Let i(t) be the second derivative of 1/20*t**5 + 0*t**2 + t + o*t**3 + 0 + 0*t**4. Factor i(s).
s**3
Factor -2/7*t**3 - 22/7*t**2 - 30/7*t + 54/7.
-2*(t - 1)*(t + 3)*(t + 9)/7
Let v(s) be the first derivative of s**4/20 + 4*s**3/5 + 18*s**2/5 + 32*s/5 + 95. Solve v(a) = 0.
-8, -2
Find y such that 4/7*y**2 + 376/7*y + 8836/7 = 0.
-47
Suppose -9*m + 13*m = 8. Let k(q) be the first derivative of 0*q**m + 1/3*q**4 + 2/9*q**3 + 2/15*q**5 + 6 + 0*q. Factor k(r).
2*r**2*(r + 1)**2/3
Factor -22528*z**2 - 4*z**4 - 33261*z**2 + 51076*z + 3809*z**2 + 908*z**3.
-4*z*(z - 113)**2*(z - 1)
Let k(g) = 3*g**2 - 2*g + 3. Let d be k(1). Suppose -73*i + 7 + d*i**2 - 3 + 65*i = 0. Calculate i.
1
Determine c, given that 2/21*c**5 - 4/7*c**3 + 2/3*c**4 - 118/21*c - 100/21*c**2 - 2 = 0.
-7, -1, 3
Let g be -3 - (7/(-14))/((-2)/(-352)). Suppose 2 = g*z - 84*z. Factor 0 + 5/3*s**3 - 1/3*s**z - 1/3*s - s**4.
-s*(s - 1)**2*(3*s + 1)/3
Let t be (14/(-49))/((-3)/21). Suppose 0 - 5/2*h**3 + 5/2*h**4 + 0*h + 0*h**t = 0. Calculate h.
0, 1
Suppose 740 = 11*l + 674. Let y(h) be the second derivative of 1/2*h**2 + 1/12*h**3 - 13/40*h**5 + 0 - 12*h - 1/12*h**l - 3/8*h**4. Factor y(v).
-(v + 1)**3*(5*v - 2)/2
Suppose -l - 2 = -0*l - 2*d, -12 = -2*l - 4*d. Let v = 13/15 - 8/15. Solve 1/3*c**l + v*c + 0 = 0.
-1, 0
Suppose 33*l + 2*l = 175. Let h(g) be the second derivative of -1/90*g**6 + 2*g + 0*g**3 + 1/252*g**7 + 0*g**2 + 0*g**4 + 0 + 1/120*g**l. Factor h(p).
p**3*(p - 1)**2/6
Factor -1/2*m**4 - 363/2*m**2 - 33/2*m**3 + 0 - 1331/2*m.
-m*(m + 11)**3/2
Let r(z) be the first derivative of -2*z**3/3 + 9*z**2/2 + 5*z + 17. Let k(y) = 2*y**2 - 10*y - 4. Let t(m) = 5*k(m) + 4*r(m). Suppose t(d) = 0. Calculate d.
0, 7
Suppose -18*g - 6 = -20*g. Suppose 0 = g*x + 2*x - 15. Factor -2*b**2 - 6*b**x + 3*b**4 - 4*b**2 - b**5 + 4*b**5 + 3 + 3*b.
3*(b - 1)**2*(b + 1)**3
Let h(j) be the third derivative of 17*j**5/20 - 4*j**4 - 2*j**3 + 54*j**2 - j. Find u, given that h(u) = 0.
-2/17, 2
Let c(g) be the third derivative of 13*g**2 + 0 + 0*g + 1/90*g**6 + 1/15*g**5 + 1/9*g**4 + 0*g**3. Solve c(y) = 0.
-2, -1, 0
Let f be (36/(-20))/((-9)/15). Suppose 15/2*d**2 - 6*d**f + 3/2*d**4 - 3*d + 0 = 0. Calculate d.
0, 1, 2
Let m(p) = 7*p - 33. Let l(a) = 2*a**3 - 10*a**2 + a. Let z be l(5). Let t be m(z). Factor -4/5 - 2/5*c**4 + 14/5*c + 2*c**3 - 18/5*c**t.
-2*(c - 2)*(c - 1)**3/5
Suppose -12*g - 7*g - 22*g = 0. Factor -2*f**4 + 4/5*f - 14/5*f**2 + 18/5*f**3 + 2/5*f**5 + g.
2*f*(f - 2)*(f - 1)**3/5
Factor 0*q + 0 + 3/5*q**4 + 9/5*q**3 + 6/5*q**2.
3*q**2*(q + 1)*(q + 2)/5
Let d(i) be the first derivative of -7*i**7/2 + 42*i**6 - 759*i**5/5 + 120*i**4 - 32*i**3 + 27*i - 22. Let r(n) be the first derivative of d(n). Factor r(q).
