Polynomials (Manipulation and Zeros)

NZ Level 7 (NZC) Level 2 (NCEA)

Further applications of remainder and factor theorem

The polynomials $4x^2-7x-15$4`x`2−7`x`−15 and $5x^2+13x+k$5`x`2+13`x`+`k` have a common factor of $x+p$`x`+`p`, where $p$`p` is an integer.

a

Using the fact that $x+p$`x`+`p` is a factor of $4x^2-7x-15$4`x`2−7`x`−15, solve for the value of $p$`p`.

b

Using the fact that $x+p$`x`+`p` is a factor of $5x^2+13x+k$5`x`2+13`x`+`k`, solve for $k$`k`.

Easy

Approx 7 minutes

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