Solved on Feb 07, 2024

Find the two missing values in the equation $g^{2}-4 g-21=(g-\square)(g+\square)$ to show equivalent expressions.

STEP 1

Assumptions
1. We are given a quadratic expression $g^{2}-4g-21$ .
2. We need to factor this expression into the form $(g-\square)(g+\square)$ .
3. The symbol $\square$ represents the numbers we need to find.

STEP 2

Recognize that the given quadratic expression is in the standard form $ax^2 + bx + c$ , where $a=1$ , $b=-4$ , and $c=-21$ .

STEP 3

Understand that factoring a quadratic expression involves finding two numbers that multiply to $ac$ (which is $1 \times -21 = -21$ ) and add up to $b$ (which is $-4$ ).

STEP 4

List the pairs of factors of $ac=-21$ considering both positive and negative factors because the product is negative.
$\begin{align} 1 \times -21 &= -21 \\ -1 \times 21 &= -21 \\ 3 \times -7 &= -21 \\ -3 \times 7 &= -21 \\ \end{align}$

STEP 5

Identify the pair of factors from the list in STEP_4 that add up to $b=-4$ .
$3 + (-7) = -4$

STEP 6

Use the identified pair of factors to write the quadratic expression as two binomials.
$g^{2}-4g-21 = (g-7)(g+3)$

STEP 7

Now we can fill in the squares in the original equation with the numbers we found.
$g^{2}-4g-21=(g-7)(g+3)$
So the complete equation with the equivalent expressions is:
$g^{2}-4g-21=(g-7)(g+3)$

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Find the two missing values in the equation $g^{2}-4 g-21=(g-\square)(g+\square)$ to show equivalent expressions.

STEP 1

Assumptions
1. We are given a quadratic expression $g^{2}-4g-21$ .
2. We need to factor this expression into the form $(g-\square)(g+\square)$ .
3. The symbol $\square$ represents the numbers we need to find.

STEP 2

Recognize that the given quadratic expression is in the standard form $ax^2 + bx + c$ , where $a=1$ , $b=-4$ , and $c=-21$ .

STEP 3

Understand that factoring a quadratic expression involves finding two numbers that multiply to $ac$ (which is $1 \times -21 = -21$ ) and add up to $b$ (which is $-4$ ).

STEP 4

List the pairs of factors of $ac=-21$ considering both positive and negative factors because the product is negative.
$\begin{align} 1 \times -21 &= -21 \\ -1 \times 21 &= -21 \\ 3 \times -7 &= -21 \\ -3 \times 7 &= -21 \\ \end{align}$

STEP 5

Identify the pair of factors from the list in STEP_4 that add up to $b=-4$ .
$3 + (-7) = -4$

STEP 6

Use the identified pair of factors to write the quadratic expression as two binomials.
$g^{2}-4g-21 = (g-7)(g+3)$

STEP 7

Now we can fill in the squares in the original equation with the numbers we found.
$g^{2}-4g-21=(g-7)(g+3)$
So the complete equation with the equivalent expressions is:
$g^{2}-4g-21=(g-7)(g+3)$

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Find the two missing values in the equation g2−4g−21=(g−□)(g+□)g^{2}-4 g-21=(g-\square)(g+\square)g2−4g−21=(g−□)(g+□) to show equivalent expressions.

STEP 1

Assumptions1. We are given a quadratic expression g2−4g−21g^{2}-4g-21g2−4g−21.2. We need to factor this expression into the form (g−□)(g+□)(g-\square)(g+\square)(g−□)(g+□).3. The symbol □\square□ represents the numbers we need to find.

STEP 2

Recognize that the given quadratic expression is in the standard form ax2+bx+cax^2 + bx + cax2+bx+c, where a=1a=1a=1, b=−4b=-4b=−4, and c=−21c=-21c=−21.

STEP 3

Understand that factoring a quadratic expression involves finding two numbers that multiply to acacac (which is 1×−21=−211 \times -21 = -211×−21=−21) and add up to bbb (which is −4-4−4).

STEP 4

STEP 5

Identify the pair of factors from the list in STEP_4 that add up to b=−4b=-4b=−4.3+(−7)=−4 3 + (-7) = -4 3+(−7)=−4

STEP 6

Use the identified pair of factors to write the quadratic expression as two binomials.g2−4g−21=(g−7)(g+3) g^{2}-4g-21 = (g-7)(g+3) g2−4g−21=(g−7)(g+3)

STEP 7

Now we can fill in the squares in the original equation with the numbers we found.g2−4g−21=(g−7)(g+3) g^{2}-4g-21=(g-7)(g+3) g2−4g−21=(g−7)(g+3)So the complete equation with the equivalent expressions is:g2−4g−21=(g−7)(g+3) g^{2}-4g-21=(g-7)(g+3) g2−4g−21=(g−7)(g+3)

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the two missing values in the equation $g^{2}-4 g-21=(g-\square)(g+\square)$ to show equivalent expressions.

Assumptions
1. We are given a quadratic expression $g^{2}-4g-21$ .
2. We need to factor this expression into the form $(g-\square)(g+\square)$ .
3. The symbol $\square$ represents the numbers we need to find.

Recognize that the given quadratic expression is in the standard form $ax^2 + bx + c$ , where $a=1$ , $b=-4$ , and $c=-21$ .

Understand that factoring a quadratic expression involves finding two numbers that multiply to $ac$ (which is $1 \times -21 = -21$ ) and add up to $b$ (which is $-4$ ).

Identify the pair of factors from the list in STEP_4 that add up to $b=-4$ .
$3 + (-7) = -4$

Use the identified pair of factors to write the quadratic expression as two binomials.
$g^{2}-4g-21 = (g-7)(g+3)$

Now we can fill in the squares in the original equation with the numbers we found.
$g^{2}-4g-21=(g-7)(g+3)$
So the complete equation with the equivalent expressions is:
$g^{2}-4g-21=(g-7)(g+3)$