consider this polynomial function.

\p(x) = x^3 + 7x^2 - 4x - 28\

what is the remainder when $p(x)$ is divided by each of these expressions?

type the answer in each box. use numerals instead of words.

$x - 3$:
$x + 4$:

Question

consider this polynomial function.

\p(x) = x^3 + 7x^2 - 4x - 28\

what is the remainder when $p(x)$ is divided by each of these expressions?

type the answer in each box. use numerals instead of words.

$x - 3$:
$x + 4$:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Linear Equations", "Function Evaluation" ], "new_concepts": [ "Remainder Theorem" ], "current_concepts": [ "Solving Linear Equations", "Function Evaluation", "Remainder Theorem" ] } ## Evaluate the polynomial at x = 3 $$ \begin{aligned} p(3) &= 3^3 + 7(3)^2 - 4(3) - 28 \ &= 27 + 7(9) - 12 - 28 \ &= 27 + 63 - 12 - 28 \ &= 90 - 40 \ &= 50 \end{aligned} $$ ## Evaluate the polynomial at x = -4 $$ \begin{aligned} p(-4) &= (-4)^3 + 7(-4)^2 - 4(-4) - 28 \ &= -64 + 7(16) + 16 - 28 \ &= -64 + 112 + 16 - 28 \ &= 48 + 16 - 28 \ &= 64 - 28 \ &= 36 \end{aligned} $$ Consider this polynomial function. $p(x) = x^3 + 7x^2 - 4x - 28$ What is the remainder when $p(x)$ is divided by each of these expressions? $x - 3$: 50 $x + 4$: 36 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Remainder Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Evaluate the polynomial at x = 3

Evaluate the polynomial at x = -4

Answer: