(q) = -16*q**4 + 9*q**3 - 19*q**2 + 9*q + 6. Let u(v) = t*y(v) - 6*s(v). Solve u(x) = 0.
1
Let f(y) be the third derivative of -y**6/60 - y**5/6 - 7*y**4/12 - y**3 + 7*y**2. Find l such that f(l) = 0.
-3, -1
Factor 5*u**5 + 3*u**3 + 98*u**2 - 40 - 20*u - 20*u**4 - 48*u**2 + 2*u**3.
5*(u - 2)**3*(u + 1)**2
Let m(h) = -8*h - 2 + 7*h**2 + 3 - 1 + h**3. Let p be m(-8). What is d in 0*d - 2*d**4 + p + 8/5*d**3 - 2/5*d**2 + 4/5*d**5 = 0?
0, 1/2, 1
Let o(k) be the first derivative of k**7/525 - k**6/150 + k**4/30 - k**3/15 - k**2 + 3. Let f(s) be the second derivative of o(s). Factor f(a).
2*(a - 1)**3*(a + 1)/5
Let i = -150 + 150. Factor -3/5*z**2 + i + 0*z.
-3*z**2/5
Let h(a) be the second derivative of a**10/120960 - a**9/20160 + a**8/8960 - a**7/10080 - a**4/2 + 3*a. Let x(g) be the third derivative of h(g). Factor x(o).
o**2*(o - 1)**3/4
Suppose -2*h - 3*h + 3*m = -52, -4*h + 5*m = -52. Suppose -5*v - 6 = -h*v. Factor v*y**2 - y - 3*y - 4*y**2 - 2.
-2*(y + 1)**2
Let k = -15/47 - -92/141. Find c such that 1/3*c**3 - 2/3 - k*c + 2/3*c**2 = 0.
-2, -1, 1
Let a(r) be the first derivative of -r**3/9 - r**2/3 - r/3 + 12. Factor a(h).
-(h + 1)**2/3
Let b(y) be the first derivative of 3*y**4/4 + 13*y**3 + 47. Factor b(i).
3*i**2*(i + 13)
Let n(p) be the first derivative of -p**6/140 - p**5/30 + 4*p**3/21 + 4*p**2 - 6. Let j(q) be the second derivative of n(q). Solve j(h) = 0 for h.
-2, -1, 2/3
Suppose -52 = 4*y - 4*d, -y = -d - 4*d + 33. Let h be (-3)/(-3)*y/(-3). Factor h*p**3 - 10/3*p**2 + 2/3*p + 0.
2*p*(p - 1)*(4*p - 1)/3
Let v(r) be the third derivative of -r**6/40 + r**5/4 - r**4 + 2*r**3 + 2*r**2. Determine q so that v(q) = 0.
1, 2
Let s(u) be the second derivative of 1/66*u**4 + 1/11*u**3 + 0 + 2/11*u**2 - 4*u. Suppose s(k) = 0. What is k?
-2, -1
Let d(x) be the first derivative of 2/21*x**3 + 0*x - 3/14*x**4 + 1 + 6/35*x**5 + 0*x**2 - 1/21*x**6. Find h, given that d(h) = 0.
0, 1
Factor 0 - 1/5*c**4 + 0*c**2 - 1/5*c**5 + 0*c**3 + 0*c.
-c**4*(c + 1)/5
Let z(d) be the third derivative of -d**7/7560 + d**4/3 - 3*d**2. Let m(u) be the second derivative of z(u). Factor m(o).
-o**2/3
Let w be 17/((-136)/(-80)) + -5. Factor -1/2*l**2 - 1/2*l**3 + 1/2*l**w + 1/2*l**4 + 0*l + 0.
l**2*(l - 1)*(l + 1)**2/2
Solve -12/5*q**5 - 9/5*q**2 + 9/5*q**4 - 3/5*q + 0 + 3*q**3 = 0.
-1, -1/4, 0, 1
Let x(d) be the second derivative of -d**4/12 + d**2/2 - 41*d. Let x(a) = 0. What is a?
-1, 1
Let u(r) be the third derivative of -2*r**8/147 + 8*r**7/735 - r**6/420 - 7*r**2. Factor u(b).
-2*b**3*(4*b - 1)**2/7
Let b = 215/3 + -71. Let u(g) be the first derivative of 1/6*g**4 + 2 - 2/3*g + g**2 - b*g**3. Solve u(i) = 0.
1
Let u(a) be the third derivative of -1/48*a**4 + 0*a**3 + 0*a + 2*a**2 - 1/360*a**5 + 0. Factor u(r).
-r*(r + 3)/6
Let l(r) be the first derivative of -r**4/28 + 4*r**3/21 - 5*r**2/14 + 2*r/7 + 15. Factor l(q).
