**p = 0.
-1, 2/13
Let m(x) be the first derivative of 3*x**2 - 1/2*x**3 - 6*x - 13. Factor m(y).
-3*(y - 2)**2/2
Suppose -u = 7*u - 32. Let n be (-20)/(-6) - u*4/8. Factor 5/3*i**2 - 4*i + n.
(i - 2)*(5*i - 2)/3
Let v(k) be the third derivative of -k**8/168 + 4*k**7/15 - 13*k**6/4 - 14*k**5/15 + 49*k**4/3 - k**2 + 48*k. Find u, given that v(u) = 0.
-1, 0, 1, 14
Let w(k) = -26*k**2 + 14*k + 4. Let v(h) be the second derivative of 17*h**4/12 - 3*h**3/2 - 3*h**2/2 - h. Let t(x) = 8*v(x) + 5*w(x). Factor t(z).
2*(z - 1)*(3*z + 2)
Let p be 3219/1131 + (-4)/(-26). Let 22/3*s**2 - 2*s**p - 16/3*s - 8/3 = 0. What is s?
-1/3, 2
Find k, given that -32/11 + 6/11*k**2 - 4/11*k = 0.
-2, 8/3
Let f be ((-264)/84)/((7/(-7))/1). Factor -30/7*m**2 + 18/7*m - 6/7*m**4 - 4/7 + f*m**3.
-2*(m - 1)**3*(3*m - 2)/7
Suppose -888 = -8*x + 16. Let i = 341/3 - x. Factor -m**3 - m - i + 8/3*m**2.
-(m - 2)*(m - 1)*(3*m + 1)/3
Suppose 2*j - 5 - 3 = 0. Let w be (22/(-4))/(12/(-24)). Factor -16*x**4 - 8 + w*x**2 + j*x**3 + 0*x**3 + 12*x**4 - 4*x + x**2.
-4*(x - 2)*(x - 1)*(x + 1)**2
Determine p, given that -27/2*p + 6*p**3 - 21/4*p**2 + 0 = 0.
-9/8, 0, 2
Let m be -2 - -8 - (-1 + -25). Let f be (3 - 2 - 4)*m/(-48). Solve 3/2*h**4 + 3/2*h**f - 3*h**3 + 0*h + 0 = 0 for h.
0, 1
Let w(x) = 3*x**5 - 6*x**4 + 4*x**3 - 2*x**2 - 3*x - 4. Let m(a) = -5*a**5 + 11*a**4 - 8*a**3 + 3*a**2 + 6*a + 7. Let q(f) = 4*m(f) + 7*w(f). Factor q(y).
y*(y - 1)**2*(y + 1)*(y + 3)
Let r(x) = x**3 + 8*x**2 + 2. Let g be r(-8). Let 35*l**3 - 10*l**3 + 0*l**3 + 15*l**g = 0. Calculate l.
-3/5, 0
Let g = -66 - -68. Let c be ((-14)/(-315))/(g + (-117)/60). Find n, given that c*n**3 - 2/9*n**4 - 2/3*n**2 + 8/9 - 8/9*n = 0.
-1, 1, 2
Let g be (1 - 1) + -2 + 4. Suppose 4 + y**2 - 5 - y - g + 3*y = 0. Calculate y.
-3, 1
Let o(h) = -h + 1. Let q be o(-1). Factor 25 + 16 + 67 + 2*d**q - 36*d + d**2.
3*(d - 6)**2
Suppose -n = -22 + 10. Suppose 28 = 4*d + n. Factor 2/9*g**2 - 4/9 + 2/3*g**3 + 2/9*g**d - 2/3*g.
2*(g - 1)*(g + 1)**2*(g + 2)/9
Suppose 7/2*m**2 - 1/2*m**4 + 0 + 2*m + m**3 = 0. Calculate m.
-1, 0, 4
Solve 12/11*b**4 - 14*b**3 + 114/11*b**2 - 48/11 + 76/11*b = 0 for b.
-2/3, 1/2, 1, 12
Let a(u) be the second derivative of -u**6/240 - 3*u**5/32 - 61*u**4/96 - 7*u**3/16 + 49*u**2/8 - 2*u + 1. Find q, given that a(q) = 0.
-7, -2, 1
Let v = -593 - -1241. Let g = 8430/13 - v. Find t, given that 2/13*t**2 + 4/13 - g*t = 0.
1, 2
Let f(g) be the third derivative of -g**7/525 + g**6/50 - 4*g**5/75 + 15*g**2 + 9. Suppose f(v) = 0. What is v?
0, 2, 4
Let b(h) be the first derivative of -h**3/2 - 27*h**2/8 + 39*h/2 - 31. Find d, given that b(d) = 0.
-13/2, 2
Let z = -65 - -46. Let b = -16 - z. Factor 1/2*a**b + 1/4 + 0*a**2 - 1/4*a**4 - 1/2*a.
