Answer:
Explanation:
Using long division:
13x^2 + 13x + 15 <------------Quotient
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2x^2 - 3x - 5 ) 26x^4 - 13x^3 - 74x^2 - 46x - 24
26x^4 - 39x^3 - 65x^2
26x^3 - 9x^2 - 46x
26x^3 - 39x^2 - 65x
30x^2 + 19x - 24
30x^2 - 45x - 75
64x + 51 <---- Remainder. Division algorithm:
a = bq + r
Here a = the original expression , b = the divisor (2x^2 - 3x - 5), q is the quotient and r = the remainder,
26x^4 - 13x^3 - 74x^2 - 46x - 24 = (2x^2 - 3x - 5)(13x^2 + 13x + 15) + 64x + 51
= 2x^2(13x^2 + 13x + 15) - 3x(13x^2 + 13x + 15) - 5(13x^2 + 13x + 15) + 64x + 51
= 26x^4 + 26x^3 + 30x^2 - 39x^3 - 39x^2 - 45x - 65x^2 - 65x - 75+64x+51
= 25x^4 - 13x^3 - 74x^2 - 46x - 24 which is the same as the above.