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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].
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