Answer :
To find the product of [tex]\((x-7)(2x-5)\)[/tex], follow these steps:
1. Distribute each term in the first binomial to each term in the second binomial. This is also known as the FOIL method (First, Outer, Inner, Last):
[tex]\[
(x-7)(2x-5) = x \cdot 2x + x \cdot (-5) + (-7) \cdot 2x + (-7) \cdot (-5)
\][/tex]
2. Multiply the terms:
- First: [tex]\( x \cdot 2x = 2x^2 \)[/tex]
- Outer: [tex]\( x \cdot (-5) = -5x \)[/tex]
- Inner: [tex]\( (-7) \cdot 2x = -14x \)[/tex]
- Last: [tex]\( (-7) \cdot (-5) = 35 \)[/tex]
3. Sum these results to form a single polynomial:
[tex]\[
2x^2 + (-5x) + (-14x) + 35
\][/tex]
4. Combine like terms ([tex]\(-5x\)[/tex] and [tex]\(-14x\)[/tex]):
[tex]\[
2x^2 - 5x - 14x + 35 = 2x^2 - 19x + 35
\][/tex]
Therefore, the product is:
[tex]\[
2x^2 - 19x + 35
\][/tex]
This matches choice E in the given options. Thus, the correct answer is:
E. [tex]\(2x^2 - 19x + 35\)[/tex]
1. Distribute each term in the first binomial to each term in the second binomial. This is also known as the FOIL method (First, Outer, Inner, Last):
[tex]\[
(x-7)(2x-5) = x \cdot 2x + x \cdot (-5) + (-7) \cdot 2x + (-7) \cdot (-5)
\][/tex]
2. Multiply the terms:
- First: [tex]\( x \cdot 2x = 2x^2 \)[/tex]
- Outer: [tex]\( x \cdot (-5) = -5x \)[/tex]
- Inner: [tex]\( (-7) \cdot 2x = -14x \)[/tex]
- Last: [tex]\( (-7) \cdot (-5) = 35 \)[/tex]
3. Sum these results to form a single polynomial:
[tex]\[
2x^2 + (-5x) + (-14x) + 35
\][/tex]
4. Combine like terms ([tex]\(-5x\)[/tex] and [tex]\(-14x\)[/tex]):
[tex]\[
2x^2 - 5x - 14x + 35 = 2x^2 - 19x + 35
\][/tex]
Therefore, the product is:
[tex]\[
2x^2 - 19x + 35
\][/tex]
This matches choice E in the given options. Thus, the correct answer is:
E. [tex]\(2x^2 - 19x + 35\)[/tex]
