Math / Algebra

QuestionUse the given zeros to write the complete factored form of $f(x)$ . $f(x)=2 x^{2}-13 x+20 ;$ zeros: $\frac{5}{2}$ and 4 $f(x)=$ $\square$ (Type your answer in factored form. Use integers or fractions for any numbers in

Studdy Solution

STEP 1

1. The polynomial $f(x) = 2x^2 - 13x + 20$ is a quadratic polynomial.
2. The given zeros of the polynomial are $\frac{5}{2}$ and $4$ .
3. A polynomial can be expressed in factored form using its zeros.

STEP 2

1. Use the zeros to write the factors of the polynomial.
2. Write the complete factored form of the polynomial.

STEP 3

Given the zeros of the polynomial are $\frac{5}{2}$ and $4$ , we can write the factors as $(x - \text{zero})$ . Therefore, the factors are:
$\left(x - \frac{5}{2}\right) \quad \text{and} \quad (x - 4)$

STEP 4

Since the leading coefficient of the polynomial is $2$ , we need to include this in the factored form. The complete factored form of the polynomial is:
$f(x) = 2 \left(x - \frac{5}{2}\right)(x - 4)$

STEP 5

Simplify the expression by removing the fraction. Multiply the factor $\left(x - \frac{5}{2}\right)$ by $2$ to eliminate the fraction:
$f(x) = 2 \left(x - \frac{5}{2}\right)(x - 4)$ $f(x) = (2x - 5)(x - 4)$
The complete factored form of $f(x)$ is:
$f(x) = (2x - 5)(x - 4)$

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QuestionUse the given zeros to write the complete factored form of $f(x)$ . $f(x)=2 x^{2}-13 x+20 ;$ zeros: $\frac{5}{2}$ and 4 $f(x)=$ $\square$ (Type your answer in factored form. Use integers or fractions for any numbers in

Studdy Solution

STEP 1

1. The polynomial $f(x) = 2x^2 - 13x + 20$ is a quadratic polynomial.
2. The given zeros of the polynomial are $\frac{5}{2}$ and $4$ .
3. A polynomial can be expressed in factored form using its zeros.

STEP 2

1. Use the zeros to write the factors of the polynomial.
2. Write the complete factored form of the polynomial.

STEP 3

Given the zeros of the polynomial are $\frac{5}{2}$ and $4$ , we can write the factors as $(x - \text{zero})$ . Therefore, the factors are:
$\left(x - \frac{5}{2}\right) \quad \text{and} \quad (x - 4)$

STEP 4

Since the leading coefficient of the polynomial is $2$ , we need to include this in the factored form. The complete factored form of the polynomial is:
$f(x) = 2 \left(x - \frac{5}{2}\right)(x - 4)$

STEP 5

Simplify the expression by removing the fraction. Multiply the factor $\left(x - \frac{5}{2}\right)$ by $2$ to eliminate the fraction:
$f(x) = 2 \left(x - \frac{5}{2}\right)(x - 4)$ $f(x) = (2x - 5)(x - 4)$
The complete factored form of $f(x)$ is:
$f(x) = (2x - 5)(x - 4)$

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QuestionUse the given zeros to write the complete factored form of f(x)f(x)f(x). f(x)=2x2−13x+20;f(x)=2 x^{2}-13 x+20 ;f(x)=2x2−13x+20; zeros: 52\frac{5}{2}25​ and 4 f(x)=f(x)=f(x)= □\square□ (Type your answer in factored form. Use integers or fractions for any numbers in

Studdy Solution

STEP 1

1. The polynomial f(x)=2x2−13x+20 f(x) = 2x^2 - 13x + 20 f(x)=2x2−13x+20 is a quadratic polynomial.2. The given zeros of the polynomial are 52 \frac{5}{2} 25​ and 4 4 4.3. A polynomial can be expressed in factored form using its zeros.

STEP 2

1. Use the zeros to write the factors of the polynomial.2. Write the complete factored form of the polynomial.

STEP 3

Given the zeros of the polynomial are 52 \frac{5}{2} 25​ and 4 4 4, we can write the factors as (x−zero) (x - \text{zero}) (x−zero). Therefore, the factors are:(x−52)and(x−4) \left(x - \frac{5}{2}\right) \quad \text{and} \quad (x - 4) (x−25​)and(x−4)

STEP 4

Since the leading coefficient of the polynomial is 2 2 2, we need to include this in the factored form. The complete factored form of the polynomial is:f(x)=2(x−52)(x−4) f(x) = 2 \left(x - \frac{5}{2}\right)(x - 4) f(x)=2(x−25​)(x−4)

STEP 5

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QuestionUse the given zeros to write the complete factored form of $f(x)$ . $f(x)=2 x^{2}-13 x+20 ;$ zeros: $\frac{5}{2}$ and 4 $f(x)=$ $\square$ (Type your answer in factored form. Use integers or fractions for any numbers in

1. The polynomial $f(x) = 2x^2 - 13x + 20$ is a quadratic polynomial.
2. The given zeros of the polynomial are $\frac{5}{2}$ and $4$ .
3. A polynomial can be expressed in factored form using its zeros.

1. Use the zeros to write the factors of the polynomial.
2. Write the complete factored form of the polynomial.

Given the zeros of the polynomial are $\frac{5}{2}$ and $4$ , we can write the factors as $(x - \text{zero})$ . Therefore, the factors are:
$\left(x - \frac{5}{2}\right) \quad \text{and} \quad (x - 4)$

Since the leading coefficient of the polynomial is $2$ , we need to include this in the factored form. The complete factored form of the polynomial is:
$f(x) = 2 \left(x - \frac{5}{2}\right)(x - 4)$