Answer :
To solve the problem of finding the result of the product [tex]\((3x + 7)(2x - 5)\)[/tex], we can use the distributive property, often referred to as the FOIL method for binomials. The FOIL method helps us remember to multiply every term in the first binomial by every term in the second binomial. Here's how you can do it step-by-step:
1. First: Multiply the first terms in each binomial:
[tex]\(3x \cdot 2x = 6x^2\)[/tex]
2. Outer: Multiply the outer terms in the product:
[tex]\(3x \cdot (-5) = -15x\)[/tex]
3. Inner: Multiply the inner terms in the product:
[tex]\(7 \cdot 2x = 14x\)[/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\(7 \cdot (-5) = -35\)[/tex]
Now, combine the results:
- The [tex]\(x^2\)[/tex] term is simply [tex]\(6x^2\)[/tex].
- The [tex]\(x\)[/tex] terms are [tex]\(-15x\)[/tex] and [tex]\(14x\)[/tex]. Adding these together gives:
[tex]\(-15x + 14x = -1x\)[/tex].
- The constant term is [tex]\(-35\)[/tex].
Putting all the pieces together, the polynomial expression is:
[tex]\[6x^2 - 1x - 35\][/tex]
This corresponds to option (3): [tex]\(6x^2 - x - 35\)[/tex].
1. First: Multiply the first terms in each binomial:
[tex]\(3x \cdot 2x = 6x^2\)[/tex]
2. Outer: Multiply the outer terms in the product:
[tex]\(3x \cdot (-5) = -15x\)[/tex]
3. Inner: Multiply the inner terms in the product:
[tex]\(7 \cdot 2x = 14x\)[/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\(7 \cdot (-5) = -35\)[/tex]
Now, combine the results:
- The [tex]\(x^2\)[/tex] term is simply [tex]\(6x^2\)[/tex].
- The [tex]\(x\)[/tex] terms are [tex]\(-15x\)[/tex] and [tex]\(14x\)[/tex]. Adding these together gives:
[tex]\(-15x + 14x = -1x\)[/tex].
- The constant term is [tex]\(-35\)[/tex].
Putting all the pieces together, the polynomial expression is:
[tex]\[6x^2 - 1x - 35\][/tex]
This corresponds to option (3): [tex]\(6x^2 - x - 35\)[/tex].
