Suppose 3*n - 4 = -n. Let g be (-1 - (-5 + n)) + 1. Factor -22/3*u**3 - 8*u**g - 8/3*u**2 - 1/3*u + 0 - 3*u**5.
-u*(u + 1)**2*(3*u + 1)**2/3
Let o(t) = t**2 + 6*t - 5. Let g be o(-7). Let p be 23/7 - g/7. Factor w + 2*w**2 - w**p - 6 - 4*w**2 + 3*w**2 + 5.
-(w - 1)**2*(w + 1)
Let n(q) be the second derivative of -q**4/3 - 5*q**3/6 - q**2/2 - 3*q. Factor n(k).
-(k + 1)*(4*k + 1)
Let n(w) be the third derivative of w**7/105 + 3*w**6/20 + 4*w**5/5 + 4*w**4/3 - 23*w**2. Solve n(f) = 0 for f.
-4, -1, 0
Let z(c) be the first derivative of c**6/240 - c**5/120 - c**4/48 + c**3/12 + 3*c**2/2 + 3. Let q(a) be the second derivative of z(a). What is w in q(w) = 0?
-1, 1
Let i(o) be the first derivative of -o**7/140 + o**6/45 - o**5/60 - 4*o**3/3 + 6. Let v(u) be the third derivative of i(u). Factor v(p).
-2*p*(p - 1)*(3*p - 1)
Let h(a) = -a**2 - 10*a + 11. Let o be h(-11). Factor 2/7*n**2 - 2/7 + o*n.
2*(n - 1)*(n + 1)/7
Let t(q) be the first derivative of 0*q**2 + 0*q + 3 + 1/3*q**3 + 1/32*q**5 + 7/480*q**6 - 1/16*q**4. Let v(m) be the third derivative of t(m). Factor v(w).
3*(w + 1)*(7*w - 2)/4
Let s(f) be the second derivative of 0 + 1/27*f**4 + 0*f**3 - 1/30*f**5 + 1/189*f**7 + 2*f + 0*f**2 + 0*f**6. Determine z so that s(z) = 0.
-2, 0, 1
Let -3/5*m**3 + 0*m + 0 - 3/5*m**2 = 0. What is m?
-1, 0
Let h(i) = -i**3 - 4*i**2 - 5*i - 3. Let a be h(-3). Let c be 2 - (5/3)/((-21)/(-14)). Factor 2/9 - c*f**a + 2/9*f**4 - 8/9*f + 4/3*f**2.
2*(f - 1)**4/9
Factor 4*p**3 + 8*p**2 + 3*p**3 - 3*p**3 - 12*p**4.
-4*p**2*(p - 1)*(3*p + 2)
Let y = 1 + 1. Solve -2*k**2 - k**4 + 2*k + y*k**5 - 2*k**2 + 2 + 3*k**4 - 4*k**3 = 0 for k.
-1, 1
Let z(h) be the first derivative of -h**4/26 - 10*h**3/39 - 7*h**2/13 - 6*h/13 + 7. Factor z(c).
-2*(c + 1)**2*(c + 3)/13
Suppose 0*b + 5*t + 10 = 4*b, -5*t + 15 = b. Factor -3*c**3 + 7 + 6*c**4 - c**5 - 7 - 2*c**b.
-3*c**3*(c - 1)**2
Suppose n - 8 = 4*s - 17, -s + 3 = -n. Factor -2/7*x**3 + 2/7*x + 2/7*x**s - 2/7.
-2*(x - 1)**2*(x + 1)/7
Let y(s) be the third derivative of 0*s**3 + 4*s**2 + 0*s + 1/210*s**5 + 0 - 1/42*s**4. Factor y(v).
2*v*(v - 2)/7
Factor -6*g - 21*g**3 + 14*g**3 + 13*g**3 - 2*g**2 + 4 - 2*g**4.
-2*(g - 2)*(g - 1)**2*(g + 1)
Let a(l) = l**3 + 2*l**2 - l. Let x be a(-2). Factor 3 + 27*s**2 + 3*s**4 - 9*s**x - 4*s - 12*s**3 + 0 - 8*s.
3*(s - 1)**4
Suppose 2*j - k - 3*k - 22 = 0, 2*k = -j - 9. Let c(u) be the first derivative of 6*u**2 + 4*u + 5/3*u**3 - j. Factor c(t).
(t + 2)*(5*t + 2)
Factor 0 + 0*r**2 - 1/3*r**3 + 0*r.
-r**3/3
Let j = -9 + 4. Let d(v) = -1. Let w(g) = g**2 - g - 5. Let f(u) = j*d(u) + w(u). Suppose f(a) = 0. Calculate a.
