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Answer :
To use synthetic division to divide [tex]\(-35c^3 + 13c^2 + 46c - 26\)[/tex] by [tex]\(7c - 4\)[/tex], we follow these steps:
1. Identify the divisor's root: The divisor is [tex]\(7c - 4\)[/tex], which can be rewritten in the form [tex]\(7(c - \frac{4}{7})\)[/tex]. So, the root we use for synthetic division is [tex]\(\frac{4}{7}\)[/tex].
2. Set up the synthetic division: Write down the coefficients of the dividend polynomial [tex]\(-35c^3 + 13c^2 + 46c - 26\)[/tex], which are [tex]\([-35, 13, 46, -26]\)[/tex].
3. Perform synthetic division:
- Begin with the first coefficient, [tex]\(-35\)[/tex].
- Multiply [tex]\(-35\)[/tex] by the root [tex]\(\frac{4}{7}\)[/tex] and add the result to the second coefficient (13).
- Continue this process for each subsequent coefficient.
Here is the step-by-step breakdown:
- Start with [tex]\(-35\)[/tex].
- Multiply [tex]\(-35\)[/tex] by [tex]\(\frac{4}{7}\)[/tex] to get [tex]\(-20\)[/tex]. Add this to 13, getting a new value of [tex]\(-7\)[/tex].
- Multiply [tex]\(-7\)[/tex] by [tex]\(\frac{4}{7}\)[/tex] to get [tex]\(-4\)[/tex]. Add this to 46, resulting in 42.
- Multiply 42 by [tex]\(\frac{4}{7}\)[/tex] to get 24. Add this to [tex]\(-26\)[/tex], resulting in [tex]\(-2\)[/tex].
4. Result:
- The coefficients of the quotient polynomial are [tex]\([-35, -7, 42]\)[/tex], which correspond to [tex]\(-35c^2 - 7c + 42\)[/tex].
- The remainder is [tex]\(-2\)[/tex].
Therefore, when dividing [tex]\(-35c^3 + 13c^2 + 46c - 26\)[/tex] by [tex]\(7c - 4\)[/tex], the quotient is [tex]\(-35c^2 - 7c + 42\)[/tex] with a remainder of [tex]\(-2\)[/tex].
1. Identify the divisor's root: The divisor is [tex]\(7c - 4\)[/tex], which can be rewritten in the form [tex]\(7(c - \frac{4}{7})\)[/tex]. So, the root we use for synthetic division is [tex]\(\frac{4}{7}\)[/tex].
2. Set up the synthetic division: Write down the coefficients of the dividend polynomial [tex]\(-35c^3 + 13c^2 + 46c - 26\)[/tex], which are [tex]\([-35, 13, 46, -26]\)[/tex].
3. Perform synthetic division:
- Begin with the first coefficient, [tex]\(-35\)[/tex].
- Multiply [tex]\(-35\)[/tex] by the root [tex]\(\frac{4}{7}\)[/tex] and add the result to the second coefficient (13).
- Continue this process for each subsequent coefficient.
Here is the step-by-step breakdown:
- Start with [tex]\(-35\)[/tex].
- Multiply [tex]\(-35\)[/tex] by [tex]\(\frac{4}{7}\)[/tex] to get [tex]\(-20\)[/tex]. Add this to 13, getting a new value of [tex]\(-7\)[/tex].
- Multiply [tex]\(-7\)[/tex] by [tex]\(\frac{4}{7}\)[/tex] to get [tex]\(-4\)[/tex]. Add this to 46, resulting in 42.
- Multiply 42 by [tex]\(\frac{4}{7}\)[/tex] to get 24. Add this to [tex]\(-26\)[/tex], resulting in [tex]\(-2\)[/tex].
4. Result:
- The coefficients of the quotient polynomial are [tex]\([-35, -7, 42]\)[/tex], which correspond to [tex]\(-35c^2 - 7c + 42\)[/tex].
- The remainder is [tex]\(-2\)[/tex].
Therefore, when dividing [tex]\(-35c^3 + 13c^2 + 46c - 26\)[/tex] by [tex]\(7c - 4\)[/tex], the quotient is [tex]\(-35c^2 - 7c + 42\)[/tex] with a remainder of [tex]\(-2\)[/tex].
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