Expand the given product of a binomial and a trinomial, combine like terms, and determine … — Armed Services Vocational Aptitude Battery (ASVAB)

Expand the given product of a binomial and a trinomial, combine like terms, and determine the values of the missing coefficients.

Answer:When the expression

(3x - 5)(2x^2 + 4x - 7)

is fully expanded and simplified, the resulting polynomial in standard form is

6x^3 +

【2】

x^2 +

【-41】

x + 35

The coefficient for the x^2 term is 2, and the coefficient for the x term is -41.

By distributing each term of the binomial

(3x - 5)

to every term of the trinomial

(2x^2 + 4x - 7)

, we get six terms. Grouping and combining the like terms yields an

x^2

coefficient of

12 - 10 = 2

and an

x

coefficient of

-21 - 20 = -41

Distribute the first term of the binomial,

3x

, to each term in the trinomial.

3x(2x^2) + 3x(4x) + 3x(-7) = 6x^3 + 12x^2 - 21x

To apply the distributive property for the first part of the polynomial multiplication.

Distribute the second term of the binomial,

-5

, to each term in the trinomial.

-5(2x^2) - 5(4x) - 5(-7) = -10x^2 - 20x + 35

To apply the distributive property for the second part, being careful to carry the negative sign.

Combine the results and group the like terms.

6x^3 + (12x^2 - 10x^2) + (-21x - 20x) + 35

To arrange the expression so that coefficients of terms with the same exponent can be simplified.

Simplify the grouped terms.

6x^3 + 2x^2 - 41x + 35

By adding the coefficients:

12 - 10 = 2

and

-21 - 20 = -41

Distributive Property with Polynomials

You can use the 'box method' (a grid) by creating a 2x3 table with

3x

and

-5

on the rows, and

2x^2

4x

, and

-7

on the columns. Multiply the row and column headers to fill each cell, then add all the cells together along the diagonals to combine like terms.

Estimated Time:1m 30s

Question