Question

1. $12x^2 - 2x$ 36. $12u^7 - 9u^5$ 37. $10r^3 - 35r$ 38. $-144a^8 + 24a^6$ 39. $12x^2 + 16x - 8$ 40. $9 - 3y - 15y^2$ 41. $100 - 75z - 50z^2$ 42. $42t^3 - 21t^2 + 7$ 43. $9x^4 + 6x^3 + 18x^2$ 44. $32a^5 - 2a^3 + 6a$

Explanation:

Let's solve one of these problems, say problem 35: \(12x^2 - 2x\)

Step1: Identify the GCF

The terms are \(12x^2\) and \(-2x\). The GCF of 12 and 2 is 2, and the GCF of \(x^2\) and \(x\) is \(x\). So the GCF is \(2x\).

Step2: Factor out the GCF

Divide each term by \(2x\): \(\frac{12x^2}{2x} = 6x\) and \(\frac{-2x}{2x} = -1\). So we get \(2x(6x - 1)\).

Another example, problem 37: \(10r^3 - 35r\)

Step1: Find the GCF

For \(10r^3\) and \(-35r\), GCF of 10 and 35 is 5, GCF of \(r^3\) and \(r\) is \(r\). So GCF is \(5r\).

Step2: Factor out GCF

Divide each term by \(5r\): \(\frac{10r^3}{5r} = 2r^2\) and \(\frac{-35r}{5r} = -7\). Thus, \(5r(2r^2 - 7)\).

For problem 43: \(9x^4 + 6x^3 + 18x^2\)

Step1: Determine GCF

GCF of 9, 6, 18 is 3; GCF of \(x^4\), \(x^3\), \(x^2\) is \(x^2\). So GCF is \(3x^2\).

Step2: Factor out GCF

Divide each term by \(3x^2\): \(\frac{9x^4}{3x^2}=3x^2\), \(\frac{6x^3}{3x^2}=2x\), \(\frac{18x^2}{3x^2}=6\). So we have \(3x^2(3x^2 + 2x + 6)\).

Answer:

\(2x(6x - 1)\)