*4 + 0*y + 0*y**3 - 3/2*y**2 - 15 + 6/5*y**5. Let i(z) = 0. Calculate z.
-1, 0, 1/2
Let m(r) be the second derivative of 5*r**4/12 - 19*r**3/3 - 8*r**2 + 5*r + 5. Suppose m(i) = 0. Calculate i.
-2/5, 8
Let m(h) be the first derivative of -3*h**4/4 + 4*h**3/9 + 3*h**2/2 - 4*h/3 - 94. Factor m(z).
-(z - 1)*(z + 1)*(9*z - 4)/3
Let y(v) be the second derivative of 0 - 1/12*v**3 - 1/12*v**4 + 0*v**2 - 1/40*v**5 - 14*v. Factor y(o).
-o*(o + 1)**2/2
Let w(v) be the third derivative of -v**7/42 + 11*v**5/6 - 5*v**4 - 75*v**3/2 + 12*v**2 + 13. Let w(h) = 0. What is h?
-5, -1, 3
Suppose 2549 = -4*b + 2561. Factor -3/4*v**4 + 0 + 0*v**b - 3/2*v + 9/4*v**2.
-3*v*(v - 1)**2*(v + 2)/4
Let r be 248/7 + 18/(-42). Let b be (-4)/r*((-21)/(-14) + -4). Factor -8/7*m - 4/7*m**3 + 10/7*m**2 + b.
-2*(m - 1)**2*(2*m - 1)/7
Let z(j) = -40*j**2. Let t(p) = 5*p**2. Let w(b) = 25*t(b) + 3*z(b). Let w(r) = 0. Calculate r.
0
Let c(s) = -s**2 + 1. Let b(u) = u**2 - 1. Suppose -3*o + 2*g = 4*g - 22, 2*g = o + 6. Let h(p) = o*c(p) + 7*b(p). Factor h(f).
3*(f - 1)*(f + 1)
Suppose -10*b - 9 = -7*b. Let u be (48/(-56))/(b/14). Factor 133 + 2*m**u - 133 - 2*m**5.
-2*m**4*(m - 1)
Let g(d) be the first derivative of -d**3/15 + 13*d**2/2 - 64*d/5 - 419. Factor g(m).
-(m - 64)*(m - 1)/5
Let x(w) = w**3 - w**2 + w - 1. Let n(o) = 3*o**4 + 76*o**3 - 35*o**2 - 202*o - 102. Let y(p) = -n(p) + 2*x(p). Suppose y(b) = 0. Calculate b.
-25, -1, -2/3, 2
Let m(r) = -8*r**2 + 8*r - 4. Let o(g) be the third derivative of 23*g**5/60 - 25*g**4/24 + 11*g**3/6 + 33*g**2. Let c(y) = 11*m(y) + 4*o(y). Factor c(n).
4*n*(n - 3)
Suppose -k - 3*b + 15 = 0, -3*k + 55 - 2 = b. Let z = k + -14. Factor -241*y**3 + 243*y**3 - z*y + 2*y.
2*y*(y - 1)*(y + 1)
Suppose 4*m = -17*m + 53*m - 64. Determine k, given that -5 + 15/2*k + 15/2*k**m - 5*k**3 = 0.
-1, 1/2, 2
Let t(d) = 4*d**3 - d**2 + 6*d - 4. Let p(h) = -5*h**3 + h**2 - 7*h + 5. Let r(x) = -5*p(x) - 6*t(x). Factor r(w).
(w - 1)*(w + 1)**2
Let s(x) be the first derivative of 0*x + 1/4*x**5 + 17/16*x**4 - 3 + 4/3*x**3 + 1/2*x**2. Factor s(a).
a*(a + 1)*(a + 2)*(5*a + 2)/4
Let o be -6*(-4)/(-18)*(-247)/(-4). Let a = 84 + o. Let 1/3*l**3 - 1 - 1/3*l**2 - a*l = 0. What is l?
-1, 3
Suppose 55 = 6*f + 5*f. Suppose 0 = f*k + r - 2, -2*k + 5*r - 8 = r. Suppose -1/3*p + k + 1/6*p**2 = 0. What is p?
0, 2
Factor -3*u + 0*u**2 - 10*u**2 + 4*u**2 + 3*u**2.
-3*u*(u + 1)
Let a be (4371/155 + -27)*(-5)/(-4). Let a*g - g**2 + 0 + 1/6*g**3 = 0. What is g?
0, 3
Let y(z) be the third derivative of -z**6/300 + z**4/15 + 68*z**2. Factor y(m).
-2*m*(m - 2)*(m + 2)/5
Let n be (-42)/(3*(-4)/12). Let -195*p**3 - 33*p**5 + 8*p**2 + 67*p**2 - n*p**5 - 10*p + 115*p**4 + 90*p**4 = 0. Calculate p.
