Question

Find values for a, b, c, and d to make equation an identity.

(3x³-2ax² + bx + 1) - (cx³ + 5x² - 7x + 9) = -x³ + x² - 2x + 4d

Answer 1

a = 2, b = 5, c = 4, and d = -2.

Explanation:

In order for the equation to be an identity, the coefficients of each degree term on both sides of the equation must be equal.

Equating the coefficients of the x³ terms, we get:

3 - c = -1

c = 4

Equating the coefficients of the x² terms, we get:

-2a + 5 = 1

a = 2

Equating the coefficients of the x terms, we get:

b - 7 = -2

b = 5

Equating the constant terms, we get:

1 - 9 = 4d

d = -2

Therefore, the values of a, b, c, and d that make the equation an identity are:

a = 2, b = 5, c = 4, and d = -2.