Polynomial combining like terms (SAT) practice

Distribute the minus sign: $(5x^2 + 3x + 2) - 2x^2 + 5$. Combine $x^2$ terms: $5x^2 - 2x^2 = 3x^2$. The $x$ term stays $3x$. Combine constants: $2 + 5 = 7$. Result: $3x^2 + 3x + 7$.

Combine $x^2$ terms: $x^2 + 2x^2 = 3x^2$. The $x$ terms cancel: $4x - 4x = 0$. Combine constants: $-5 + 9 = 4$. Result: $3x^2 + 4$.

Combine $x^2$ terms: $x^2 + 4x^2 = 5x^2$. The constants cancel: $6 - 6 = 0$. Result: $5x^2$.

Distribute the minus sign: $(4x^2 - x + 6) - 2x^2 - 3x + 1$. Combine $x^2$ terms: $4x^2 - 2x^2 = 2x^2$. Combine $x$ terms: $-x - 3x = -4x$. Combine constants: $6 + 1 = 7$. Result: $2x^2 - 4x + 7$.

Distribute the minus sign: $(5x^2 + 3) - x^2 + 2x$. Combine $x^2$ terms: $5x^2 - x^2 = 4x^2$. The $x$ term is $2x$. The constant stays $3$. Result: $4x^2 + 2x + 3$.

Combine $x^2$ terms: $2x^2 - x^2 = x^2$. Combine $x$ terms: $7x + 2x = 9x$. Combine constants: $1 - 4 = -3$. Result: $x^2 + 9x - 3$.

Distribute the minus sign: $(9x^2 - 4x) - 3x^2 + 4x - 5$. Combine $x^2$ terms: $9x^2 - 3x^2 = 6x^2$. The $x$ terms cancel: $-4x + 4x = 0$. The constant is $-5$. Result: $6x^2 - 5$.

Distribute the minus sign: $(7x^2 + 2x - 3) - 5x^2 + 2x - 1$. Combine $x^2$ terms: $7x^2 - 5x^2 = 2x^2$. Combine $x$ terms: $2x + 2x = 4x$. Combine constants: $-3 - 1 = -4$. Result: $2x^2 + 4x - 4$.