The polynomial 2x^3–ax^2+5bx+4b has a factor x–2 and, when divided by x+1, a remainder of –15 is obtained. Find the values of a and b.?
With these values of a and b, factorize the polynomial completely. Hence, or otherwise, find all the real factors of 2x^6–11x^4+10x^2+8. Fill in the blank:
a=?
b=?
The complete factorized forms of the polynomials are :
2x^3 − ?x^2 +? x +? = ?
2x^6 − 11x^4 + 10x^2 + 8 =? .
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f(x) = 2x³ − ax² + 5bx + 4b
f(2) = −4a + 14b + 16 = 0
f(−1) = −a − b − 2 = −15
a = 11, b = 2
f(x) = 2x³ − 11x² + 10x + 8
f(x) = (x−2) (2x²−7x−4)
f(x) = (x−2) (x−4) (2x+1)
2x^6 − 11x^4 + 10x² + 8
= (x²−2) (x²−4) (2x²+1)
= (x−√2) (x+√2) (x−2) (x+2) (2x²+1)
f(x)= 2x^3–ax^2+5bx+4b
f(2)=0 and f(-1)=-15
solve 2 equations for the value of a , b