0, 1/3, 2/5, 1
Let y(a) be the first derivative of a**5/5 - a**4 - a**3/3 + 8*a**2 - 12*a + 17. Solve y(c) = 0 for c.
-2, 1, 2, 3
What is u in 0 - 2/3*u**2 + 0*u = 0?
0
Let s be (-2)/(-14)*(1 - 231/378). Let x(p) be the first derivative of -6 + 1/2*p**2 + 3/2*p + s*p**3. Let x(f) = 0. What is f?
-3
Let j(d) = -3*d**4 + 2*d**3 + 13*d**2 + 4. Let n(s) be the first derivative of 2*s**5/5 - 3*s**4/4 - 4*s**3 - 3*s - 6. Let v(f) = -3*j(f) - 4*n(f). Factor v(p).
p**2*(p + 3)**2
Let r(c) be the first derivative of 12 - 2/3*c**3 - 1/9*c**2 + 0*c - 6/5*c**5 - 3/2*c**4. Factor r(g).
-2*g*(3*g + 1)**3/9
Let t(p) = 3*p - 93. Let f be t(31). Let k(m) be the third derivative of 1/660*m**6 + 0*m**5 + 1/1155*m**7 + f*m**4 + 0 + 6*m**2 + 0*m**3 + 0*m. Factor k(d).
2*d**3*(d + 1)/11
Suppose 19*t + 4 = 20*t. Factor -6/5*m**3 + 6/5*m + 3/5*m**2 + 0 - 3/5*m**t.
-3*m*(m - 1)*(m + 1)*(m + 2)/5
Determine z, given that -16/15*z**3 + 16/15 + 14/5*z**2 - 44/15*z + 2/15*z**4 = 0.
1, 2, 4
Suppose 3*b = -3*y - 12, -106*y + 101*y = -b - 4. Solve 1/9*z**5 - 2/9*z**3 + 0*z - 1/9*z**4 + y + 0*z**2 = 0 for z.
-1, 0, 2
Solve 615*k**5 - 254*k**2 - 625*k**5 - k**2 - 30 - 205*k**3 - 145*k - 75*k**4 = 0 for k.
-3, -2, -1, -1/2
Suppose 8*o = 34*o + 294 - 294. Factor o*i + 0 + 2/9*i**3 - 2/9*i**2.
2*i**2*(i - 1)/9
Let l(u) be the second derivative of u**6/10 - 9*u**5/4 + 12*u**4 + 32*u**3 - 3*u + 37. Factor l(a).
3*a*(a - 8)**2*(a + 1)
Let o(l) = 2*l**2 - 17*l + 38. Let c be o(3). Suppose -1 = -f - 0*f. Suppose f + 52*i**2 + c + 2 + 60*i = 0. Calculate i.
-1, -2/13
Let y be (-4977)/(-84)*(-24)/(-9). Let a = -154 + y. Solve 0*t**2 + 0*t**3 + 0*t + 0 - 1/4*t**a + 1/4*t**5 = 0 for t.
0, 1
Factor 22/7*w**4 + 0*w + 0 - 12/7*w**2 + 10/7*w**3.
2*w**2*(w + 1)*(11*w - 6)/7
Let z = 10 + -8. Let k(x) be the first derivative of -1/5*x**z + 0*x - 1/15*x**3 + 1. Solve k(i) = 0 for i.
-2, 0
Let v(a) be the first derivative of -2*a**5 - 735*a**4/4 - 14045*a**3/3 - 9900*a**2 - 6480*a + 233. Find g such that v(g) = 0.
-36, -1, -1/2
Let f = -376 - -378. Let q(k) be the first derivative of 2*k**f - 8/3*k**3 + 4 + k**4 + 0*k. Solve q(v) = 0.
0, 1
Let k(c) be the third derivative of c**7/420 - 5*c**6/6 + 1633*c**5/20 + 2525*c**4/6 + 10201*c**3/12 - 3*c**2 + 68*c. Factor k(o).
(o - 101)**2*(o + 1)**2/2
Determine a, given that 5*a**4 + a**5 + 0*a**4 + a**2 - 6*a**4 + 23*a**3 - 24*a**3 = 0.
-1, 0, 1
Let f be 15/(-125)*70/(-21). Let -16/5 - f*o**2 + 12/5*o = 0. Calculate o.
2, 4
Let l(t) be the second derivative of 0 + 1/7*t**2 + 13*t - 2/21*t**3 + 1/42*t**4. Determine z, given that l(z) = 0.
1
Suppose 18 = u - 4*d, -d + 28 = 4*u - 6*d. Let f be (u - (-9)/(-12))/(3/4). Let 3*j**2 + 2/3 - 7/3*j + 1/3*j**4 - f*j**3 = 0. Calculate j.
