**2
Let h(l) be the second derivative of -1/8*l**3 + 2*l + 0 - 1/16*l**4 + 1/20*l**6 + 1/8*l**2 + 7/80*l**5. Suppose h(z) = 0. Calculate z.
-1, 1/3, 1/2
Let f(n) be the first derivative of -1/8*n**4 + 0*n + 1/4*n**2 + 1/4*n**5 - 5/12*n**3 - 1. Factor f(s).
s*(s - 1)*(s + 1)*(5*s - 2)/4
Let i(v) be the second derivative of -v**6/900 + v**5/150 - v**4/60 + v**3/6 + 2*v. Let x(n) be the second derivative of i(n). Factor x(m).
-2*(m - 1)**2/5
Let c(q) be the first derivative of -q**5/40 + q**4/24 + q**3/12 - q**2/4 - 2*q + 2. Let i(k) be the first derivative of c(k). Let i(l) = 0. Calculate l.
-1, 1
Factor -1/2 + 1/3*i + 1/6*i**2.
(i - 1)*(i + 3)/6
Let z(u) be the third derivative of u**7/420 + u**6/120 - u**5/40 - u**4/12 + u**3/3 + u**2. Factor z(w).
(w - 1)**2*(w + 2)**2/2
Let n(f) be the second derivative of -f**6/150 - 3*f**5/100 + f**4/12 + f**3/10 - 2*f**2/5 - 11*f. Factor n(x).
-(x - 1)**2*(x + 1)*(x + 4)/5
Let x = -148 + 150. Let 2/3*l**4 + 0*l + 0 + 8/3*l**x - 8/3*l**3 = 0. Calculate l.
0, 2
Let c be 25 - 23 - (-8)/(-6). Factor 1/3*r**2 + 1/3*r - c.
(r - 1)*(r + 2)/3
Let r(h) be the first derivative of 0*h**3 + 1/2*h**2 - 1/120*h**4 - 1/300*h**5 + 4 + 0*h. Let s(m) be the second derivative of r(m). What is u in s(u) = 0?
-1, 0
Suppose 2*w - w - 4 = -u, -w = -2*u + 2. Determine a so that 8*a**3 - 20*a - 4*a**3 - 8 - 4*a**w + 4*a**4 - 8*a**2 = 0.
-1, 2
Let f = -32 + -47. Let w = 239/3 + f. What is u in 0 + 0*u + 2/3*u**2 + w*u**3 = 0?
-1, 0
Let h be ((-160)/(-6100))/((-2)/10). Let k = 50/549 - h. Let -2/9*q**2 + 0 + k*q = 0. What is q?
0, 1
Find g such that 3/4*g**2 + 1/4*g**3 - 1/4*g - 3/4 = 0.
-3, -1, 1
Factor x + 1/2*x**2 - 3/2.
(x - 1)*(x + 3)/2
Let v(j) = -j**2 + j - 1. Let t(c) be the second derivative of c**2/2 + 2*c. Let a(f) = -t(f) - v(f). Suppose a(s) = 0. What is s?
0, 1
Let p = 163 + -1138/7. Determine r so that 0 - 4/7*r + p*r**3 - 4/7*r**2 = 0.
-2/3, 0, 2
Let r(i) = 9*i**3 - 31*i**2 + 75*i - 45. Let y(h) = 10*h**3 - 30*h**2 + 75*h - 45. Let g(q) = -5*r(q) + 4*y(q). Factor g(j).
-5*(j - 3)**2*(j - 1)
Let i(n) = n**2 + 3*n + 3. Let j(m) = 3*m**2 + 8*m + 8. Let l(c) = -8*i(c) + 3*j(c). Factor l(t).
t**2
Let l(v) be the third derivative of v**7/735 - v**5/70 + v**4/42 - v**2 + 25. Factor l(o).
2*o*(o - 1)**2*(o + 2)/7
Let c = 0 - -2/3. Let o be (-12)/((-7)/(28/9)). Let 2/3 - 8/3*j**5 - 8/3*j + o*j**3 + c*j**4 - 4/3*j**2 = 0. Calculate j.
-1, 1/4, 1
Let k(c) be the third derivative of c**11/332640 - c**10/56700 + c**9/45360 - c**5/30 - 2*c**2. Let w(d) be the third derivative of k(d). What is l in w(l) = 0?
0, 2/3, 2
Let o(v) = 2*v**3 - 4*v**2 + 2*v + 1. Let d(j) be the first derivative of -j**4/4 + j**3/3 - j - 6. Let z(f) = -3*d(f) - 3*o(f). Suppose z(g) = 0. Calculate g.
0, 1, 2
Let u(g) be the first derivative of g**6/2 - 6*g**5/5 + 3*g**4/4 + 12. Factor u(l).
