Answered

Explore IDNLearn.com's extensive Q&A database and find the answers you're looking for. Discover reliable and timely information on any topic from our network of experienced professionals.

For the polynomial [tex]P(x)=4x^2+3x-6[/tex] and [tex]c=4[/tex], find [tex]P(c)[/tex] by (a) direct substitution and (b) the remainder theorem.

(a) Find [tex]P(4)[/tex] by direct substitution.

[tex]P(4) = \square[/tex] (Type an integer.)

Sagot :

GinnyAnsweridn
To find [tex]\( P(4) \)[/tex] for the polynomial [tex]\( P(x) = 4x^2 + 3x - 6 \)[/tex] by direct substitution, follow these steps:

1. Start with the given polynomial [tex]\( P(x) = 4x^2 + 3x - 6 \)[/tex].
2. Substitute [tex]\( x = 4 \)[/tex] into the polynomial.

[tex]\[ P(4) = 4(4)^2 + 3(4) - 6 \][/tex]

3. Calculate [tex]\( 4(4)^2 \)[/tex]:

[tex]\[ 4(4)^2 = 4 \times 16 = 64 \][/tex]

4. Calculate [tex]\( 3(4) \)[/tex]:

[tex]\[ 3(4) = 3 \times 4 = 12 \][/tex]

5. Substitute the calculated values back into the expression:

[tex]\[ P(4) = 64 + 12 - 6 \][/tex]

6. Perform the addition and subtraction:

[tex]\[ 64 + 12 = 76 \][/tex]
[tex]\[ 76 - 6 = 70 \][/tex]

So, [tex]\( P(4) = 70 \)[/tex].
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.