Asked by Shannon Michaud on Jun 13, 2024
Verified
Multiply (3x+5) (x2+9x−2) ( 3 x + 5 ) \left( x ^ { 2 } + 9 x - 2 \right) (3x+5) (x2+9x−2) and simplify.
A) 3x3+32x2+9x−23 x ^ { 3 } + 32 x ^ { 2 } + 9 x - 23x3+32x2+9x−2
B) 3x3+5x2+45x−23 x ^ { 3 } + 5 x ^ { 2 } + 45 x - 23x3+5x2+45x−2
C) 3x3+45x2−23 x ^ { 3 } + 45 x ^ { 2 } - 23x3+45x2−2
D) 3x3+5x2+39x−103 x ^ { 3 } + 5 x ^ { 2 } + 39 x - 103x3+5x2+39x−10
E) 3x3+32x2+39x−103 x ^ { 3 } + 32 x ^ { 2 } + 39 x - 103x3+32x2+39x−10
Multiply
The process of combining two numbers or quantities to get their product.
Simplify
Reducing a mathematical expression or equation to its most basic form without changing its value.
- Use special product strategies to streamline the simplification process of polynomial expressions.
Verified Answer
AT
Azozz TashkandiJun 17, 2024
Final Answer :
E
Explanation :
We can use the distributive property to multiply the expression:
(3x+5)(x2+9x−2)=3x(x2+9x−2)+5(x2+9x−2)=3x3+27x2−6x+5x2+45x−10=3x3+32x2+39x−10\begin{align*}&(3x+5)(x^2+9x-2)\\=&3x(x^2+9x-2)+5(x^2+9x-2)\\=&3x^3+27x^2-6x+5x^2+45x-10\\=&3x^3+32x^2+39x-10\end{align*}===(3x+5)(x2+9x−2)3x(x2+9x−2)+5(x2+9x−2)3x3+27x2−6x+5x2+45x−103x3+32x2+39x−10
Therefore, the correct answer is $\boxed{\textbf{(E)}}$.
(3x+5)(x2+9x−2)=3x(x2+9x−2)+5(x2+9x−2)=3x3+27x2−6x+5x2+45x−10=3x3+32x2+39x−10\begin{align*}&(3x+5)(x^2+9x-2)\\=&3x(x^2+9x-2)+5(x^2+9x-2)\\=&3x^3+27x^2-6x+5x^2+45x-10\\=&3x^3+32x^2+39x-10\end{align*}===(3x+5)(x2+9x−2)3x(x2+9x−2)+5(x2+9x−2)3x3+27x2−6x+5x2+45x−103x3+32x2+39x−10
Therefore, the correct answer is $\boxed{\textbf{(E)}}$.
Learning Objectives
- Use special product strategies to streamline the simplification process of polynomial expressions.