Given the polynomials [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
[tex]\[ A = x^2 + 5x + 17 \][/tex]
[tex]\[ B = 9x^2 - 9x + 2 \][/tex]
We need to find the factors of [tex]\( A - B \)[/tex].
Step-by-Step Solution:
1. Subtract the polynomials: Calculate [tex]\( A - B \)[/tex].
[tex]\[
A - B = (x^2 + 5x + 17) - (9x^2 - 9x + 2)
\][/tex]
2. Distribute the subtraction through the terms:
[tex]\[
A - B = x^2 + 5x + 17 - 9x^2 + 9x - 2
\][/tex]
3. Combine like terms:
Combining the [tex]\( x^2 \)[/tex] terms:
[tex]\[
x^2 - 9x^2 = -8x^2
\][/tex]
Combining the [tex]\( x \)[/tex] terms:
[tex]\[
5x + 9x = 14x
\][/tex]
Combining the constant terms:
[tex]\[
17 - 2 = 15
\][/tex]
So,
[tex]\[
A - B = -8x^2 + 14x + 15
\][/tex]
4. Factor the resulting polynomial:
The polynomial [tex]\( -8x^2 + 14x + 15 \)[/tex] can be factored into:
[tex]\[
-(2x - 5)(4x + 3)
\][/tex]
So, the factors of [tex]\( A - B \)[/tex] are:
[tex]\[
-(2x - 5)(4x + 3)
\][/tex]