-3*q*(q - 4)**2*(7*q - 2)**2
Let q(k) be the first derivative of 4*k**5/5 + 58*k**4 + 1120*k**3 - 116*k**2 - 3364*k - 200. Suppose q(l) = 0. Calculate l.
-29, -1, 1
Let b(a) be the second derivative of -a**8/5376 - a**7/672 + a**6/576 + a**5/32 + 5*a**4/6 - 9*a. Let w(h) be the third derivative of b(h). Factor w(c).
-5*(c - 1)*(c + 1)*(c + 3)/4
Let -7*p**2 + 9/4*p - 3*p**4 + 1/4*p**5 + 0 + 15/2*p**3 = 0. What is p?
0, 1, 9
Let p be 35 - (-1)/(1/1). Factor p*n**4 - 16*n**3 + 12*n**2 - 30*n**4 - 2 + 0.
2*(n - 1)**3*(3*n + 1)
Let v = -4617 + 32323/7. Suppose v*f + 0 - 2/7*f**2 = 0. What is f?
0, 2
Let n be 0/(-3*2 + (16 - 12)). Let b(f) be the first derivative of -1/6*f**4 + 1/18*f**6 + 0*f + n*f**5 + 1/6*f**2 + 0*f**3 - 4. Factor b(k).
k*(k - 1)**2*(k + 1)**2/3
Let m(t) be the first derivative of 5/11*t**4 + 5/11*t**2 + 2/11*t - 3 + 1/33*t**6 + 20/33*t**3 + 2/11*t**5. Find c, given that m(c) = 0.
-1
Let s(k) be the second derivative of -k**4/12 - k**3/3 + 4*k**2 + 188*k. Factor s(u).
-(u - 2)*(u + 4)
Let m(b) = 8*b**3 - b**2 + 4*b + 6. Let c be m(-1). Let w be ((-99)/18 - c) + 10/(-8). Solve -1/4*l**3 + 0 + 0*l**2 + 0*l + w*l**4 = 0.
0, 1
Solve -39*l**2 + 39 + 3/4*l - 3/4*l**3 = 0.
-52, -1, 1
Suppose 0 = 4*z - 12. Let v be (z/14*27)/(60/70). Let -73/4*r**2 - 1 - 9/4*r**3 - 8*r - v*r**5 + 81/4*r**4 = 0. What is r?
-1/3, 2
Factor 2/7*v**3 + 0 - 16/7*v + 4/7*v**2.
2*v*(v - 2)*(v + 4)/7
Let p be 8/(-36) - (-29)/9. Let -7*g - 4*g**2 + 4*g**3 - g + 3*g - p*g = 0. Calculate g.
-1, 0, 2
Suppose 3*k + 5*a + 149 = -29, 0 = 4*k + a + 226. Let b be 17/(-12) + 2 + 14/k. Determine o so that b*o**3 + 1/3 - 1/3*o**2 - 1/3*o = 0.
-1, 1
Let 148*l**2 - 129 - 25*l**3 - 66 - 7*l**3 - 99 + 2*l**4 - 112*l = 0. Calculate l.
-1, 3, 7
Let n(b) be the second derivative of 8*b**7/189 + 68*b**6/135 + 23*b**5/9 + 43*b**4/6 + 12*b**3 + 12*b**2 - 7*b + 1. Solve n(z) = 0 for z.
-2, -3/2
Let z be (3 - (-294)/24) + 4 + -4 - 4. Solve -z*b**2 - 15*b + 5/2*b**3 + 15/4*b**4 - 5 = 0 for b.
-1, -2/3, 2
Factor -1521 - 125*w**2 + 506*w + 94*w + 241 + 200*w.
-5*(5*w - 16)**2
Let u(o) be the third derivative of -27*o**2 + 1/12*o**4 + 0*o + 0 + 1/35*o**7 + 0*o**3 - 1/10*o**5 - 1/60*o**6. Determine d, given that u(d) = 0.
-1, 0, 1/3, 1
Let l(q) = -6*q**3 - 570*q**2 - 500*q. Let m(x) = 2*x**3 + 190*x**2 + 168*x. Let v(b) = -5*l(b) - 16*m(b). Solve v(z) = 0 for z.
-94, -1, 0
Solve 67*i**2 - 5*i**3 + 31*i**2 - 141*i + 8*i**3 - 32*i**2 + 72 = 0.
-24, 1
Let x be (-1)/(((-4)/104)/(3/6)). Suppose -7*l = 6*l - x. Factor -3/2*z + 1/2*z**2 + l.
(z - 2)*(z - 1)/2
Let -4/5*y**2 - 128/5*y - 1024/5 = 0. What is y?
-16
Suppose 0 = -3*k + 7*k - 20. Let o(h) = 301*h + 12*h**3 - 150*h - 4*h**3 - 159*h. Let f(v) = 12*v**3 - 12*v. Let d(y) = k*f(y) - 8*o(y). Factor d(i).
