Math / Algebra

Question $5 x^{4}-45 x^{2}$

Studdy Solution

STEP 1

1. The expression $5x^4 - 45x^2$ is a polynomial in terms of $x$ .
2. We can factor the expression to simplify it.

STEP 2

1. Identify and factor out the greatest common factor (GCF).
2. Further factor the resulting polynomial, if possible.

STEP 3

Identify and factor out the greatest common factor (GCF) from $5x^4 - 45x^2$ .
$5x^4 - 45x^2 = 5x^2(x^2 - 9)$

STEP 4

Notice that $x^2 - 9$ is a difference of squares, which can be factored further.
$x^2 - 9 = (x + 3)(x - 3)$

STEP 5

Substitute the factored form of $x^2 - 9$ back into the expression.
$5x^2(x^2 - 9) = 5x^2(x + 3)(x - 3)$
Solution: The factored form of $5x^4 - 45x^2$ is:
$5x^2(x + 3)(x - 3)$

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Question $5 x^{4}-45 x^{2}$

Studdy Solution

STEP 1

1. The expression $5x^4 - 45x^2$ is a polynomial in terms of $x$ .
2. We can factor the expression to simplify it.

STEP 2

1. Identify and factor out the greatest common factor (GCF).
2. Further factor the resulting polynomial, if possible.

STEP 3

Identify and factor out the greatest common factor (GCF) from $5x^4 - 45x^2$ .
$5x^4 - 45x^2 = 5x^2(x^2 - 9)$

STEP 4

Notice that $x^2 - 9$ is a difference of squares, which can be factored further.
$x^2 - 9 = (x + 3)(x - 3)$

STEP 5

Substitute the factored form of $x^2 - 9$ back into the expression.
$5x^2(x^2 - 9) = 5x^2(x + 3)(x - 3)$
Solution: The factored form of $5x^4 - 45x^2$ is:
$5x^2(x + 3)(x - 3)$

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Question5x4−45x25 x^{4}-45 x^{2}5x4−45x2

Studdy Solution

STEP 1

1. The expression 5x4−45x25x^4 - 45x^25x4−45x2 is a polynomial in terms of xxx.2. We can factor the expression to simplify it.

STEP 2

1. Identify and factor out the greatest common factor (GCF).2. Further factor the resulting polynomial, if possible.

STEP 3

Identify and factor out the greatest common factor (GCF) from 5x4−45x25x^4 - 45x^25x4−45x2.5x4−45x2=5x2(x2−9) 5x^4 - 45x^2 = 5x^2(x^2 - 9) 5x4−45x2=5x2(x2−9)

STEP 4

Notice that x2−9x^2 - 9x2−9 is a difference of squares, which can be factored further.x2−9=(x+3)(x−3) x^2 - 9 = (x + 3)(x - 3) x2−9=(x+3)(x−3)

STEP 5

Substitute the factored form of x2−9x^2 - 9x2−9 back into the expression.5x2(x2−9)=5x2(x+3)(x−3) 5x^2(x^2 - 9) = 5x^2(x + 3)(x - 3) 5x2(x2−9)=5x2(x+3)(x−3)Solution: The factored form of 5x4−45x25x^4 - 45x^25x4−45x2 is:5x2(x+3)(x−3) 5x^2(x + 3)(x - 3) 5x2(x+3)(x−3)

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Question $5 x^{4}-45 x^{2}$

1. The expression $5x^4 - 45x^2$ is a polynomial in terms of $x$ .
2. We can factor the expression to simplify it.

1. Identify and factor out the greatest common factor (GCF).
2. Further factor the resulting polynomial, if possible.

Identify and factor out the greatest common factor (GCF) from $5x^4 - 45x^2$ .
$5x^4 - 45x^2 = 5x^2(x^2 - 9)$

Notice that $x^2 - 9$ is a difference of squares, which can be factored further.
$x^2 - 9 = (x + 3)(x - 3)$

Substitute the factored form of $x^2 - 9$ back into the expression.
$5x^2(x^2 - 9) = 5x^2(x + 3)(x - 3)$
Solution: The factored form of $5x^4 - 45x^2$ is:
$5x^2(x + 3)(x - 3)$