0, 1
Let a(k) be the second derivative of k**4/12 - k**3/6 - 19*k. Factor a(t).
t*(t - 1)
Let s(j) be the first derivative of 1/3*j**6 - 2/3*j**2 + 10/9*j**3 + 1 - 1/6*j**4 - 2/3*j**5 + 0*j. Solve s(u) = 0.
-1, 0, 2/3, 1
Let r(w) be the first derivative of w**2/2 + 7*w - 2. Let f be r(-6). Find v such that 0*v + 5*v - v**2 - f - 3*v = 0.
1
Factor 10*a**2 + 5*a**3 - 7*a - 2 - 8 + 2*a.
5*(a - 1)*(a + 1)*(a + 2)
Let l(n) be the first derivative of 2*n**5/45 + n**4/3 + 8*n**3/9 + 8*n**2/9 + 36. Determine o, given that l(o) = 0.
-2, 0
Let j(z) be the third derivative of z**6/540 - z**5/90 - z**3/6 - 6*z**2. Let f(a) be the first derivative of j(a). Solve f(y) = 0 for y.
0, 2
Let c = -4 - -8. Solve 3*u**2 - 3*u**2 + 2*u**3 + 2*u**c = 0 for u.
-1, 0
Let q(l) be the second derivative of 5*l**8/1176 - 4*l**7/245 + 3*l**6/140 - l**5/105 - 2*l**2 - l. Let d(m) be the first derivative of q(m). Factor d(k).
2*k**2*(k - 1)**2*(5*k - 2)/7
Let y(x) be the third derivative of -5*x**7/126 - x**6/6 - 23*x**5/90 - x**4/6 - x**3/18 + 8*x**2. Factor y(b).
-(b + 1)**2*(5*b + 1)**2/3
Let t(c) = -7*c - 6. Let j be t(-3). Let x = 17 - j. Factor g**x + 8/3*g + 4/3.
(g + 2)*(3*g + 2)/3
Let g(r) be the third derivative of -r**6/30 - 2*r**5/15 + r**4/2 - 3*r**2 + 3*r. Factor g(z).
-4*z*(z - 1)*(z + 3)
Let p be (-2)/(-2)*(1 - -4). Suppose p*s - 15 - 5 = 0. What is a in 1/3 + 4/3*a + 1/3*a**s + 2*a**2 + 4/3*a**3 = 0?
-1
Let v be (-326)/(-6) + (-1)/3. Factor -10*m**2 + 4 + 72*m + 52*m**2 + 12 + 66*m**2 + v*m**3.
2*(3*m + 2)**3
Let d(w) be the third derivative of -w**8/840 + w**7/240 - w**6/360 - w**5/240 - w**3/6 - w**2. Let h(f) be the first derivative of d(f). Factor h(i).
-i*(i - 1)**2*(4*i + 1)/2
Let r(t) be the third derivative of t**6/24 + 3*t**5/4 + 5*t**4/3 + 5*t**2. Factor r(m).
5*m*(m + 1)*(m + 8)
Let q(y) be the first derivative of -48*y**5/5 - 9*y**4 - 3*y**3 - 3*y**2/8 - 3. Factor q(i).
-3*i*(4*i + 1)**3/4
Factor -41 + 12*r - 18*r**3 + 6*r**4 + 23 + 3*r**5 - 12*r**2 + 27*r.
3*(r - 1)**3*(r + 2)*(r + 3)
Let k = 2 - 3. Let t = 2 - k. Find i such that -i**t + i - 4*i - i + 5*i = 0.
-1, 0, 1
Let b = 12 - 12. Let o(c) be the third derivative of 1/420*c**6 + 0*c**3 + 0 + b*c + 2*c**2 - 1/210*c**5 - 1/84*c**4 + 1/735*c**7. Determine p so that o(p) = 0.
-1, 0, 1
Let n(x) be the third derivative of 1/2*x**4 + 1/5*x**5 + 1/40*x**6 + 0*x**3 + 0*x + x**2 + 0. Let n(b) = 0. Calculate b.
-2, 0
Let q be (2 + 239/(-120))/(12/24). Let u(d) be the third derivative of 1/15*d**5 + 0 + 2*d**2 + q*d**6 + 1/12*d**4 + 0*d + 0*d**3. Factor u(p).
2*p*(p + 1)**2
Let w(u) be the first derivative of 3 - 5/7*u**2 + 4/7*u + 2/7*u**4 - 8/35*u**5 + 1/21*u**6 + 4/21*u**3. Determine a, given that w(a) = 0.
-1, 1, 2
Solve 8*o**2 + 0*o**3 - 5*o**3 - 6*o + 3*o**3 = 0 for o.
0, 1, 3
Let k be (-1)/12 + 2/(32/12). Find c, given that c**4 - 5/3*c**3 + 5/3*c + k - 5/3*c**2 = 0.
