Question

factoring by greatest common factor (gcf)
use your knowledge of greatest common factor to answer questions 1 and 2.

1. what is the greatest common factor of

$6x^2 - 3x + 18$?
a. 3
b. 3x
c. 6x
d. there is no gcf

1. which of the following polynomials cannot

be factored by factoring out a gcf?
a. $9x^2 - 81x + 27$
b. $15x^2 + 3x$
c. $2x + 4$
d. $3x^2 + 12x + 14$
in 3 - 6, factor each polynomial.

1. $16x^2 - 22x$
2. $-7t^2 - 42t - 49$
3. $-10r^2 + 25r$
4. $6x^2 + 144x - 12$

Explanation:

Question 1

Step1: Find GCF of coefficients

Coefficients: 6, -3, 18. GCF of 6, 3, 18 is 3.

Step2: Check variable terms

Terms: \(6x^2\), \(-3x\), \(18\). The term 18 has no \(x\), so GCF has no \(x\).

• Option a: \(9x^2 - 81x + 27\), GCF is 9.
• Option b: \(15x^2 + 3x\), GCF is 3x.
• Option c: \(2x + 4\), GCF is 2.
• Option d: \(3x^2 + 12x + 14\). GCF of 3, 12, 14: GCF(3,12)=3, GCF(3,14)=1. So no GCF to factor out.

Step1: Find GCF of \(16x^2\) and \(-22x\)

GCF of 16 and 22 is 2; GCF of \(x^2\) and \(x\) is \(x\). So GCF is \(2x\).

Step2: Factor out GCF

\(16x^2 - 22x = 2x(8x - 11)\)

Answer:

a. 3

Question 2