Multiply the binomials (x - 5) and (x + 2). Fill in the missing values for the resulting e… — Armed Services Vocational Aptitude Battery (ASVAB)

Multiply the binomials $(x - 5)$ and $(x + 2)$ . Fill in the missing values for the resulting expanded expression $x^2 + bx + c$ .

Cevap:The value of

b

is 【-3】.
The value of

c

is 【-10】.

The value of b is -3 and the value of c is -10.

By applying the FOIL method, you multiply the First terms (

x \times x = x^2

), Outer terms (

x \times 2 = 2x

), Inner terms (

-5 \times x = -5x

), and Last terms (

-5 \times 2 = -10

). Combining the like terms (

2x - 5x

) results in

-3x

. The fully expanded expression is

x^2 - 3x - 10

. Comparing this to the standard form

x^2 + bx + c

, we find that the coefficient for the middle term

b

-3

and the constant term

c

-10

Use the FOIL method to distribute the terms in the binomials.

(x \times x) + (x \times 2) + (-5 \times x) + (-5 \times 2)

Each term in the first binomial, including its sign, must be multiplied by each term in the second binomial.

Perform the multiplications for each pair.

x^2 + 2x - 5x - 10

This expands the product using the rules for multiplying positive and negative numbers.

Combine the like terms.

x^2 - 3x - 10

Adding the middle terms (

2x

and

-5x

) simplifies the expression into the standard form

x^2 + bx + c

Multiplying Polynomials

Soru