Asked by Evelyn McNair on Mar 10, 2024
Verified
Multiply the polynomials and simplify. x2+5x−6×3x+4\begin{array} { r } x ^ { 2 } + 5 x - 6 \\\times \quad 3 x + 4 \\\hline\end{array}x2+5x−6×3x+4
A) 3x3+19x2+5x−63 x ^ { 3 } + 19 x ^ { 2 } + 5 x - 63x3+19x2+5x−6
B) 3x3+4x2+2x−243 x ^ { 3 } + 4 x ^ { 2 } + 2 x - 243x3+4x2+2x−24
C) 3x3+19x2+2x−243 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 243x3+19x2+2x−24
D) 3x3+4x2+20x−63 x ^ { 3 } + 4 x ^ { 2 } + 20 x - 63x3+4x2+20x−6
E) 3x3+20x2−63 x ^ { 3 } + 20 x ^ { 2 } - 63x3+20x2−6
A) 3x3+19x2+5x−63 x ^ { 3 } + 19 x ^ { 2 } + 5 x - 63x3+19x2+5x−6
B) 3x3+4x2+2x−243 x ^ { 3 } + 4 x ^ { 2 } + 2 x - 243x3+4x2+2x−24
C) 3x3+19x2+2x−243 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 243x3+19x2+2x−24
D) 3x3+4x2+20x−63 x ^ { 3 } + 4 x ^ { 2 } + 20 x - 63x3+4x2+20x−6
E) 3x3+20x2−63 x ^ { 3 } + 20 x ^ { 2 } - 63x3+20x2−6
Polynomials
Polynomials are mathematical expressions consisting of variables and coefficients that involve only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
- Invoke special product guidelines to simplify expressions that include polynomials.
Verified Answer
WA
Wyatt Adcock
Mar 10, 2024
Final Answer :
C
Explanation :
Using distributivity of multiplication over addition, we get
(x2+5x−6)⋅(3x+4)=x2⋅(3x)+x2⋅(4)+5x⋅(3x)+5x⋅(4)−6⋅(3x)−6⋅(4)=3x3+4x2+15x2+20x−18x−24=3x3+19x2+2x−24\begin{align*}&(x^2 + 5x - 6) \cdot (3x + 4)\\&= x^2\cdot(3x)+x^2\cdot(4)+5x\cdot(3x)+5x\cdot(4)-6\cdot(3x)-6\cdot(4)\\&= 3x^3+4x^2+15x^2+20x-18x-24\\&= 3x^3+19x^2+2x-24\end{align*}(x2+5x−6)⋅(3x+4)=x2⋅(3x)+x2⋅(4)+5x⋅(3x)+5x⋅(4)−6⋅(3x)−6⋅(4)=3x3+4x2+15x2+20x−18x−24=3x3+19x2+2x−24
Therefore, the correct answer is (C).
(x2+5x−6)⋅(3x+4)=x2⋅(3x)+x2⋅(4)+5x⋅(3x)+5x⋅(4)−6⋅(3x)−6⋅(4)=3x3+4x2+15x2+20x−18x−24=3x3+19x2+2x−24\begin{align*}&(x^2 + 5x - 6) \cdot (3x + 4)\\&= x^2\cdot(3x)+x^2\cdot(4)+5x\cdot(3x)+5x\cdot(4)-6\cdot(3x)-6\cdot(4)\\&= 3x^3+4x^2+15x^2+20x-18x-24\\&= 3x^3+19x^2+2x-24\end{align*}(x2+5x−6)⋅(3x+4)=x2⋅(3x)+x2⋅(4)+5x⋅(3x)+5x⋅(4)−6⋅(3x)−6⋅(4)=3x3+4x2+15x2+20x−18x−24=3x3+19x2+2x−24
Therefore, the correct answer is (C).
Learning Objectives
- Invoke special product guidelines to simplify expressions that include polynomials.