Question

 Shauna solve the polynomial equations given in the table determine whether each polynomial is correct select correct or incorrect for each equation

Answer 1

correct / incorrect / incorrect

Explanation:

5a - 8 + 2a² + 2a - 1 ← collect like terms

= 2a² + 7a - 9 ← correct

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b² + 6b - 4 - (3b + b²) ← distribute parenthesis by - 1

= b² + 6b - 4 - 3b - b² ← collect like terms

= 3b - 4 ≠ 2b² + 3b - 4

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9c - 4c² - (2c² + c) ← distribute parenthesis by - 1

= 9c - 4c² - 2c² - c ← collect like terms

= - 6c² + 8c ≠ - 6c² + 10c

Answer 2

correct

incorrect

incorrect

Explanation:

`\begin{aligned}(5a-8)+(2a^2+2a-1)&=5a-8+2a^2+2a-1\\& = 2a^2+5a+2a-8-1\\ & = 2a^2+7a-9\end{aligned}`

`\implies (5a-8)+(2a^2+2a-1)=2a^2+7a-9\quad\textsf{is correct}`

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`\begin{aligned}(b^2+6b-4)-(3b+b^2) &=b^2+6b-4-3b-b^2\\ & = b^2-b^2+6b-3b-4\\& = 3b-4\end{aligned}`

`\implies (b^2+6b-4)-(3b+b^2)=2b^2+3b-4\quad\textsf{is incorrect}`

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`\begin{aligned}(9c-4c^2)-(2c^2+c) &=9c-4c^2-2c^2-c\\ & = -4c^2-2c^2+9c-c\\& = -6c^2+8c\end{aligned}`

`\implies (9c-4c^2)-(2c^2+c)=-6c^2+10c\quad\textsf{is incorrect}`