Solved on Feb 28, 2024

Find the factors of the trinomial $x^{2}-4x-5$ . Options: $x-5$ , $x-2$ , $x-1$ , $x+1$ , $x+2$ , $x+5$ .

STEP 1

Assumptions
1. We are given a quadratic trinomial $x^2 - 4x - 5$ .
2. We need to find the factors of the trinomial.
3. The possible factors are given as $x-5$ , $x-2$ , $x-1$ , $x+1$ , $x+2$ , and $x+5$ .
4. To factor the trinomial, we need to find two numbers that multiply to give the constant term (-5) and add to give the coefficient of the linear term (-4).

STEP 2

We will use the factoring method to find two binomials whose product is the trinomial $x^2 - 4x - 5$ . The general form of factoring a quadratic trinomial is:
$(x + m)(x + n)$
where $m$ and $n$ are the numbers that satisfy the conditions mentioned in STEP_1.

STEP 3

We need to find two numbers $m$ and $n$ such that:
$m \cdot n = -5$ $m + n = -4$

STEP 4

List the pairs of factors of -5, considering both positive and negative values:
1. $5$ and $-1$ (since $5 \cdot -1 = -5$ )
2. $-5$ and $1$ (since $-5 \cdot 1 = -5$ )

STEP 5

Check which pair of factors also adds up to -4:
1. $5 + (-1) = 4$ (does not equal -4)
2. $-5 + 1 = -4$ (equals -4)

STEP 6

Since the pair $-5$ and $1$ satisfies both conditions, these are the numbers we will use for $m$ and $n$ .

STEP 7

Write the factors of the trinomial using the values of $m$ and $n$ :
$(x - 5)(x + 1)$

STEP 8

Check the given options to see which ones match the factors we found:
1. $x-5$ (matches one of the factors)
2. $x-2$ (does not match)
3. $x-1$ (does not match)
4. $x+1$ (matches one of the factors)
5. $x+2$ (does not match)
6. $x+5$ (does not match)

STEP 9

The factors of $x^2 - 4x - 5$ are:
$x-5 \quad \text{and} \quad x+1$

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Find the factors of the trinomial $x^{2}-4x-5$ . Options: $x-5$ , $x-2$ , $x-1$ , $x+1$ , $x+2$ , $x+5$ .

STEP 1

STEP 2

We will use the factoring method to find two binomials whose product is the trinomial $x^2 - 4x - 5$ . The general form of factoring a quadratic trinomial is:
$(x + m)(x + n)$
where $m$ and $n$ are the numbers that satisfy the conditions mentioned in STEP_1.

STEP 3

We need to find two numbers $m$ and $n$ such that:
$m \cdot n = -5$ $m + n = -4$

STEP 4

List the pairs of factors of -5, considering both positive and negative values:
1. $5$ and $-1$ (since $5 \cdot -1 = -5$ )
2. $-5$ and $1$ (since $-5 \cdot 1 = -5$ )

STEP 5

Check which pair of factors also adds up to -4:
1. $5 + (-1) = 4$ (does not equal -4)
2. $-5 + 1 = -4$ (equals -4)

STEP 6

Since the pair $-5$ and $1$ satisfies both conditions, these are the numbers we will use for $m$ and $n$ .

STEP 7

Write the factors of the trinomial using the values of $m$ and $n$ :
$(x - 5)(x + 1)$

STEP 8

Check the given options to see which ones match the factors we found:
1. $x-5$ (matches one of the factors)
2. $x-2$ (does not match)
3. $x-1$ (does not match)
4. $x+1$ (matches one of the factors)
5. $x+2$ (does not match)
6. $x+5$ (does not match)

STEP 9

The factors of $x^2 - 4x - 5$ are:
$x-5 \quad \text{and} \quad x+1$

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Find the factors of the trinomial x2−4x−5x^{2}-4x-5x2−4x−5. Options: x−5x-5x−5, x−2x-2x−2, x−1x-1x−1, x+1x+1x+1, x+2x+2x+2, x+5x+5x+5.

STEP 1

STEP 2

We will use the factoring method to find two binomials whose product is the trinomial x2−4x−5x^2 - 4x - 5x2−4x−5. The general form of factoring a quadratic trinomial is:(x+m)(x+n)(x + m)(x + n)(x+m)(x+n)where mmm and nnn are the numbers that satisfy the conditions mentioned in STEP_1.

STEP 3

We need to find two numbers mmm and nnn such that:m⋅n=−5m \cdot n = -5m⋅n=−5 m+n=−4m + n = -4m+n=−4

STEP 4

List the pairs of factors of -5, considering both positive and negative values:1. 555 and −1-1−1 (since 5⋅−1=−55 \cdot -1 = -55⋅−1=−5)2. −5-5−5 and 111 (since −5⋅1=−5-5 \cdot 1 = -5−5⋅1=−5)

STEP 5

Check which pair of factors also adds up to -4:1. 5+(−1)=45 + (-1) = 45+(−1)=4 (does not equal -4)2. −5+1=−4-5 + 1 = -4−5+1=−4 (equals -4)

STEP 6

Since the pair −5-5−5 and 111 satisfies both conditions, these are the numbers we will use for mmm and nnn.

STEP 7

Write the factors of the trinomial using the values of mmm and nnn:(x−5)(x+1)(x - 5)(x + 1)(x−5)(x+1)

STEP 8

Check the given options to see which ones match the factors we found:1. x−5x-5x−5 (matches one of the factors)2. x−2x-2x−2 (does not match)3. x−1x-1x−1 (does not match)4. x+1x+1x+1 (matches one of the factors)5. x+2x+2x+2 (does not match)6. x+5x+5x+5 (does not match)

STEP 9

The factors of x2−4x−5x^2 - 4x - 5x2−4x−5 are:x−5andx+1x-5 \quad \text{and} \quad x+1x−5andx+1

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Find the factors of the trinomial $x^{2}-4x-5$ . Options: $x-5$ , $x-2$ , $x-1$ , $x+1$ , $x+2$ , $x+5$ .

We will use the factoring method to find two binomials whose product is the trinomial $x^2 - 4x - 5$ . The general form of factoring a quadratic trinomial is:
$(x + m)(x + n)$
where $m$ and $n$ are the numbers that satisfy the conditions mentioned in STEP_1.

We need to find two numbers $m$ and $n$ such that:
$m \cdot n = -5$ $m + n = -4$

List the pairs of factors of -5, considering both positive and negative values:
1. $5$ and $-1$ (since $5 \cdot -1 = -5$ )
2. $-5$ and $1$ (since $-5 \cdot 1 = -5$ )

Check which pair of factors also adds up to -4:
1. $5 + (-1) = 4$ (does not equal -4)
2. $-5 + 1 = -4$ (equals -4)

Since the pair $-5$ and $1$ satisfies both conditions, these are the numbers we will use for $m$ and $n$ .

Write the factors of the trinomial using the values of $m$ and $n$ :
$(x - 5)(x + 1)$

Check the given options to see which ones match the factors we found:
1. $x-5$ (matches one of the factors)
2. $x-2$ (does not match)
3. $x-1$ (does not match)
4. $x+1$ (matches one of the factors)
5. $x+2$ (does not match)
6. $x+5$ (does not match)

The factors of $x^2 - 4x - 5$ are:
$x-5 \quad \text{and} \quad x+1$