-(a - 1)**3*(a + 1)/4
Let j(c) be the second derivative of -1/20*c**6 - 9*c + 0 - 3/2*c**2 - 7/12*c**4 - 2/3*c**3 - 4/15*c**5. Let m(f) be the first derivative of j(f). Factor m(w).
-2*(w + 1)**2*(3*w + 2)
Let k(v) be the second derivative of v**4/24 - 2*v**3/3 + 7*v**2/4 - 109*v. Determine x, given that k(x) = 0.
1, 7
Let u(r) be the third derivative of r**6/60 + r**5/3 + 9*r**2 - 5*r. What is j in u(j) = 0?
-10, 0
Let k(w) be the second derivative of 1/21*w**4 - 11*w + 0 - 2/21*w**3 + 0*w**2. Factor k(t).
4*t*(t - 1)/7
Let c(j) be the first derivative of 9*j**3 + 9/2*j**4 + 0*j + 6*j**2 + 3/5*j**5 + 7. Suppose c(i) = 0. What is i?
-4, -1, 0
Let o(l) be the second derivative of 1/126*l**7 - 1/30*l**5 + 15*l + 1/90*l**6 + 1/6*l**2 + 1/18*l**3 - 1/18*l**4 + 0. Let o(j) = 0. Calculate j.
-1, 1
Let v(z) = 41*z**2 + 29*z + 9. Let i(l) = 20*l**2 - 4*l**2 - 5 - 37*l**2 - 15*l. Let q(y) = 10*i(y) + 6*v(y). Find s such that q(s) = 0.
-1/3
Let q(t) be the third derivative of -2/525*t**7 + 2/15*t**4 + 2/75*t**6 - 8*t**2 + 0 - 2/15*t**3 - 2/25*t**5 + 0*t. Solve q(j) = 0.
1
Factor -931 + 26*q**3 - 24*q**3 - 348*q**2 + q**4 - 2*q**4 + 1246*q + 32*q**3.
-(q - 19)*(q - 7)**2*(q - 1)
Let q = -99 - -32. Let p = q - -69. Suppose 5/3*i + 2/3 + i**p = 0. What is i?
-1, -2/3
Factor 4*q**2 + 13*q - 30*q - 11*q + 24.
4*(q - 6)*(q - 1)
Suppose -4/3*h - 1/3*h**5 + 2*h**4 + 0 - 13/3*h**3 + 4*h**2 = 0. Calculate h.
0, 1, 2
Let d = -9 + 8. Let f be (-25)/(-5) - (-2)/d. Let 0*m**3 + 6*m - 7*m - 6*m**3 - 2*m**2 + 5*m**f = 0. Calculate m.
-1, 0
Find v such that v**3 + 8/7*v - 1/7*v**4 - 2*v**2 + 0 = 0.
0, 1, 2, 4
Let j(y) be the first derivative of -50/3*y - 13 + 10/3*y**2 - 2/9*y**3. Let j(z) = 0. What is z?
5
Suppose 50/3 - 52/3*q**2 + 2/3*q**4 + 16*q**3 - 16*q = 0. Calculate q.
-25, -1, 1
Let t be (-12)/(-54) + (-2)/9. Let v(c) be the first derivative of 2 - 3/4*c**4 + t*c**2 - c**3 + 0*c. Find u such that v(u) = 0.
-1, 0
Let y(p) be the first derivative of -p**5/300 + p**3/30 + 13*p**2/2 + 5. Let l(z) be the second derivative of y(z). Determine j, given that l(j) = 0.
-1, 1
Let g be -15 + (-1 - 35/(-30)). Let u = 31/2 + g. What is r in -u*r + 0 - 2/3*r**4 + 2/3*r**3 + 2/3*r**2 = 0?
-1, 0, 1
Suppose 5 + 6*z**2 + 1/2*z**3 + 21/2*z = 0. Calculate z.
-10, -1
Let o(d) be the second derivative of d**4/3 + 8*d**3/3 + 8*d**2 + 35*d. Solve o(y) = 0 for y.
-2
Let d(p) be the first derivative of -3/5*p**2 - 32 - 1/10*p**4 + 2/5*p**3 + 2/5*p. Factor d(c).
-2*(c - 1)**3/5
Let f(p) be the third derivative of -1/15*p**5 + p**4 - 16/3*p**3 + 0 + 0*p + 17*p**2. Factor f(k).
-4*(k - 4)*(k - 2)
Let j(p) be the second derivative of -p**4/18 - 10*p**3/9 - 16*p**2/3 - 634*p. Factor j(i).
-2*(i + 2)*(i + 8)/3
Let g(x) = 27*x**2 - 83*x + 6. Let m be g(3). Factor m + 9/8*w**4 + 0*w - 3/8*w**5 + 3/8*w**2 - 9/8*w**3.