-(q - 2)*(q - 1)**2/7
Let c(l) be the third derivative of 1/1260*l**7 + 4*l**2 + 1/120*l**5 + 0 + 0*l - 1/240*l**6 + 0*l**3 - 1/144*l**4. What is g in c(g) = 0?
0, 1
Find j, given that 9 - 9*j - 1/3*j**3 + 3*j**2 = 0.
3
Determine m so that -1/3 + 1/3*m**3 - 1/3*m + 1/3*m**2 = 0.
-1, 1
Let c = -929/33 - -85/3. Solve -c*v**2 - 2/11 + 4/11*v = 0.
1
Let n(z) be the second derivative of z**7/315 - z**6/60 - z**5/15 - 7*z**4/12 - 2*z. Let d(i) be the third derivative of n(i). Let d(o) = 0. Calculate o.
-1/2, 2
Let p be (2/(-10))/((-1)/2). Let x = -1/224 - -453/1120. Factor p - x*b**2 + 0*b.
-2*(b - 1)*(b + 1)/5
Let h(f) be the third derivative of -f**8/1344 + f**7/168 - f**6/80 - f**5/120 + 7*f**4/96 - f**3/8 - 45*f**2. Factor h(m).
-(m - 3)*(m - 1)**3*(m + 1)/4
Suppose 2*q = 5*q - 12. Let t(a) be the second derivative of 1/60*a**6 + 1/40*a**5 + 0*a**3 + 0 + 0*a**2 + 2*a + 0*a**q. What is u in t(u) = 0?
-1, 0
Let i(d) = -d + 11. Let k be (-43)/(-5) + (-6)/(-15). Let b be i(k). Find s such that 6*s**2 - 2*s**2 - 2*s**2 - b*s = 0.
0, 1
Let o(c) be the third derivative of c**8/10080 - c**7/840 + c**6/180 - c**5/60 - 3*c**2. Let x(k) be the third derivative of o(k). Factor x(f).
2*(f - 2)*(f - 1)
Let i(d) be the first derivative of -d**4/24 + d**3/9 - d**2/12 - 9. Find a, given that i(a) = 0.
0, 1
Factor 8*v**5 + 4 - 12*v**4 + 136*v**2 - 4*v**5 - 12*v + 8*v**3 - 128*v**2.
4*(v - 1)**4*(v + 1)
Let z = -47 + 49. Factor 2*o + 1/2*o**5 - 6*o**z - 3*o**4 + 13/2*o**3 + 0.
o*(o - 2)**2*(o - 1)**2/2
Let t(z) be the second derivative of 3*z**5/20 - z**4/2 - z**3/2 + 3*z**2 + 6*z. Suppose t(w) = 0. What is w?
-1, 1, 2
Let v be 2/13 + (-37)/(-13). Factor -2*z**4 - 3*z**3 - 31 + 16*z**2 - 1 + 3*z**v.
-2*(z - 2)**2*(z + 2)**2
Let z be (-12)/(-3) - 0 - 2. Suppose -z*x + 2*y + 8 = -0*x, 3*y = -x + 12. Factor x*t**2 - t**2 - 3*t**2.
2*t**2
Let b be (-2)/(-4) - 93/2. Let s = -33 - b. Suppose -4*z**3 - 2*z**2 + s*z - 5*z - 4*z**3 + 2 = 0. Calculate z.
-1, -1/4, 1
Suppose 2/3*u**4 + 0 + 0*u**2 + 0*u - 2/3*u**3 = 0. Calculate u.
0, 1
Let q = 29 - 86/3. Let x(a) be the second derivative of q*a**2 - 1/30*a**5 - 1/18*a**4 + 2*a + 1/9*a**3 + 0. Suppose x(b) = 0. Calculate b.
-1, 1
Let u(d) be the third derivative of d**8/100800 + d**5/30 - 3*d**2. Let g(f) be the third derivative of u(f). What is w in g(w) = 0?
0
Let x(n) be the second derivative of 0 + 1/15*n**3 - 1/50*n**5 + 1/30*n**4 + n**2 - n. Let t(f) be the first derivative of x(f). Factor t(c).
-2*(c - 1)*(3*c + 1)/5
Suppose 3*l - 8 = 7*l. Let k be -4*1/(0 + l). Suppose 4*s - 2*s**k + 2*s - 3*s - s**2 = 0. What is s?
0, 1
Let b(t) = 3*t**3 + 4*t**2 - 12*t. Suppose 0 = -x - 3 + 36. Let i(n) = -24*n**3 - 33*n**2 + 96*n. Let d(h) = x*b(h) + 4*i(h). Factor d(c).
