could someone help me with polynomials?

Question

Multiply the following polynomials.

(6x^2+3x+1)(x^2-5x+4)

Answer 1

Hi Seth,

Given the expression below use distributive law, that is each quantity in the first parenthesis multiplies the second parenthesis as follows;

(6x² +3x +1)(x² -5x +4)

= 6x²(x²- 5x+4) +3x(x² -5x +4)+1(x² -5x +4)  [See the distrivution of the first parenthesis]

=6x⁴ -30x³ +24x²+3x³-15x²+12x +x²-5x+4     [Add the powers of x, notice that x = x¹]

=6x⁴ - 27x³ 10x² + 7x +4      [ Add coefficients of similar powers of x, e.g -30x³ +3x³, 24x² - 15x² + x²]

 

(6x² +3x +1)(x² -5x +4) = 6x⁴- 27x³ 10x² + 7x +4