Question

factor the gcf out of each polynomial.

1. $10x^3 + 4x^2 + 8x$
2. $3x^5y + 27x^3y^2$
3. $7x^7 + 14x^6 + 28x$

factor each polynomial completely.

1. $x^2 + 8x + 7$
2. $x^2 + 10x + 21$
3. $x^2 + 9x + 20$
4. $x^2 + 11x + 30$
5. $x^2 - 10x + 24$
6. $x^2 + 2x - 48$
7. $6x^2 - 5x + 1$
8. $2x^2 + 5x + 2$
9. $4x^2 + 4x - 3$
10. $3x^2 + 3x - 6$
11. $8x^2 + 8x - 48$
12. $4x^2 - 19x - 5$

Explanation:

Let's solve problem 4: \( x^2 + 8x + 7 \)

Step 1: Identify the form

The polynomial is a quadratic of the form \( x^2 + bx + c \), where \( b = 8 \) and \( c = 7 \). We need to find two numbers that multiply to \( c \) (7) and add up to \( b \) (8).

Step 2: Find the numbers

The factors of 7 are 1 and 7. And \( 1 + 7 = 8 \), which matches \( b \).

Step 3: Factor the polynomial

Using these two numbers, we can factor the quadratic as \( (x + 1)(x + 7) \).

Answer:

\((x + 1)(x + 7)\)