3*i + 18. Let c(j) = -2*b(j) + 35*d(j). Let c(z) = 0. Calculate z.
-1, 1/3, 4
Let k(p) = -p**3 - 13*p**2 + p + 13. Let y be k(-13). Let s(a) be the third derivative of y*a**3 - 1/24*a**4 + 0*a + 1/60*a**5 - 4*a**2 + 0. Factor s(u).
u*(u - 1)
Factor -3*l**5 + 3*l**3 + 4*l - 4*l.
-3*l**3*(l - 1)*(l + 1)
Let w(l) be the third derivative of -l**6/15 + l**5/30 + 7*l**2. Factor w(s).
-2*s**2*(4*s - 1)
Let g(p) = -p**3 + p**2 + p - 21. Let i be g(0). Let f be (-69)/i + 2/(-7). Factor -5*c + 4*c - f*c + c - 3*c**2.
-3*c*(c + 1)
Let a(s) be the second derivative of -s**5/30 + s**3/3 - s**2 + 5*s. Let f(d) be the first derivative of a(d). Factor f(k).
-2*(k - 1)*(k + 1)
Let b(t) be the third derivative of -5*t**7/56 + 11*t**6/2 - 923*t**5/10 - 198*t**4 - 162*t**3 - t**2 + 18*t. Determine v, given that b(v) = 0.
-2/5, 18
Let h(n) be the first derivative of -9*n**4/32 - n**3/8 + 3*n**2/2 - 3*n/2 + 2. Factor h(l).
-3*(l - 1)*(l + 2)*(3*l - 2)/8
Factor -7 + 4 - 2 + 5*q**2.
5*(q - 1)*(q + 1)
Let t(l) be the first derivative of l**4 - 28*l**3/3 + 12*l**2 + 17. Factor t(x).
4*x*(x - 6)*(x - 1)
Let w = 374 + -4852/13. Find l such that -w*l**3 + 4/13*l + 0 - 6/13*l**2 = 0.
-1, 0, 2/5
Let m(z) be the second derivative of -z**7/14 + 3*z**5/5 - z**4/2 - 3*z**3/2 + 3*z**2 + 2*z + 17. Let m(j) = 0. Calculate j.
-2, -1, 1
Let q be (-1 - -3) + (-63)/36. Factor -1/2*k + q*k**2 + 1/4.
(k - 1)**2/4
Let s(u) be the first derivative of -u**5/50 + u**4/40 + u**3/10 - u**2/20 - u/5 + 12. Factor s(f).
-(f - 2)*(f - 1)*(f + 1)**2/10
Suppose 0*y + 5*v - 16 = 3*y, 23 = y + 4*v. Suppose z - y*z = -6. Factor o**4 - z*o**2 + 44*o - 44*o + 2*o**2.
o**2*(o - 1)*(o + 1)
Let n = -125/4 - -383/12. Factor -6 - n*d**2 + 4*d.
-2*(d - 3)**2/3
Factor 1/8*f**5 - 9/8*f + f**3 + 5/4*f**4 + 0 - 5/4*f**2.
f*(f - 1)*(f + 1)**2*(f + 9)/8
Let x be (-3)/2 + 2 + 1. Let i(p) be the first derivative of -4/3*p**2 - x*p**4 - 8/3*p**3 + 1 + 0*p. Let i(k) = 0. Calculate k.
-2/3, 0
Solve 5/6*q**2 - 1/3*q**3 - 1/3 - 1/6*q = 0 for q.
-1/2, 1, 2
Factor 0*c - 3*c - 3*c + 4*c + c**2 + 1.
(c - 1)**2
Let b(t) be the first derivative of -4/7*t**2 + 3 + 4/21*t**3 + 0*t. Factor b(m).
4*m*(m - 2)/7
Suppose 20 = 2*b + 4*h, -b + 5*h - 19 = -2*b. Suppose 2*a = r - 1 + 4, -4*a = b*r - 24. Factor p**5 + 2*p**4 - a*p + 0*p + 2*p - 2*p**2.
p*(p - 1)*(p + 1)**3
Let a = 1982/9 - 220. Find n such that 0*n**3 + 0*n**2 - 2/9*n**4 + 0 + a*n**5 + 0*n = 0.
0, 1
Let x = 64/3 - 21. Let s(j) be the second derivative of 2*j - 2/15*j**5 - 4/9*j**3 + x*j**4 + 1/3*j**2 + 1/45*j**6 + 0. Suppose s(n) = 0. Calculate n.
1
Factor -4*s - 14*s**2 + 9*s**3 + s**3 + 8*s**4 + 0*s**3.
2*s*(s - 1)*(s + 2)*(4*s + 1)
Let b = 7/15 + -4/15. Let 1/5*i**2 + b - 2/5*i = 0. What is i?
