2. Let m(z) be the third derivative of a(z). Determine i so that m(i) = 0.
0
Let u(w) = -7*w**4 - 7*w**3 + 6*w**2 + 12*w - 6. Let r(n) = -n**4 - n**3 + n**2 + 2*n - 1. Let o(j) = 6*r(j) - u(j). Factor o(f).
f**3*(f + 1)
Let n = -34 + 37. Suppose 25*i + 21*i**2 - 20*i**3 + 2*i**4 + 3*i**2 + 32*i**n + 6 - 5*i = 0. What is i?
-3, -1
Let -10/9*l + 4/3*l**2 - 2/9*l**3 + 0 = 0. Calculate l.
0, 1, 5
Let u(m) = 3*m**2 + 8*m - 11. Let j(c) = -c**2 - 3*c**2 + 7 - 3*c + 2*c**2 - 2*c. Let k(n) = 8*j(n) + 5*u(n). Determine x so that k(x) = 0.
-1, 1
Let f(n) be the second derivative of n**7/5040 - n**6/480 - n**5/60 + 2*n**4 - 28*n. Let l(r) be the third derivative of f(r). Find k, given that l(k) = 0.
-1, 4
Let s(k) = -k**3 + k**2 + k + 3. Let o be s(0). What is x in -19*x + 34*x - o*x**2 - 6 - 2*x**2 - 4 = 0?
1, 2
Factor -8501*w - 47 + 8606*w + 5*w**2 + 47.
5*w*(w + 21)
Let r = 123063/497 + -652/71. Let y = -238 + r. Factor 0 + 1/7*g**3 + 1/7*g**5 - 2/7*g - y*g**2 + 3/7*g**4.
g*(g - 1)*(g + 1)**2*(g + 2)/7
Let p be 3/6*(-2)/1. Let k be (1/(-1))/p + 3. Factor -k + 6*m**2 - 2*m - 5 + 1 - 6*m - 2*m**4 + 4*m**3.
-2*(m - 2)**2*(m + 1)**2
Let x be -74*(-4)/6*(-9)/(-6). Factor -x*j**2 + 38*j**2 + 33*j**2 - 3*j.
-3*j*(j + 1)
Let s(m) be the third derivative of -1/4*m**5 + 1/12*m**6 + 0*m**4 + 0*m**3 + 0 + 0*m + 4*m**2 + 1/42*m**7. Factor s(k).
5*k**2*(k - 1)*(k + 3)
Factor 151*u**3 - 10*u - 299*u**3 + 153*u**3 - 5*u**2.
5*u*(u - 2)*(u + 1)
Let z(i) be the second derivative of -1/2*i**3 + 13*i + 0 - i**4 + 0*i**2 - 3/4*i**5 - 1/5*i**6. Factor z(c).
-3*c*(c + 1)**2*(2*c + 1)
Let u be -1*13/(195/(-30)). Suppose 0*n - 1/5*n**5 + 0 - 1/5*n**3 + 0*n**u - 2/5*n**4 = 0. What is n?
-1, 0
Solve 1/4*x**4 + 1/4*x**2 - 5/8*x**3 + 0*x + 0 = 0 for x.
0, 1/2, 2
Let s(z) = 6*z**2 + 2*z - 2. Let v be (-1 - (-12)/2)/1. Let x(h) = -13*h**2 - 5*h + 3. Let y(l) = v*s(l) + 2*x(l). Factor y(u).
4*(u - 1)*(u + 1)
Let d(f) be the third derivative of f**6/30 + 13*f**5/15 + 16*f**4/3 + 40*f**3/3 + 88*f**2. Solve d(i) = 0 for i.
-10, -2, -1
Let y(z) be the third derivative of 0*z + 12*z**2 + 1/12*z**4 - 1/60*z**5 + 0 + 0*z**3. Find t such that y(t) = 0.
0, 2
Let d(r) be the third derivative of 5*r**8/4032 + 17*r**7/1008 + r**6/24 - 13*r**5/60 - 10*r**2. Let k(z) be the third derivative of d(z). Factor k(p).
5*(p + 3)*(5*p + 2)
Factor -234/5*k - 6/5*k**3 + 168/5 + 72/5*k**2.
-6*(k - 7)*(k - 4)*(k - 1)/5
Let r(y) = -2*y**2 + 3*y + 2. Let g be r(0). Factor 14*d**g + 15*d**2 - 19*d**2 - d.
d*(10*d - 1)
Let g(o) = o**3 - o**2 + o - 1. Let u = 18 + -38. Let q(w) = -16*w**3 + 28*w**2 - 16*w + 20. Let z(b) = u*g(b) - q(b). Determine l, given that z(l) = 0.
-1, 0
Let q be 3/(10 - 190/40). Let b(g) be the first derivative of q*g + 1/7*g**2 + 9 - 2/21*g**3. Factor b(i).