3*l**3*(l - 1)**2
Let m(w) be the second derivative of -w**4/48 - w**3/24 + w**2/4 - 7*w. Determine p, given that m(p) = 0.
-2, 1
Determine q, given that 0*q**2 - 2/3*q**3 + 0*q + 0 = 0.
0
Let w(x) be the third derivative of 0 + 3*x**2 - 1/8*x**4 - 3/80*x**5 + 0*x + 1/2*x**3. Find h such that w(h) = 0.
-2, 2/3
Let j be ((-84)/(-72))/(14/18). Factor -9/2*h**2 + 9/2*h - j + 3/2*h**3.
3*(h - 1)**3/2
Let h be ((-10)/45)/((-8)/6). Let a(q) be the first derivative of 1/12*q**4 - 1 - 2/3*q + 2/9*q**3 - h*q**2. Factor a(l).
(l - 1)*(l + 1)*(l + 2)/3
Suppose -4*f - l - 3 = 4*l, 9 = -3*l. Factor -1/3*n**4 - 4/3*n**f - 1/3 - 2*n**2 - 4/3*n.
-(n + 1)**4/3
Let n(o) be the second derivative of -1/3*o**3 - 1/150*o**5 + 0*o**2 + 1/900*o**6 + 0 + 1/60*o**4 - 4*o. Let d(t) be the second derivative of n(t). Factor d(j).
2*(j - 1)**2/5
Let -2*g**2 + 8/5*g + 2/5*g**3 + 0 = 0. What is g?
0, 1, 4
Let v be (-2)/(-3) + 13/3. Suppose -8 = -v*j + 7. Factor 4/3*y**j + 0*y + 0 + 2/3*y**4 + 2/3*y**2.
2*y**2*(y + 1)**2/3
Let j = -5 + 64. Let f = -529/9 + j. Determine l, given that -f*l**4 + 0 + 2/9*l + 2/3*l**3 - 2/3*l**2 = 0.
0, 1
Let t be (-85)/(-102)*2/10. Let q(o) be the second derivative of -o + 0 - 1/24*o**4 - 1/4*o**2 - t*o**3. Factor q(x).
-(x + 1)**2/2
Let t(o) be the third derivative of -o**6/40 - 6*o**2. Factor t(s).
-3*s**3
Factor -3*j**2 - j**2 + j**4 + j**3 + 11*j**2 - 3*j - 6*j**3.
j*(j - 3)*(j - 1)**2
Factor -1/2*n**2 + 1/2*n**4 + n + 1/2*n**5 + 0 - 3/2*n**3.
n*(n - 1)**2*(n + 1)*(n + 2)/2
Let r(z) be the third derivative of z**6/360 - z**4/72 - 5*z**2. Factor r(o).
o*(o - 1)*(o + 1)/3
Let f(q) be the first derivative of -2*q**6/3 - 116*q**5/5 - 322*q**4 - 6664*q**3/3 - 7546*q**2 - 9604*q - 36. Determine h so that f(h) = 0.
-7, -1
Let l(h) be the second derivative of 3*h**6/20 + 5*h**5/8 + 7*h**4/8 + h**3/4 - h**2/2 - 5*h. Determine c, given that l(c) = 0.
-1, 2/9
Let v = 2 + 0. Solve -6*a**3 - 3 + 2*a**4 + 6*a + 2*a**v - 2 + 1 = 0.
-1, 1, 2
Factor 5*n - 110*n**2 - 3*n**3 + 3*n**4 - 2*n + 107*n**2.
3*n*(n - 1)**2*(n + 1)
Let d = 10 + 13. Suppose 8 = y - 2*z, -5*y + 3 = 5*z + d. Factor 10/3*f**4 + y + 0*f + 4/3*f**2 + 14/3*f**3.
2*f**2*(f + 1)*(5*f + 2)/3
Factor 3*a**2 + 2*a - 5/2*a**3 + 1/2*a**4 - 4.
(a - 2)**3*(a + 1)/2
Let y be 0*((-52)/(-16))/(-13). Suppose y + 0*i + 2/13*i**2 = 0. Calculate i.
0
Let o(c) = -c**2 + 3*c + 1. Let j be o(2). Determine l, given that -l**2 - l**4 - l + 3*l**j + 2*l**2 - 2*l**3 = 0.
-1, 0, 1
Let o(j) be the second derivative of 1/12*j**4 + 0 - 1/2*j**2 + 0*j**3 - 1/30*j**5 + j. Let q(c) be the first derivative of o(c). What is a in q(a) = 0?
0, 1
Solve 0*c**3 + 0*c + 4/3*c**4 - 8/3*c**2 + 4/3 = 0.
-1, 1
Suppose 0 = s - 1 - 3. Factor -6*o**2 - 3*o**5 - 2*o**2 + 3*o**s + 8*o**2.