3*c*(c - 2)*(c + 2)
Let h(b) be the third derivative of -b**5/20 - b**4/4 - b**3/2 - 7*b**2. Factor h(a).
-3*(a + 1)**2
Let b(c) be the first derivative of -c**6/9 + 2*c**5/15 + c**4/6 - 2*c**3/9 + 20. Factor b(s).
-2*s**2*(s - 1)**2*(s + 1)/3
Suppose -5*j + 2*j - 5 = c, -c - 2*j - 3 = 0. Let a = c - 1. Factor a + 4/3*g + 2/3*g**2.
2*g*(g + 2)/3
Suppose -4*b + 20 = 2*a - 0*b, -3*b + 13 = a. Determine d so that -4*d**3 + 1/2*d**a + 0*d - 27/2 + 9*d**2 = 0.
-1, 3
Let z(s) be the second derivative of 0*s**5 + 0*s**3 + 0*s**2 + 1/30*s**6 + 2*s - 1/12*s**4 + 0. What is m in z(m) = 0?
-1, 0, 1
Let f be (-8)/90*(-15)/40. Let i(l) be the second derivative of 0*l**3 + 0*l**2 + 3*l - f*l**5 - 1/18*l**4 + 0. Suppose i(n) = 0. What is n?
-1, 0
Let j be (-8)/2 - (-7)/1. Let y(u) be the third derivative of 1/120*u**6 + 1/350*u**7 + u**2 + 1/300*u**5 + 0*u + 0*u**j - 1/120*u**4 + 0. Factor y(c).
c*(c + 1)**2*(3*c - 1)/5
Let s be (-2 + 0)/(-4)*26. Let l = -13 + s. Find y such that 1/5*y**5 + 1/5*y**3 + 0 - 2/5*y**4 + 0*y**2 + l*y = 0.
0, 1
Let c(q) be the third derivative of q**6/60 - 2*q**5/15 + 5*q**4/12 - 2*q**3/3 + 7*q**2. Determine l so that c(l) = 0.
1, 2
Let x(l) be the third derivative of l**5/30 + l**4/6 - l**3 - l**2. Determine b, given that x(b) = 0.
-3, 1
Solve -13*h**4 - 3*h**4 + 3*h**3 + 8*h**3 + h**2 - 3*h**2 + 7*h**5 = 0 for h.
0, 2/7, 1
Let k be -2 + (-2)/2 - -9. Factor -9*t**2 + 0*t**2 + 6 - 3*t**3 + k + 0*t**2.
-3*(t - 1)*(t + 2)**2
Let u(l) be the third derivative of l**6/60 - l**5/15 + 5*l**2. Factor u(y).
2*y**2*(y - 2)
Let o be -4 + (126/(-60))/(4/(-10)). Let c(s) be the first derivative of 4 - o*s**2 + s + 5/8*s**4 - 1/3*s**3. Let c(n) = 0. Calculate n.
-1, 2/5, 1
Let j(h) = 139*h**4 + 281*h**3 - 385*h**2 - 69*h + 30. Let w(r) = -416*r**4 - 844*r**3 + 1155*r**2 + 206*r - 90. Let o(i) = -11*j(i) - 4*w(i). Solve o(y) = 0.
-3, -1/3, 2/9, 1
Let m(d) be the first derivative of 12*d**5/35 - 11*d**4/7 + 44*d**3/21 - 2*d**2/7 - 8*d/7 - 7. Let m(x) = 0. Calculate x.
-1/3, 1, 2
Suppose 0 = r - 0*r - 5. Suppose r*n = 2*n. Factor n + 1 - 2*t + 1 - 2*t**2 + 2*t**3.
2*(t - 1)**2*(t + 1)
Let c(v) = -10*v**5 + 5*v**4 + 15*v**3 + 5*v**2 + 5*v + 5. Let o(j) = 5*j**5 - 3*j**4 - 8*j**3 - 3*j**2 - 3*j - 3. Let m(a) = 3*c(a) + 5*o(a). Factor m(l).
-5*l**3*(l - 1)*(l + 1)
Let i be 12/20 - (0 - 3). Solve i*m**2 - 4/5*m - 14/5*m**3 + 0 = 0 for m.
0, 2/7, 1
Solve 2 + 1/2*z**4 - z**3 - 3/2*z**2 + 2*z = 0.
-1, 2
Suppose 3/4*c**3 + 1/4*c + 0 - 3*c**5 + 5/2*c**4 - 9/8*c**2 = 0. Calculate c.
-2/3, 0, 1/2
Factor 27/2 - 9*a + 3/2*a**2.
3*(a - 3)**2/2
Let l = -331 + 2989/9. Suppose -8/9*q - l*