Answer :
To find [tex]\( g(-2) \)[/tex] for the polynomial [tex]\( g(x) = 19x^3 + 29x^2 - 1 \)[/tex] using synthetic division, follow these steps:
1. Set up the synthetic division:
Write the coefficients of the polynomial in order. If any term is missing, use a zero for its coefficient. For [tex]\( g(x) = 19x^3 + 29x^2 + 0x - 1 \)[/tex], the coefficients are: [tex]\( 19, 29, 0, -1 \)[/tex].
2. Use the value to be evaluated:
The value of [tex]\( x \)[/tex] you are evaluating the polynomial at is [tex]\(-2\)[/tex].
3. Perform synthetic division:
- Start with the first coefficient, which is [tex]\( 19 \)[/tex], and bring it down.
- Multiply this number by [tex]\(-2\)[/tex] (the value to be evaluated) and add it to the next coefficient.
- [tex]\( 19 \)[/tex] is brought down.
- [tex]\( 19 \times (-2) = -38 \)[/tex]. Add this to the next coefficient: [tex]\( 29 + (-38) = -9 \)[/tex].
- Multiply the result [tex]\(-9\)[/tex] by [tex]\(-2\)[/tex]:
- [tex]\(-9 \times (-2) = 18\)[/tex]. Add this to the next coefficient: [tex]\( 0 + 18 = 18 \)[/tex].
- Multiply [tex]\( 18 \)[/tex] by [tex]\(-2\)[/tex]:
- [tex]\( 18 \times (-2) = -36\)[/tex]. Add this to the last coefficient: [tex]\(-1 + (-36) = -37\)[/tex].
4. The final result:
The result of this process, [tex]\(-37\)[/tex], is the value of [tex]\( g(-2) \)[/tex].
Thus, [tex]\( g(-2) \)[/tex] is [tex]\(-37\)[/tex].
1. Set up the synthetic division:
Write the coefficients of the polynomial in order. If any term is missing, use a zero for its coefficient. For [tex]\( g(x) = 19x^3 + 29x^2 + 0x - 1 \)[/tex], the coefficients are: [tex]\( 19, 29, 0, -1 \)[/tex].
2. Use the value to be evaluated:
The value of [tex]\( x \)[/tex] you are evaluating the polynomial at is [tex]\(-2\)[/tex].
3. Perform synthetic division:
- Start with the first coefficient, which is [tex]\( 19 \)[/tex], and bring it down.
- Multiply this number by [tex]\(-2\)[/tex] (the value to be evaluated) and add it to the next coefficient.
- [tex]\( 19 \)[/tex] is brought down.
- [tex]\( 19 \times (-2) = -38 \)[/tex]. Add this to the next coefficient: [tex]\( 29 + (-38) = -9 \)[/tex].
- Multiply the result [tex]\(-9\)[/tex] by [tex]\(-2\)[/tex]:
- [tex]\(-9 \times (-2) = 18\)[/tex]. Add this to the next coefficient: [tex]\( 0 + 18 = 18 \)[/tex].
- Multiply [tex]\( 18 \)[/tex] by [tex]\(-2\)[/tex]:
- [tex]\( 18 \times (-2) = -36\)[/tex]. Add this to the last coefficient: [tex]\(-1 + (-36) = -37\)[/tex].
4. The final result:
The result of this process, [tex]\(-37\)[/tex], is the value of [tex]\( g(-2) \)[/tex].
Thus, [tex]\( g(-2) \)[/tex] is [tex]\(-37\)[/tex].
