Answer:
The answer is (C)
Step-by-step explanation:
Let us multiply the two trinomials and simplify the product to find the correct choice.
[tex](2x^{2}+4x-3)(x^{2}-2x+5)[/tex]
To find the product multiply each term in the first bracket by the second bracket, then add the like terms
[tex]2x^{2} (x^{2}-2x+5)=2x^{2}(x^{2})+2x^{2}(-2x)+2x^{2}(5)=2x^{4}-4x^{3}+10x^{2}[/tex]
[tex]4x(x^{2}-2x+5)=4x(x^{2})+4x(-2x)+4x(5)=4x^{3}-8x^{2}+20x[/tex]
[tex](-3)(x^{2}-2x+5)=(-3)(x^{2})+(-3)(-2x)+(-3)(5)=-3x^{2}+6x-15[/tex]
Now let us add the like terms.
[tex]2x^{4}-4x^{3}+10x^{2}+4x^{3}-8x^{2}+20x-3x^{2}+6x-15=[/tex]
[tex]2x^{4}+(-4x^{3}+4x^{3})+(10x^{2}-8x^{2}-3x^{2})+(6x+20x)-15=[/tex]
Simplify each term
[tex]2x^{4}+(0)x^{3}-x^{2}+26x-15=[/tex]
[tex]2x^{4}-x^{2}+26x-15[/tex]
By comparing it with the choices
The answer is (C)
