Question Subtract $7x^2 + 4x - 9$ from $5x^2 + 10x - 5$ . Express the result as a trinomial in descending degree order.

Studdy Solution

STEP 1

Assumptions
1. We are given two polynomials: $7x^{2}+4x-9$ and $5x^{2}+10x-5$ .
2. We need to subtract the first polynomial from the second.
3. The result should be expressed as a trinomial in descending degree order.

STEP 2

To subtract the polynomial $7x^{2}+4x-9$ from $5x^{2}+10x-5$ , we need to change the sign of each term in the first polynomial and then add it to the corresponding term in the second polynomial.
$(5x^{2}+10x-5) - (7x^{2}+4x-9)$

STEP 3

Change the sign of each term in the first polynomial.
$(5x^{2}+10x-5) - (7x^{2}+4x-9) = 5x^{2}+10x-5 - 7x^{2} - 4x + 9$

STEP 4

Combine like terms by adding the coefficients of the $x^{2}$ terms, the $x$ terms, and the constant terms separately.
$(5x^{2} - 7x^{2}) + (10x - 4x) + (-5 + 9)$

STEP 5

Perform the subtraction for the $x^{2}$ terms.
$5x^{2} - 7x^{2} = -2x^{2}$

STEP 6

Perform the subtraction for the $x$ terms.
$10x - 4x = 6x$

STEP 7

Perform the addition for the constant terms.
$-5 + 9 = 4$

STEP 8

Combine the results from steps 5, 6, and 7 to form the resulting trinomial.
$-2x^{2} + 6x + 4$
The result of subtracting $7x^{2}+4x-9$ from $5x^{2}+10x-5$ is the trinomial $-2x^{2} + 6x + 4$ in descending degree order.

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