-1, -1/3, 1, 2
Let o(q) be the second derivative of 1/5*q**2 + 0 + 3*q - 1/6*q**4 + 3/50*q**5 + 1/15*q**3. What is r in o(r) = 0?
-1/3, 1
What is r in -14 + 9 + 32*r - 28*r**2 + 2*r**3 - 22*r**3 + 21 = 0?
-2, -2/5, 1
Suppose -6 = -3*t - 12*m + 15*m, 4*m = 0. Factor t*k**2 - 8/3*k**3 + 2/3*k + 0.
-2*k*(k - 1)*(4*k + 1)/3
Let q be 4*(-3)/9*6. Let c = q - -8. Factor -1/2*f**3 + 3/2*f**4 + 2*f**5 + c*f + 0 + 0*f**2.
f**3*(f + 1)*(4*f - 1)/2
Suppose -25*l - 20 = -30*l. Let y(t) be the first derivative of -1/3*t**l + 3 - 1/30*t**5 + 1/9*t**3 - 1/6*t + 1/9*t**6 + 1/3*t**2. Find h, given that y(h) = 0.
-1, 1/4, 1
Let u(q) be the second derivative of q**5/50 - 3*q**4/5 + 11*q**3/5 - 16*q**2/5 + 33*q. Suppose u(b) = 0. What is b?
1, 16
Suppose 3*b + 3*b - 12 = 0. Let i(a) be the third derivative of -1/30*a**5 + 0*a**3 - 1/24*a**4 - b*a**2 + 0 + 0*a - 1/120*a**6. Find z, given that i(z) = 0.
-1, 0
Let k(t) be the second derivative of t**7/840 + t**6/180 + t**3/3 + 3*t. Let f(u) be the second derivative of k(u). Solve f(w) = 0 for w.
-2, 0
Suppose 0 = -n - 2*g + 2, 17 = -5*n + 5*g + 42. Factor -18/7*i**2 - 2*i - 4/7 - 10/7*i**3 - 2/7*i**n.
-2*(i + 1)**3*(i + 2)/7
Let b(n) be the first derivative of 1 + 0*n**2 + 2/9*n**3 + 0*n + 1/12*n**4. Factor b(g).
g**2*(g + 2)/3
Let z = 487/2 - 239. Find q, given that z*q**3 + 1/2*q - 2*q**4 - 3*q**2 + 0 = 0.
0, 1/4, 1
Let l = -30 + 32. Let i(g) be the first derivative of -l - 1/6*g**4 - 2/3*g**3 + 0*g**2 + 8/3*g. Determine a so that i(a) = 0.
-2, 1
Let j(p) be the first derivative of 2*p + 1/4*p**4 + 3 + 0*p**3 - 3/2*p**2. What is q in j(q) = 0?
-2, 1
Let c(k) be the second derivative of -1/210*k**7 - 1/150*k**6 + 0 + 4*k + 1/50*k**5 + 1/30*k**4 - 1/10*k**2 - 1/30*k**3. Factor c(x).
-(x - 1)**2*(x + 1)**3/5
Let g = -5 - -6. Let d(s) be the first derivative of -4*s - 3/2*s**4 + 2/5*s**5 + g + 2/3*s**3 + 3*s**2. Factor d(z).
2*(z - 2)*(z - 1)**2*(z + 1)
Let x(d) be the second derivative of d**5/50 + 11*d**4/60 + 17*d**3/30 + 3*d**2/5 + 3*d + 15. What is s in x(s) = 0?
-3, -2, -1/2
Let c = 287 - 284. Solve 3*r + 0 + 3/2*r**5 - 3/2*r**4 - 9/2*r**c + 3/2*r**2 = 0 for r.
-1, 0, 1, 2
Let z be (12/(-20))/(1*4/(-20)). Let b(y) be the first derivative of -1/12*y**z + 2 + 1/8*y**4 - 1/4*y**2 + 1/4*y. Factor b(x).
(x - 1)*(x + 1)*(2*x - 1)/4
Let y(q) be the second derivative of q**5/4 + 35*q**4/12 + 25*q**3/2 + 45*q**2/2 - 13*q. Solve y(k) = 0 for k.
-3, -1
Let i(z) = 3*z**3 - z**2 + z. Let g be i(1). Let c = -26/15 - -12/5. Determine k so that 7*k**2 - 28/3*k**4 + c - 13/3*k + 8/3*k**g = 0.
-1, 2/7, 1/2
Let f = 20 - 20. Let r(x) be the third derivative of -2*x**2 - 1/72*x**4 - 1/90*x**5 + 0 + 1/18*x**3 + f*x. Find z such that r(z) = 0.
-1, 1/2
Let d =