Answer :
To find the product of the two polynomial expressions [tex]\( p(x) = 5x - 1 \)[/tex] and [tex]\( a(x) = 7x + 2 \)[/tex], follow these steps:
1. Set up the expression to multiply:
You need to multiply each term in [tex]\( p(x) \)[/tex] by each term in [tex]\( a(x) \)[/tex]. So, you have:
[tex]\[
(5x - 1)(7x + 2)
\][/tex]
2. Apply the distributive property (FOIL method for binomials):
- First: Multiply the first terms in each binomial:
[tex]\[
5x \cdot 7x = 35x^2
\][/tex]
- Outer: Multiply the outer terms:
[tex]\[
5x \cdot 2 = 10x
\][/tex]
- Inner: Multiply the inner terms:
[tex]\[
-1 \cdot 7x = -7x
\][/tex]
- Last: Multiply the last terms:
[tex]\[
-1 \cdot 2 = -2
\][/tex]
3. Combine all these results:
- Add up all the terms:
[tex]\[
35x^2 + 10x - 7x - 2
\][/tex]
4. Simplify the expression:
- Combine like terms:
[tex]\[
35x^2 + (10x - 7x) - 2 = 35x^2 + 3x - 2
\][/tex]
Thus, the product of the polynomials [tex]\( p(x) \)[/tex] and [tex]\( a(x) \)[/tex] is [tex]\( 35x^2 + 3x - 2 \)[/tex], which matches with the first multiple choice answer option given.
1. Set up the expression to multiply:
You need to multiply each term in [tex]\( p(x) \)[/tex] by each term in [tex]\( a(x) \)[/tex]. So, you have:
[tex]\[
(5x - 1)(7x + 2)
\][/tex]
2. Apply the distributive property (FOIL method for binomials):
- First: Multiply the first terms in each binomial:
[tex]\[
5x \cdot 7x = 35x^2
\][/tex]
- Outer: Multiply the outer terms:
[tex]\[
5x \cdot 2 = 10x
\][/tex]
- Inner: Multiply the inner terms:
[tex]\[
-1 \cdot 7x = -7x
\][/tex]
- Last: Multiply the last terms:
[tex]\[
-1 \cdot 2 = -2
\][/tex]
3. Combine all these results:
- Add up all the terms:
[tex]\[
35x^2 + 10x - 7x - 2
\][/tex]
4. Simplify the expression:
- Combine like terms:
[tex]\[
35x^2 + (10x - 7x) - 2 = 35x^2 + 3x - 2
\][/tex]
Thus, the product of the polynomials [tex]\( p(x) \)[/tex] and [tex]\( a(x) \)[/tex] is [tex]\( 35x^2 + 3x - 2 \)[/tex], which matches with the first multiple choice answer option given.