-3*w**2*(w - 1)**3/8
Let l = 59 + -54. Let q(p) = -3*p**3 + 6*p**2 - 3. Let t(s) = -7*s**3 + 11*s**2 - 5. Let z(a) = l*q(a) - 3*t(a). Determine d, given that z(d) = 0.
0, 1/2
What is d in 70688/5 + 2/5*d**2 - 752/5*d = 0?
188
Let f(v) be the first derivative of -v**8/420 - v**7/21 - 5*v**6/18 + v**3/3 + 1. Let r(w) be the third derivative of f(w). Find t, given that r(t) = 0.
-5, 0
Factor -2/7*o**5 - 940/7*o**2 - 290/7*o**3 - 40/7*o**4 - 200*o - 112.
-2*(o + 2)**3*(o + 7)**2/7
Let h = 2254 + -2249. Let t(c) be the third derivative of -3*c**4 + 12*c**2 + 0 - 8*c**3 - 1/40*c**6 - 9/20*c**h + 0*c. Factor t(f).
-3*(f + 1)*(f + 4)**2
Let k be (-7)/(-3) - (-8)/12. Let y = 137/210 + -19/42. Factor y*r**k + 0*r**2 - 2/5 - 3/5*r.
(r - 2)*(r + 1)**2/5
Let x be (-160)/(-72) + (-4)/18. Suppose -2*o + 4 = -x. Solve 0*y**3 + 2*y**3 + 0*y**o - y**2 - y**2 = 0.
0, 1
Let j(h) = -4*h**5 - 2*h**4 + 3*h**3 - h**2 + 4*h + 3. Let x(n) = 3*n**5 + 2*n**4 - 2*n**3 - 3*n - 2. Let k(f) = 4*j(f) + 6*x(f). Determine p so that k(p) = 0.
-1, 0, 1
Let v(a) be the third derivative of 0*a + 0 + 1/16*a**6 + 1/5*a**5 - 1/2*a**3 + 1/16*a**4 - 3*a**2. Find w such that v(w) = 0.
-1, 2/5
Let m(c) = c**2 - c - 5. Suppose 0 = q - 3*w - 10, 2*q - 4*w - 16 = 0. Let j(u) = -4. Let x(h) = q*m(h) - 5*j(h). Suppose x(t) = 0. Calculate t.
0, 1
Suppose 2*o + 2*c - 18 = -10, 4*o + 3*c - 20 = 0. Suppose -5*a = n - o, 0 - 6 = -2*a + n. Factor 0*h + 8/3*h**3 + 0 - 2/3*h**a - 8/3*h**4.
-2*h**2*(2*h - 1)**2/3
Suppose -k + 2*a = -2*k + 8, 4*k + a - 46 = 0. Find u, given that -k*u**2 - 1061 + 1061 - 9*u - 3*u**3 = 0.
-3, -1, 0
Let h be (34/4)/(14/28). Factor 9*p**2 - 2*p**5 + 14*p**4 + p**5 - h*p**4 - 10*p**2 - 3*p**3.
-p**2*(p + 1)**3
Let v = -13251 + 119260/9. Suppose 1/3*s - 2/9 - v*s**2 = 0. Calculate s.
1, 2
Let k(c) be the third derivative of -c**5/60 - 11*c**4/8 + 17*c**3/3 + 159*c**2. Factor k(m).
-(m - 1)*(m + 34)
Suppose 5*i - 2*b = 25, 3*i = -i - 4*b - 8. Solve 4*v - 49*v**4 + 10*v**3 + i*v**3 + 8*v**3 + 24*v**2 = 0 for v.
-2/7, 0, 1
Let n(w) be the second derivative of -35*w - 304/25*w**6 + 0 + 3/10*w**2 - 9/10*w**4 + 192/35*w**7 - 7/10*w**3 + 186/25*w**5. Solve n(a) = 0.
-1/6, 1/4, 1
Let y(i) = -i**2 - 53*i - 430. Let m be y(-43). Let b(s) be the first derivative of 0*s - 2/7*s**4 - 10 + 0*s**5 + 2/7*s**2 + 2/21*s**6 + m*s**3. Factor b(g).
4*g*(g - 1)**2*(g + 1)**2/7
Let x(t) be the first derivative of t**5/20 - t**4/8 - t**3/4 + t**2/2 + t - 139. Factor x(z).
(z - 2)**2*(z + 1)**2/4
Factor -2*w + 0 - 1/4*w**2.
-w*(w + 8)/4
Let u(g) = 5*g**4 + 7*g**3 + 6*g**2 + 4*g + 4. Let j(v) = v**4 + v**3 + v**2 + v + 1. Let k be -4 + (-15)/(-5) + 5. Let t(c) = k*j(c) - u