Factor each trinomial. Then match the polynomial (term) on the left with its factored form (definition) on the right.Match Term Definition

x2 – 8x – 20 A) (x – 5)(x + 4)

x2 + 8x – 20 B) (x – 10)(x + 2)

x2 – x – 20 C) Prime

x2 – 9x – 20 D) (x – 2)(x + 10)

Answer:

Step-by-step explanation:

The given equation is:

Simplifying the above equation, we get

therefore, the equation matches with (B) .

The given equation is :

Simplifying the above equation, we get

therefore, the equation matches with (D)

The given equation is:

Simplifying the above equation, we get

therefore, the equation matches with (A) .

The given equation is:

This equation ca't be firther simplified or factorised, thus the equation matches with (C) Prime.

the correct matches for the polynomials are:

A) (x – 5)(x + 4) matches with x^2 – x – 20.

B) (x – 10)(x + 2) matches with x^2 + 8x – 20.

C) Prime does not match any of the given terms.

D) (x – 2)(x + 10) matches with x^2 – 9x – 20.

How did we arrive at these assertions?

Let's factor each trinomial and match them with their factored forms:

x² – 8x – 20:

To factor this trinomial, we need to find two numbers that multiply to give -20 and add up to -8. The numbers that satisfy these conditions are -10 and 2. Therefore, the factored form is (x – 10)(x + 2). Match: A.

x² + 8x – 20:

For this trinomial, we once again look for two numbers that multiply to give -20 and add up to 8. The numbers are -2 and 10. Hence, the factored form is (x – 2)(x + 10). Match: D.

x² – x – 20:

Here, we seek two numbers that multiply to give -20 and add up to -1. The numbers -5 and 4 satisfy these conditions. Thus, the factored form is (x – 5)(x + 4). Match: A.

x² – 9x – 20:

Similar to the previous trinomials, we search for two numbers that multiply to give -20 and add up to -9. The numbers are -10 and 1. So, the factored form is (x – 10)(x + 1). Match: B.

Matching the terms with their factored forms:

A) (x – 5)(x + 4) matches with x² – x – 20.

B) (x – 10)(x + 2) matches with x² + 8x – 20.

C) Prime does not match any of the given terms.

D) (x – 2)(x + 10) matches with x² – 9x – 20.

Therefore, the correct matches are:

A) (x – 5)(x + 4) matches with x² – x – 20.

B) (x – 10)(x + 2) matches with x² + 8x – 20.

C) Prime does not match any of the given terms.

D) (x – 2)(x + 10) matches with x² – 9x – 20.

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