1, 2
Let x(q) be the third derivative of -q**9/2520 - q**8/2240 + q**7/840 - q**4/6 + 11*q**2. Let c(p) be the second derivative of x(p). Factor c(w).
-3*w**2*(w + 1)*(2*w - 1)
Factor -1/4*d**2 + 15/4 + 7/2*d.
-(d - 15)*(d + 1)/4
Let c be 4 - (50/(-40) + 13/4). Let k(b) be the third derivative of 0*b**6 - 1/270*b**5 + 0*b + 0*b**4 + 1/945*b**7 + c*b**2 + 0 + 0*b**3. Factor k(a).
2*a**2*(a - 1)*(a + 1)/9
Suppose 156 = -x + 3*x + 2*y, -3*x + 209 = -2*y. Let o = x + -71. Find g such that -2/15*g**5 + 2/3*g**4 + 0*g + 0 - 16/15*g**3 + 8/15*g**o = 0.
0, 1, 2
Determine l, given that 36/5*l + 0 + 4/5*l**4 - 4*l**3 + 12/5*l**2 = 0.
-1, 0, 3
Let x(c) be the first derivative of -29 + 1/18*c**4 - 1/9*c**2 + 0*c + 0*c**3. Let x(v) = 0. What is v?
-1, 0, 1
Let v(r) be the first derivative of 4*r**5/5 + 12*r**4 - 80*r**3 + 128*r**2 - 215. Factor v(q).
4*q*(q - 2)**2*(q + 16)
Let x(w) be the second derivative of w**9/1512 + w**8/420 - w**6/90 - w**5/60 - 29*w**3/6 - 4*w. Let o(d) be the second derivative of x(d). Factor o(y).
2*y*(y - 1)*(y + 1)**3
Let u = -20305 - -20386. Factor 675/2*f**2 - u + 567/2*f + 237/2*f**3 + 27/2*f**4.
3*(f + 3)**3*(9*f - 2)/2
Factor -6/5 - 12/5*b**2 - 3*b - 3/5*b**3.
-3*(b + 1)**2*(b + 2)/5
Let n(t) = -t**4 - 61*t**3 + 331*t**2 - 767*t + 586. Let r(q) = -6*q**4 - 306*q**3 + 1656*q**2 - 3840*q + 2928. Let u(o) = 21*n(o) - 4*r(o). Factor u(j).
3*(j - 11)*(j - 3)**2*(j - 2)
Let w be 20 + -4 + (3 - -1). Suppose -18*p - 64 = -w*p. Solve 32/3 + 2*i**4 + 40/3*i**3 + 32*i**2 + p*i = 0.
-2, -2/3
Suppose 2*p - 14 = -2*w, 0 = 48*w - 51*w - 5*p + 31. Factor -9/5*m + 3/5*m**w + 6/5.
3*(m - 2)*(m - 1)/5
Let l(g) = -g**3 + 7*g**2 - 4*g - 8. Let u be l(6). Factor u*c**2 + 20*c + 0*c**2 - 6*c**2 - 20 - 30.
-2*(c - 5)**2
Suppose -2*p + 5*i = -37, 0 = -5*p - 14*i + 18*i + 33. Solve -1/3*z**3 + p + 5/3*z + 1/3*z**2 = 0.
-1, 3
Let m be ((-6)/5)/(2 - (-23)/(-10)). Let w be ((-188)/40 - -5)*m/6. Factor -w*c + 2/5*c**3 - 1/5*c**4 - 1/5 + 2/5*c**2 - 1/5*c**5.
-(c - 1)**2*(c + 1)**3/5
Factor 7/2*i**2 + 5/2*i**4 + 0 + i + 1/2*i**5 + 9/2*i**3.
i*(i + 1)**3*(i + 2)/2
Let u(x) be the second derivative of x**6/3 - 3*x**5/10 - 2*x**4 - 4*x**3/3 - 2*x + 5. Factor u(a).
2*a*(a - 2)*(a + 1)*(5*a + 2)
Let f(y) be the second derivative of y**8/168 - 8*y**7/105 + 4*y**6/15 - 5*y**2 - 22*y. Let g(k) be the first derivative of f(k). Suppose g(q) = 0. Calculate q.
0, 4
Let x(m) be the first derivative of 0*m**3 + 0*m + 2/5*m**4 - 4/25*m**5 - 2/5*m**6 + 0*m**2 + 35. Let x(n) = 0. What is n?
-1, 0, 2/3
Let i(x) = -x**3 - 6*x**2 - 10*x - 5. Let k be i(-4). Factor -22*z + 14*z - 3*z**3 + z**k - 8*z**2.
-2*z*(z + 2)**2
Let k be 2/(-3) - (-136)/24. Let a(w) be the first derivative of -1/20*w**k + 5 + 0*w**3 + 0*w + 0*w**2 + 1/16*w**4. Factor a(f).
-f**3*(f - 1)/4
