!]

Check your understanding

1) Factor $9x^2+6x+12x+8$9, x, start superscript, 2, end superscript, plus, 6, x, plus, 12, x, plus, 8.

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Choose 1 answer:

• (Choice A, Checked)

  A
• (Choice B)

  B
• (Choice C)

  C
• (Choice D)

  D