-4*i*(i - 1)*(i + 1)
Factor 136*c**4 - 4*c**2 + 19*c**3 - 76*c**4 + c**5 - 5*c**2 - 71*c**4.
c**2*(c - 9)*(c - 1)**2
Suppose -68*h**3 - 415*h + 180 + 553*h + 70*h**3 + 32*h**2 = 0. Calculate h.
-10, -3
Let h be (-4)/14 + (-5478)/(-14). Let -h*c + 25*c**4 + 270*c**2 - 209*c - 22*c**4 + 375 - 48*c**3 = 0. What is c?
1, 5
Suppose 58*v**3 - 42*v**2 + v**2 - 38*v**2 - 2*v**4 + 23*v**2 = 0. Calculate v.
0, 1, 28
Let k(u) be the second derivative of u**8/2940 + u**7/1470 - u**6/315 + u**3/6 - 12*u. Let h(o) be the second derivative of k(o). Factor h(f).
4*f**2*(f - 1)*(f + 2)/7
Factor 1/2*l**2 + 0 + 3/2*l**3 - l.
l*(l + 1)*(3*l - 2)/2
Let u = -7 - -6. Let k = 2 - u. Factor -n**5 - k*n**4 + n - 2*n**5 - n.
-3*n**4*(n + 1)
Let g(w) = -15*w**3 + 13*w**2 + 5. Let b(d) = -76*d**3 + 64*d**2 + 24. Suppose 2*k = 5*k + 72. Let y(s) = k*g(s) + 5*b(s). Factor y(o).
-4*o**2*(5*o - 2)
Let n(g) = 1 + 0 + g + g**2 - 2 - g**4. Let m(i) = 2*i**5 + 2*i**4 - 6*i**3 - 6*i**2 + 10*i - 2. Let k(s) = -2*m(s) + 4*n(s). Find h, given that k(h) = 0.
-2, 0, 1
Find d, given that d**3 + 4*d - 8*d**2 - 2*d**4 + 6 + 4*d**4 - 5*d**3 + 0*d**4 = 0.
-1, 1, 3
Let f(p) = p**2 - 11*p - 9. Let d be f(12). Let -16*c - d*c**4 + 6*c + c + 0*c - 21*c**2 - 15*c**3 = 0. What is c?
-3, -1, 0
Solve 3/2*f**2 + f**4 - 31/2*f - 21/2 + 15/2*f**3 = 0 for f.
-7, -1, 3/2
Let u(y) = -17*y + 6. Let q be u(2). Let v = 65/2 + q. Suppose 0 - 3/2*r**3 - 3*r - v*r**2 = 0. What is r?
-2, -1, 0
Let t(a) be the second derivative of 2*a**6/3 - 13*a**5/4 + 55*a**4/12 - 5*a**3/3 - 3*a + 4. Find s, given that t(s) = 0.
0, 1/4, 1, 2
Let f(n) be the first derivative of 0*n - 8*n**3 + 9 - 3/5*n**5 + 6*n**2 + 15/4*n**4. Factor f(d).
-3*d*(d - 2)**2*(d - 1)
Let f(u) be the second derivative of 5*u**4/36 - 65*u**3/6 - 40*u - 3. Factor f(l).
5*l*(l - 39)/3
Let s(j) be the first derivative of -j**6/840 + 3*j**5/140 + j**4/8 + 2*j**3 - 5. Let t(n) be the third derivative of s(n). Let t(h) = 0. Calculate h.
-1, 7
Let 56/5 - 22/5*t + 2/5*t**2 = 0. What is t?
4, 7
Let u(s) be the second derivative of 5*s**4/12 - 260*s**3/3 + 6760*s**2 - 241*s. Factor u(q).
5*(q - 52)**2
Let w(b) be the first derivative of -4*b**5/5 + 4*b**4 + 20*b**3/3 - 236. Factor w(l).
-4*l**2*(l - 5)*(l + 1)
Let g(r) = 7*r + 24. Let o be g(-3). Suppose -3 + 13*v**2 + v - 2*v**o - 11*v**2 + 9*v + 9 = 0. Calculate v.
-1, 3
Let n = -915 + 920. Let w(k) be the third derivative of 0*k**4 + 0 + 0*k - 1/24*k**6 + 0*k**3 - 1/12*k**n - 2*k**2. Suppose w(y) = 0. What is y?
-1, 0
Let v(t) be the third derivative of 8*t**7/1155 + 9*t**6/220 + 3*t**5/110 + 378*t**2 - t. Factor v(p).
2*p**2*(p + 3)*(8*p + 3)/11
Let u(m) be the second derivative of 1/48*m**4 + 3/8*m**2 + 1/6*m**3 + 0 + 16*m. Factor u(j).
(j + 