Question

factor each polynomial. remember to check if a gcf can be factored out of the polynomial.

1. $a^2 - 6a - 7$
2. $c^2 - 7c + 12$
3. $h^2 - 11h + 24$
4. $b^2 + 12b + 36$
5. $h^2 - 11h + 18$
6. $n^2 + 14n + 49$

$x^2 + 5x - 24$

1. $-2x^2 - 16x - 24$

Explanation:

Let's solve problem 4: \(a^{2}-6a - 7\)

Step 1: Find two numbers

We need two numbers that multiply to \(-7\) (the constant term) and add up to \(-6\) (the coefficient of the middle term). The numbers are \(-7\) and \(1\) because \(-7\times1=-7\) and \(-7 + 1=-6\).

Step 2: Factor the polynomial

Using the two numbers found, we can factor the quadratic polynomial as follows:
\(a^{2}-6a - 7=(a - 7)(a+ 1)\)

Step 1: Find two numbers

We need two numbers that multiply to \(12\) (the constant term) and add up to \(-7\) (the coefficient of the middle term). The numbers are \(-3\) and \(-4\) because \((-3)\times(-4)=12\) and \(-3+(-4)=-7\).

Step 2: Factor the polynomial

Using the two numbers found, we can factor the quadratic polynomial as follows:
\(c^{2}-7c + 12=(c - 3)(c - 4)\)

Step 1: Find two numbers

We need two numbers that multiply to \(24\) (the constant term) and add up to \(-11\) (the coefficient of the middle term). The numbers are \(-3\) and \(-8\) because \((-3)\times(-8)=24\) and \(-3+(-8)=-11\).

Step 2: Factor the polynomial

Using the two numbers found, we can factor the quadratic polynomial as follows:
\(h^{2}-11h + 24=(h - 3)(h - 8)\)

Answer:

\((a - 7)(a + 1)\)

Let's solve problem 5: \(c^{2}-7c + 12\)