Math / Algebra

Question1. Circle all of the following polynomials that are DEGREE 2: [1 mark] $\begin{array}{llll} 2 x+3 & -4 x^{2}+3 x-1 & (x+3)(x-2) & (x+4)^{2}-8 \end{array}$

Studdy Solution

STEP 1

1. A polynomial of degree 2 is a quadratic polynomial, which has the highest power of $x$ as 2.
2. We need to identify which of the given expressions are quadratic polynomials.

STEP 2

1. Analyze each polynomial to determine its degree.
2. Circle the polynomials that are of degree 2.

STEP 3

Analyze the polynomial $2x + 3$ :
- The highest power of $x$ is 1. - Therefore, it is not a degree 2 polynomial.

STEP 4

Analyze the polynomial $-4x^2 + 3x - 1$ :
- The highest power of $x$ is 2. - Therefore, it is a degree 2 polynomial.

STEP 5

Analyze the polynomial $(x+3)(x-2)$ :
- Expand the expression: $(x+3)(x-2) = x^2 - 2x + 3x - 6 = x^2 + x - 6$ - The highest power of $x$ is 2. - Therefore, it is a degree 2 polynomial.

STEP 6

Analyze the polynomial $(x+4)^2 - 8$ :
- Expand the expression: $(x+4)^2 - 8 = (x^2 + 8x + 16) - 8 = x^2 + 8x + 8$ - The highest power of $x$ is 2. - Therefore, it is a degree 2 polynomial.

STEP 7

Circle the polynomials that are of degree 2:
- $-4x^2 + 3x - 1$ - $(x+3)(x-2)$ - $(x+4)^2 - 8$
The polynomials that are degree 2 are:
$\boxed{-4x^2 + 3x - 1, \ (x+3)(x-2), \ (x+4)^2 - 8}$

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Question1. Circle all of the following polynomials that are DEGREE 2: [1 mark] $\begin{array}{llll} 2 x+3 & -4 x^{2}+3 x-1 & (x+3)(x-2) & (x+4)^{2}-8 \end{array}$

Studdy Solution

STEP 1

1. A polynomial of degree 2 is a quadratic polynomial, which has the highest power of $x$ as 2.
2. We need to identify which of the given expressions are quadratic polynomials.

STEP 2

1. Analyze each polynomial to determine its degree.
2. Circle the polynomials that are of degree 2.

STEP 3

Analyze the polynomial $2x + 3$ :
- The highest power of $x$ is 1. - Therefore, it is not a degree 2 polynomial.

STEP 4

Analyze the polynomial $-4x^2 + 3x - 1$ :
- The highest power of $x$ is 2. - Therefore, it is a degree 2 polynomial.

STEP 5

Analyze the polynomial $(x+3)(x-2)$ :
- Expand the expression: $(x+3)(x-2) = x^2 - 2x + 3x - 6 = x^2 + x - 6$ - The highest power of $x$ is 2. - Therefore, it is a degree 2 polynomial.

STEP 6

Analyze the polynomial $(x+4)^2 - 8$ :
- Expand the expression: $(x+4)^2 - 8 = (x^2 + 8x + 16) - 8 = x^2 + 8x + 8$ - The highest power of $x$ is 2. - Therefore, it is a degree 2 polynomial.

STEP 7

Circle the polynomials that are of degree 2:
- $-4x^2 + 3x - 1$ - $(x+3)(x-2)$ - $(x+4)^2 - 8$
The polynomials that are degree 2 are:
$\boxed{-4x^2 + 3x - 1, \ (x+3)(x-2), \ (x+4)^2 - 8}$

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Question1. Circle all of the following polynomials that are DEGREE 2: [1 mark] 2x+3−4x2+3x−1(x+3)(x−2)(x+4)2−8\begin{array}{llll} 2 x+3 & -4 x^{2}+3 x-1 & (x+3)(x-2) & (x+4)^{2}-8 \end{array}2x+3​−4x2+3x−1​(x+3)(x−2)​(x+4)2−8​

Studdy Solution

STEP 1

1. A polynomial of degree 2 is a quadratic polynomial, which has the highest power of x x x as 2.2. We need to identify which of the given expressions are quadratic polynomials.

STEP 2

1. Analyze each polynomial to determine its degree.2. Circle the polynomials that are of degree 2.

STEP 3

Analyze the polynomial 2x+3 2x + 3 2x+3:- The highest power of x x x is 1. - Therefore, it is not a degree 2 polynomial.

STEP 4

Analyze the polynomial −4x2+3x−1 -4x^2 + 3x - 1 −4x2+3x−1:- The highest power of x x x is 2. - Therefore, it is a degree 2 polynomial.

STEP 5

Analyze the polynomial (x+3)(x−2) (x+3)(x-2) (x+3)(x−2):- Expand the expression: (x+3)(x−2)=x2−2x+3x−6=x2+x−6 (x+3)(x-2) = x^2 - 2x + 3x - 6 = x^2 + x - 6 (x+3)(x−2)=x2−2x+3x−6=x2+x−6 - The highest power of x x x is 2. - Therefore, it is a degree 2 polynomial.

STEP 6

Analyze the polynomial (x+4)2−8 (x+4)^2 - 8 (x+4)2−8:- Expand the expression: (x+4)2−8=(x2+8x+16)−8=x2+8x+8 (x+4)^2 - 8 = (x^2 + 8x + 16) - 8 = x^2 + 8x + 8 (x+4)2−8=(x2+8x+16)−8=x2+8x+8 - The highest power of x x x is 2. - Therefore, it is a degree 2 polynomial.

STEP 7

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Question1. Circle all of the following polynomials that are DEGREE 2: [1 mark] $\begin{array}{llll} 2 x+3 & -4 x^{2}+3 x-1 & (x+3)(x-2) & (x+4)^{2}-8 \end{array}$

1. A polynomial of degree 2 is a quadratic polynomial, which has the highest power of $x$ as 2.
2. We need to identify which of the given expressions are quadratic polynomials.

1. Analyze each polynomial to determine its degree.
2. Circle the polynomials that are of degree 2.

Analyze the polynomial $2x + 3$ :
- The highest power of $x$ is 1. - Therefore, it is not a degree 2 polynomial.

Analyze the polynomial $-4x^2 + 3x - 1$ :
- The highest power of $x$ is 2. - Therefore, it is a degree 2 polynomial.

Analyze the polynomial $(x+3)(x-2)$ :
- Expand the expression: $(x+3)(x-2) = x^2 - 2x + 3x - 6 = x^2 + x - 6$ - The highest power of $x$ is 2. - Therefore, it is a degree 2 polynomial.

Analyze the polynomial $(x+4)^2 - 8$ :
- Expand the expression: $(x+4)^2 - 8 = (x^2 + 8x + 16) - 8 = x^2 + 8x + 8$ - The highest power of $x$ is 2. - Therefore, it is a degree 2 polynomial.