Q:

Please help me with these questions thank you.

Accepted Solution

A:
Answer:1. 4[tex]x^{3}[/tex] + 26x² + 4x - 482. 2[tex]x^{3}[/tex] - 23x² + 60x - 323. [tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 84. 2[tex]x^{7}[/tex] + [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 3x + 12Step-by-step explanation:To multiply polynomials, simply distribute whatever's outside the largest set of parenthesis, then combine like terms.1) Distribute the parenthesis (x + 6):x(4x² + 2x - 8)  +  6(4x² + 2x - 8)4[tex]x^{3}[/tex] + 2x² -8x  +  6(4x² + 2x -8)4[tex]x^{3}[/tex] + 2x² -8x + 24x² + 12x - 48Combine like terms:4[tex]x^{3}[/tex] + 26x² + 4x - 482) Distribute the parenthesis (x - 8):x(2x² - 7x + 4)  +  (-8)(2x² - 7x + 4)2[tex]x^{3}[/tex] - 7x² + 4x  +  (-8)(2x² - 7x + 4)2[tex]x^{3}[/tex] - 7x² + 4x  +  -16x² + 56x - 32Combine like terms:2[tex]x^{3}[/tex] - 23x² + 60x - 323) Distribute the parenthesis (x + 2):x([tex]x^{4}[/tex] + 7x² - 4)  +  2([tex]x^{4}[/tex] + 7x² - 4)[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x  +  2([tex]x^{4}[/tex] + 7x² - 4)[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8No like terms to combine, so:[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 84) Distribute the parenthesis (x + 4):x(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)  +  4(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)2[tex]x^{7}[/tex] - 7[tex]x^{6}[/tex] + 3x  +  4(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)2[tex]x^{7}[/tex] - 7[tex]x^{6}[/tex] + 3x + 8  [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 12Combine like terms:2[tex]x^{7}[/tex] + [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 3x + 12hope this helps!