-3*o**4*(o - 1)
Let 0*h**4 + 0 - 2/3*h**5 + 2*h**3 - 4/3*h**2 + 0*h = 0. What is h?
-2, 0, 1
Let n(x) = -4*x**2 + 3*x + 1. Let m(u) = -u**2 + u + 1. Let j(a) = 2*m(a) - n(a). Let v be j(1). Factor -9*s + s - 24*s**v + 0*s**2 + 14*s**3.
2*s*(s - 2)*(7*s + 2)
Let d(k) be the first derivative of k - 1/6*k**3 - 3 - 1/4*k**2. Factor d(m).
-(m - 1)*(m + 2)/2
Let a(l) = l**2 - l + 7. Let d(b) = b**3 + 6*b**2 + 6*b + 3. Let h be d(-5). Let v(t) = 2. Let x(y) = h*a(y) + 7*v(y). Factor x(k).
-2*k*(k - 1)
Suppose 0 + 16/3*k**2 - 10/3*k**3 - 8/3*k + 2/3*k**4 = 0. Calculate k.
0, 1, 2
Let o(n) be the third derivative of -n**5/15 - n**4 - 16*n**3/3 - 33*n**2. Factor o(a).
-4*(a + 2)*(a + 4)
Let m(x) = x**3 - x**2 - x - 1. Let c(a) = -23*a**3 - 77*a**2 - 65*a - 21. Let h(t) = -c(t) + 5*m(t). Factor h(p).
4*(p + 1)**2*(7*p + 4)
Let l be -3*4/(-42) - (-1300)/546. What is z in -10/3*z**2 + 2/3*z**3 - l + 16/3*z = 0?
1, 2
Let l = 8 + -5. Suppose 0 = -l*r - r + 8. Solve -r - 3 + 6*k + 1 - 2*k**2 = 0.
1, 2
Let s be 2*((-14)/(-12))/7. Let z(t) be the first derivative of 1/4*t**4 - 1/2*t**2 + t + 1 - s*t**3. Factor z(f).
(f - 1)**2*(f + 1)
Let i(m) be the third derivative of 0*m**4 + 0 - 1/60*m**6 - m**2 + 1/15*m**5 - 1/35*m**7 + 0*m**3 + 0*m. Factor i(l).
-2*l**2*(l + 1)*(3*l - 2)
Let l(m) be the third derivative of m**5/150 + m**4/30 + m**3/15 - 5*m**2. Factor l(j).
2*(j + 1)**2/5
Suppose 3/2*w - 3/4 - 3/4*w**2 = 0. Calculate w.
1
Let y be (14/126)/(1/6). Factor 2/3 + y*b**2 + 4/3*b.
2*(b + 1)**2/3
Let k(q) be the second derivative of q**7/63 - q**6/15 + q**5/15 + q**4/9 - q**3/3 + q**2/3 + 15*q. Factor k(a).
2*(a - 1)**4*(a + 1)/3
Solve -3/8*k**4 + 3/8*k**2 + 3*k + 3/2 + 3/8*k**5 - 15/8*k**3 = 0.
-1, 2
Let n(c) = -9*c**2 - 12*c - 13. Let l(d) = 4*d**2 + 6*d + 6. Let z(s) = -5*l(s) - 2*n(s). Factor z(w).
-2*(w + 1)*(w + 2)
Let z(m) be the first derivative of -m**4/2 - 8*m**3/3 + 44. Find o, given that z(o) = 0.
-4, 0
Let u(p) = 13*p - 1. Let l be u(1). Let 6*n**3 - 3*n**4 + 4*n**3 + 9*n - 27*n**2 - 6 + l*n + 5*n**3 = 0. Calculate n.
1, 2
Let v = -2962/3 + 988. Determine a so that 5/3*a**2 - a**5 + 0 + v*a - 5/3*a**4 + 1/3*a**3 = 0.
-1, -2/3, 0, 1
Let u(k) be the first derivative of -1/5*k**5 + 2/3*k**3 + 0*k**2 + 0*k**4 + 2 - k. Suppose u(a) = 0. Calculate a.
-1, 1
Let j be (4/1*-1)/(-11). Let b = j - 1/33. Let 2/3 - m + b*m**2 = 0. What is m?
1, 2
Let v be (-2 + 2)/(16 + -17). Let h(d) be the second derivative of v*d**3 + 1/15*d**6 + 0*d**2 - 2*d + 1/30*d**5 + 0 + 0*d**4. Factor h(w).
2*w**3*(3*w + 1)/3
Let l(a) = 21*a**2 - a + 3. Suppose -4*t + 16 + 24 = 0. Let b(g) = -41*g**2 + 3*g - 5. Let d(w