Question

factoring ax² + bx + c
independent practice
name
date
pd
factor each of the polynomials in 1 - 6 and use the answer bank to check your work. not all
choices will be used.
(2x - 5) (6x - 1) (x + 9) (7x - 2) (x + 2) (3x - 1) (6x + 1)
(x - 9) (4x + 3) (3x + 1) (4x - 3) (x - 1) (2x + 3) (7x + 2)

1. 7x² + 16x + 4
2. 3x² + 26x - 9
3. 12x² - 28x - 5
4. 6x² - 55x + 9
5. 4x² - x - 3
6. 21x² + x - 2

use your knowledge of factoring to answer questions 7 and 8.

1. fernando and risa are factoring

5x² - x - 6. they each made a chart below
selected a pair of inte
student
explain
ning.

1. lawson is pouring a rectangular

slab for his doghouse. the slab w
area of 5x² + 12x - 9 square fee
expressions that represent pos
dimensions for the length and
concrete slab.

Explanation:

Step1: Factor \(7x^{2}+16x + 4\)

For \(ax^{2}+bx + c\) (\(a = 7\), \(b=16\), \(c = 4\)), find two numbers \(m\) and \(n\) such that \(m\times n=a\times c=7\times4 = 28\) and \(m + n=b = 16\). The numbers are \(14\) and \(2\).

$$
LATEXBLOCK0
$$

Step2: Factor \(3x^{2}+26x-9\)

For \(ax^{2}+bx + c\) (\(a = 3\), \(b = 26\), \(c=-9\)), find two numbers \(m\) and \(n\) such that \(m\times n=a\times c=3\times(-9)=-27\) and \(m + n=b = 26\). The numbers are \(27\) and \(-1\).

$$
LATEXBLOCK1
$$

Step3: Factor \(12x^{2}-28x-5\)

For \(ax^{2}+bx + c\) (\(a = 12\), \(b=-28\), \(c=-5\)), find two numbers \(m\) and \(n\) such that \(m\times n=a\times c=12\times(-5)=-60\) and \(m + n=b=-28\). The numbers are \(-30\) and \(2\).

$$
LATEXBLOCK2
$$

Step4: Factor \(6x^{2}-55x + 9\)

For \(ax^{2}+bx + c\) (\(a = 6\), \(b=-55\), \(c = 9\)), find two numbers \(m\) and \(n\) such that \(m\times n=a\times c=6\times9 = 54\) and \(m + n=b=-55\). The numbers are \(-54\) and \(-1\).

$$
LATEXBLOCK3
$$

Step5: Factor \(4x^{2}-x-3\)

For \(ax^{2}+bx + c\) (\(a = 4\), \(b=-1\), \(c=-3\)), find two numbers \(m\) and \(n\) such that \(m\times n=a\times c=4\times(-3)=-12\) and \(m + n=b=-1\). The numbers are \(-4\) and \(3\).

$$
LATEXBLOCK4
$$

Step6: Factor \(21x^{2}+x-2\)

For \(ax^{2}+bx + c\) (\(a = 21\), \(b = 1\), \(c=-2\)), find two numbers \(m\) and \(n\) such that \(m\times n=a\times c=21\times(-2)=-42\) and \(m + n=b = 1\). The numbers are \(7\) and \(-6\).

$$
LATEXBLOCK5
$$

Answer:

1. \((7x + 2)(x + 2)\)
2. \((3x-1)(x + 9)\)
3. \((6x + 1)(2x-5)\)
4. \((6x-1)(x - 9)\)
5. \((4x + 3)(x-1)\)
6. \((7x-2)(3x + 1)\)