-2*(i - 2)*(i + 1)/7
Let g be 1/(-5)*20/(-24) + (-637)/(-7644). Factor 1/4*u - g*u**3 + 3/4*u**2 - 3/4.
-(u - 3)*(u - 1)*(u + 1)/4
Let j be 2*(-30)/315*-14. Suppose 5*x = 15 + 5. Let 38/3*g**2 - 8/3 - 10*g**x + 16/3*g**3 + j*g**5 - 8*g = 0. What is g?
-1, -1/4, 1, 2
Let t(n) = -n**2 + 5*n + 16. Let g be t(7). Let -b**4 + 2*b**g - 2*b**3 - b**3 + b**5 - b**2 + 2*b**3 = 0. Calculate b.
-1, 0, 1
Let m(p) = -p**3 - 24*p**2 + 30*p + 127. Let n be m(-25). Suppose 5/4*d + 0 - 1/4*d**n = 0. Calculate d.
0, 5
Let m(o) be the second derivative of 5*o**6/8 - 1659*o**5/8 + 303589*o**4/16 + 61383*o**3/2 + 36963*o**2/2 + 277*o. Let m(f) = 0. What is f?
-2/5, 111
Let n(y) be the first derivative of -y**5/30 - 5*y**4/8 + y**3/6 + 47*y**2/12 + 5*y + 155. Solve n(w) = 0 for w.
-15, -1, 2
Let q(h) be the third derivative of h**9/181440 - h**8/60480 + 7*h**5/15 - 24*h**2. Let a(n) be the third derivative of q(n). What is o in a(o) = 0?
0, 1
Let n(s) be the third derivative of -1/22*s**4 + 0 - 1/330*s**5 - 3/11*s**3 + 22*s**2 + 0*s. What is v in n(v) = 0?
-3
Let s = -207 + 211. Let l(j) be the first derivative of -2 + 6*j**2 + s*j**3 + 0*j + 3/4*j**4. Let l(q) = 0. What is q?
-2, 0
Let l(f) be the second derivative of 3/2*f**2 - 2/9*f**3 - 1/36*f**4 + 0 + 1/90*f**5 - f. Let o(h) be the first derivative of l(h). Find d, given that o(d) = 0.
-1, 2
Factor z**3 - 3*z**2 - 44*z**2 + 39*z**2 - 31*z - 22.
(z - 11)*(z + 1)*(z + 2)
Let i(l) = -2*l**3 + 7*l**2 + 9*l - 18. Let v be i(4). Factor -86*s**3 + 30*s**3 + 46*s**3 - 15*s**4 + 10*s + 15*s**v.
-5*s*(s - 1)*(s + 1)*(3*s + 2)
Let l(a) be the third derivative of 0*a**5 - 19*a**2 + 0*a**4 + 1/200*a**6 + 0 + 0*a + 0*a**3 - 1/1050*a**7. Factor l(g).
-g**3*(g - 3)/5
Find b such that -13/8*b**2 + 5/8*b + 1/4 - 19/8*b**3 + 7/4*b**5 + 11/8*b**4 = 0.
-1, -2/7, 1/2, 1
Determine v, given that -3/5*v**4 + 0 - 36/5*v**2 - 24/5*v - 18/5*v**3 = 0.
-2, 0
Find b such that -557*b**2 + b**4 + 1117*b**2 + 33*b**3 - 560*b**2 = 0.
-33, 0
Let p(x) be the first derivative of 0*x**2 + 2/27*x**3 + 0*x - 1/6*x**4 + 10. Factor p(l).
-2*l**2*(3*l - 1)/9
Let a(z) = -z**3 + 13*z**2 - 11*z - 21. Let r(y) = -2*y**2 + 15 - y - 16 + y**2. Let b(v) = -a(v) - 4*r(v). Factor b(m).
(m - 5)**2*(m + 1)
Suppose -26*u = -16*u - 33*u. Factor 2/3*l**3 + 2/9*l**4 + u + 4/9*l**2 + 0*l.
2*l**2*(l + 1)*(l + 2)/9
Let i(w) = -w**3 - 27*w**2 + 36*w + 59. Let b(u) = 4*u**3 + 136*u**2 - 180*u - 296. Let c(g) = 3*b(g) + 16*i(g). Factor c(r).
-4*(r - 2)*(r + 1)*(r + 7)
Let f(c) be the first derivative of 2*c**3/17 + 110*c**2/17 + 144*c/17 - 201. Factor f(x).
2*(x + 36)*(3*x + 2)/17
Let c be (1/(-2))/(6/(-84)). Suppose 0 = 3*l - c - 11. Factor -6*y**3 + 4*y**4 + y - y**5 - l*y + 4*y - y**2 + 5*y**2.