1
Let g(q) = 2*q**2 + 4*q + 2. Let h(u) = u**2 - 2. Let n be h(0). Let m be g(n). Factor -3*a**4 + 3/2*a + 0*a**3 + 0 - 3/2*a**5 + 3*a**m.
-3*a*(a - 1)*(a + 1)**3/2
Let v(p) be the second derivative of -p**7/21 - 7*p**6/30 + 5*p**4/6 + p**3/3 - 3*p**2/2 + 26*p. Let v(l) = 0. Calculate l.
-3, -1, 1/2, 1
Let x(c) = 6*c**3 + 2*c**2 + c + 5. Let y(m) = m**3 + 1. Let q = -1 - 1. Let a(o) = q*x(o) + 10*y(o). Factor a(t).
-2*t*(t + 1)**2
Let r = 684 - 4786/7. Factor -2/7 - 6/7*h**2 + r*h**3 + 6/7*h.
2*(h - 1)**3/7
Let i(c) = 5*c**3 - c**2 - 3*c + 1. Let u be i(1). Solve -4/9*g**3 + 0*g**u + 4/9*g - 2/9 + 2/9*g**4 = 0.
-1, 1
Let q be 3/(-9) - 7/(-3). Let m be 10/6 - ((-133)/(-21) - 5). Factor 1/3*l**q + 1/3*l - m - 1/3*l**3.
-(l - 1)**2*(l + 1)/3
Let p(k) be the third derivative of k**5/240 + 7*k**4/48 + 49*k**3/24 + 21*k**2. Factor p(d).
(d + 7)**2/4
Suppose -2*s + 6 = 3*z, -12 = 9*s - 5*s. Factor 0 + 0*i - 1/5*i**z - 1/5*i**5 + 1/5*i**2 + 1/5*i**3.
-i**2*(i - 1)*(i + 1)**2/5
Let a(t) be the first derivative of 2*t**3/3 - 3*t**2 + 5*t - 6. Let c(h) = h**2 + 1. Let j(m) = a(m) - 5*c(m). What is o in j(o) = 0?
-2, 0
Let y be 11/220*(-4)/(-6). Let h(w) be the third derivative of 0*w + y*w**5 - 1/105*w**7 + 0*w**4 + 0*w**6 + 0 + 3*w**2 + 0*w**3. Solve h(v) = 0 for v.
-1, 0, 1
Find c, given that 8/5*c - 4/5*c**2 + 0 - 4/5*c**3 = 0.
-2, 0, 1
Find d such that 2/3*d**5 - 32/3*d + 16/3*d**2 - 16/3*d**4 + 0 + 10*d**3 = 0.
-1, 0, 1, 4
Suppose -5*l - 10*l = 0. Factor l + 3/5*n**3 - 6/5*n**2 + 3/5*n.
3*n*(n - 1)**2/5
Let n(l) be the third derivative of 1/21*l**4 + 0*l + 1/105*l**5 + 0 - 2*l**2 - 1/6*l**3 + 1/1260*l**6. Let b(w) be the first derivative of n(w). Factor b(k).
2*(k + 2)**2/7
Let f(p) be the third derivative of -3*p**5/80 + p**4/32 - 6*p**2. Factor f(s).
-3*s*(3*s - 1)/4
Let q(k) be the third derivative of -3/10*k**3 + 0*k - 1/100*k**5 - 2*k**2 - 1/10*k**4 + 0. What is s in q(s) = 0?
-3, -1
Let g(u) be the second derivative of u**9/3528 - u**8/1470 - u**7/735 - 7*u**3/6 + 4*u. Let o(z) be the second derivative of g(z). Let o(k) = 0. What is k?
-2/3, 0, 2
Let r(t) be the third derivative of 1/1155*t**7 - 1/66*t**4 + 5*t**2 + 0*t + 0 + 0*t**3 + 1/330*t**6 - 1/330*t**5. Factor r(j).
2*j*(j - 1)*(j + 1)*(j + 2)/11
Let t(j) be the second derivative of j**4/12 - 2*j**3/3 + 2*j**2 - 33*j. Factor t(l).
(l - 2)**2
Let y(b) be the first derivative of b**3 + 6*b**2 + 9*b + 9. Factor y(c).
3*(c + 1)*(c + 3)
Let d be -1 + (2 - 0) + 1. Let m(x) = -x**3 - 7*x**2. Let k be m(-7). Factor -1/2*c**4 - 3/4*c**5 + 1/4*c**3 + 0 + k*c + 0*c**d.
-c**3*(c + 1)*(3*c - 1)/4
Let z be ((-8)/14)/(18/(-21)). Let q = -346/3 - -118. Factor -z*c**2 + q*c - 8/3.
-2*(c - 2)**2/3
Suppose -20 = -2*d - 2*d. Suppose -2*r - 4*l = -36, 3*r + d*l - 3*l - 38 = 0. Solve -10*g**3 - r*g + 1 - 12*g**2 + 4*g - 3*g**4 - 2 = 0.
