Find the completely factored form of the given polynomial: 2x^2 + 2x - 40 Assume all missi… — Armed Services Vocational Aptitude Battery (ASVAB)

Find the completely factored form of the given polynomial:

2x^2 + 2x - 40

Assume all missing values in the blanks are positive integers.

Answer:The completely factored expression is 【2】(x + 【5】)(x - 【4】).

The missing values are 2, 5, and 4. The completely factored expression is 2(x + 5)(x - 4).

Factoring out the greatest common factor of 2 leaves

x^2 + x - 20

. This trinomial factors into

(x + 5)(x - 4)

because 5 and -4 multiply to give -20 and add to give 1. Thus, the complete factored form is

2(x + 5)(x - 4)

, corresponding to the blank values 2, 5, and 4.

Factor out the greatest common factor (GCF) from all the terms in the polynomial.

2(x^2 + x - 20)

Identifying and extracting the GCF of 2 simplifies the remaining trinomial, making it easier to factor.

Factor the resulting quadratic trinomial

x^2 + x - 20

Find two numbers that multiply to -20 and add to 1 (the coefficient of x).

To factor a trinomial of the form

x^2 + bx + c

, you must find two factors of

c

that add up to

b

Identify the two numbers that satisfy the conditions.

The numbers are 5 and -4.

5 \times (-4) = -20

and

5 + (-4) = 1

Write the complete factorization by combining the GCF and the factored binomials.

2(x + 5)(x - 4)

This represents the original polynomial completely factored into its simplest terms.

Factoring Polynomials with a Greatest Common Factor

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