-y*(y - 1)**4
Let h be (22 + 183/(-9))*(-2)/(-20). Determine c, given that 1/3*c - h*c**2 + 0 = 0.
0, 2
Factor 31752/5 + 504/5*q + 2/5*q**2.
2*(q + 126)**2/5
Let d(j) = j**2 - 2*j + 3. Let x be (-3)/12 - 25/(-20). Let m be d(x). Determine w, given that -3*w - w + w**3 + w**2 + m*w = 0.
-2, 0, 1
Let d = -31712 - -31715. Solve 2 - 14/3*g**d - 2/3*g**2 + 14/3*g - 4/3*g**4 = 0.
-3, -1, -1/2, 1
Factor -5/6*u**3 + 25/6 + 15/2*u + 5/2*u**2.
-5*(u - 5)*(u + 1)**2/6
Let k(u) be the third derivative of 0*u - 1/896*u**8 + 0*u**4 + 0*u**3 - 1/40*u**5 + 15*u**2 + 0 - 1/280*u**7 + 7/320*u**6. Factor k(q).
-3*q**2*(q - 1)**2*(q + 4)/8
Let q(r) = r + 4. Let z be q(-2). Suppose z*p + 0 = 4. Factor 2*k**2 - 3*k**2 - k**2 - p*k.
-2*k*(k + 1)
Let f = 5076/11 - 25292/55. Factor 4/5*t**3 + f*t + 0 + 12/5*t**2.
4*t*(t + 1)*(t + 2)/5
Suppose 0 = -3*w - 2*x + 74, 0 = -3*w + 4*x - 2*x + 58. Suppose -8*m = -w - 26. Find r such that -m*r**4 + 2*r**2 + 6*r**4 - 1 - 2*r**4 + r**4 = 0.
-1, 1
Suppose 24*i = -13*i + 74. Let z(f) be the first derivative of -3*f**i + 7*f**3 - 9/4*f**4 + 5 + 0*f. Factor z(p).
-3*p*(p - 2)*(3*p - 1)
Let n(h) be the first derivative of -2*h**5/5 + h**4/2 + 2*h**3/3 - h**2 - 75. Factor n(o).
-2*o*(o - 1)**2*(o + 1)
Let h = -5953/210 - -85/3. Let k = h - -143/210. Factor -2*l**2 + 2*l**3 + k*l + 0 - 2/3*l**4.
-2*l*(l - 1)**3/3
Factor 1/3*c**3 - 8 - 14/3*c + 1/3*c**2.
(c - 4)*(c + 2)*(c + 3)/3
Let v(m) be the third derivative of -m**5/100 + 7*m**4/40 + 4*m**3/5 + 230*m**2. Find j such that v(j) = 0.
-1, 8
Let w = 2873/515130 + -2/2453. Let p(a) be the third derivative of -a**2 + w*a**5 + 0 + 0*a - 1/21*a**3 + 0*a**4. Factor p(o).
2*(o - 1)*(o + 1)/7
Let f(i) = 27*i**4 - 36*i**3 - 33*i**2 + 15. Let u(t) = -7*t**4 + 9*t**3 + 8*t**2 - 4. Let q(x) = -4*f(x) - 15*u(x). Suppose q(d) = 0. Calculate d.
-1, 0, 4
Let p(b) be the third derivative of 0*b + 0*b**3 + 0 - 1/300*b**6 - 1/15*b**4 - 2/75*b**5 - 2*b**2. Determine k, given that p(k) = 0.
-2, 0
Let j = 57 + -83. Let u be -3 + 1/((-2)/j). Factor 10 - l**3 - u.
-l**3
Let t(h) = 9*h + 5. Let l be t(-5). Let k be -3*(l/15 - -2). Let 14*x**k + 3 + 16*x**4 - 9 - 12*x**3 - 38*x**2 - 18*x**4 - 20*x = 0. What is x?
-3, -1
Suppose 159*l + 145*l - 896 = 80*l. Let 0 + 6/5*u**5 - 12/5*u**l + 12/5*u**2 + 0*u**3 - 6/5*u = 0. What is u?
-1, 0, 1
Let b be ((-96)/(-160))/(6/16). Let x(j) be the first derivative of 0*j**3 + 0*j - 7 - b*j**5 - 2/3*j**6 + 0*j**2 + 0*j**4. Factor x(z).
-4*z**4*(z + 2)
Let u = 19 + -14. Let q(z) be the first derivative of 0*z**u - 1 + 0*z**4 + 0*z**2 + 0*z + 1/2*z**6 + 0*z**3. Determine j, given that q(j) = 0.
0
Let c be 0/((-3)/6*2). Factor 5*r**3 - 3 - 7*r**2 - 2*r**3 + 9*r - 2*r**2 + c*r**2.
3*(r - 1)**3
Let d(r) be