-1, -1/3
Let b(a) = 5*a**4 + 4*a**3 - 9*a**2. Let n(u) = -u**4 - u**3 + 2*u**2. Let w(r) = 2*b(r) + 9*n(r). Suppose w(v) = 0. Calculate v.
0, 1
Let j(v) = 2*v**3 + v**2 - 2*v + 1. Let l be j(1). Factor -a**l - a**2 + a + 0*a + a.
-2*a*(a - 1)
Let k = 2 + 0. Let 2*c**k - 5*c - c + c**2 = 0. What is c?
0, 2
Factor -4/11*y**4 + 2/11*y**2 + 0*y - 2/11*y**3 + 0.
-2*y**2*(y + 1)*(2*y - 1)/11
Find y such that 2 + y**2 - 2*y**3 + 15*y**2 + 10*y**3 + 10*y = 0.
-1, -1/2
Let d(j) = j**3 - 16*j**2 + 15*j. Let v be d(15). Let t(m) be the first derivative of v*m + 1/7*m**2 + 1 + 2/21*m**3 - 2/35*m**5 - 1/14*m**4. Factor t(z).
-2*z*(z - 1)*(z + 1)**2/7
Let k be ((-1)/(-2) + 0)*12. Suppose 49 = 5*b - k. Factor 12*g**2 - 1 - 7*g**3 - b*g + 4*g**2 + 3.
-(g - 1)**2*(7*g - 2)
Let x(l) be the third derivative of l**8/672 - l**6/48 + l**4/12 - 22*l**2. Determine k so that x(k) = 0.
-2, -1, 0, 1, 2
Let s be (16/36)/(357/198). Let n = s + 2/51. Factor 0 + 2/7*v**3 - 4/7*v + n*v**2.
2*v*(v - 1)*(v + 2)/7
Let a(q) be the third derivative of q**5/210 + q**4/14 - q**3/3 + 16*q**2. Find i such that a(i) = 0.
-7, 1
Let n(k) be the first derivative of 7*k**4/30 - k**3/5 - k + 1. Let i(b) be the first derivative of n(b). Factor i(u).
2*u*(7*u - 3)/5
Let k = 4103/6 + -1365/2. Find z, given that 1/3*z**2 + k - 5/3*z = 0.
1, 4
Suppose -15 = -2*l + 7*l + 5*f, f - 3 = 0. Let i = l - -8. Factor -5*t - t**2 + i*t + 2*t.
-t*(t + 1)
Let w(x) = x**2 + 10*x - 18. Let r be w(-12). Let i be ((-8)/r)/(1/(-1)). Find a, given that 2/3*a**5 - 2/3*a + 0 - 4/3*a**4 + i*a**2 + 0*a**3 = 0.
-1, 0, 1
Let q(m) = -3*m**2 - 3*m - 4. Let w be q(-4). Let d be 14/w - 3/(-5). Factor 3/4*p**3 + 0 + 1/4*p + d*p**4 + 3/4*p**2.
p*(p + 1)**3/4
Let d = 709/3 + -235. Factor -28/3*q + 49/3*q**2 + d.
(7*q - 2)**2/3
Factor -9*o**2 + 19*o**2 - 8*o**2 - o**3 - o**3.
-2*o**2*(o - 1)
Suppose -3 = -3*s + d - 2, 15 = 3*d. Let o(h) be the second derivative of -2*h + 0*h**s + 0 + 1/6*h**4 - 2/3*h**3. Factor o(t).
2*t*(t - 2)
Let y(j) be the first derivative of 4 + 73/14*j**4 - 24/7*j**2 - 34/21*j**3 - 7/3*j**6 - 8/7*j + 6/5*j**5. Find p such that y(p) = 0.
-1, -2/7, 1
Let n be (-3)/(84/35) - 183/(-108). Factor 2/9 + n*z + 2/9*z**2.
2*(z + 1)**2/9
Suppose 0 = -77*m + 94*m. Factor 0*h + m + 3/5*h**3 + 3/5*h**5 + 0*h**2 + 6/5*h**4.
3*h**3*(h + 1)**2/5
Let s = 3 - -1. Let u be 6/(2 + 0) + 24. Find k, given that -u*k**2 - 2 + 2*k**2 + 18*k**5 - 4*k**3 - 3*k**2 + 30*k**s - 14*k = 0.
-1, -1/3, 1
Factor -6*t**3 - 14*t**3 - 4 + 6*t + 18*t**3.
-2*(t - 1)**2*(t + 2)
Let o(y) be the third derivative of -1/72*y**4 + 0*y + 0*y**7 + 1/180*y**6 + 3*y**2 - 1/1008*y**8 + 0*y**5 + 0*y**3 + 0. Determine k so