p**2 + 3. Suppose -3*h + 52 = -5*u, 5*u - 2*u = -2*h - 35. Let d(r) = n*q(r) + u*f(r). Factor d(v).
3*(v - 1)*(v + 1)
Let g(a) be the third derivative of -a**5/20 + a**4 - 7*a**3/2 + 37*a**2. Factor g(m).
-3*(m - 7)*(m - 1)
Let n(c) be the third derivative of c**9/378 + c**8/70 + 3*c**7/140 + c**6/90 - c**3/6 - 2*c**2. Let r(f) be the first derivative of n(f). Factor r(t).
2*t**2*(t + 2)*(2*t + 1)**2
Let t(x) be the second derivative of -2/3*x**3 + 3*x + 0 + 1/2*x**4 + 0*x**2. Factor t(s).
2*s*(3*s - 2)
Let q = 294 + -5583/19. Let o = q + 13/38. Factor 0 + 3/2*r**5 - 2*r**4 + r**2 + 0*r - o*r**3.
r**2*(r - 1)**2*(3*r + 2)/2
Let z be 5/25 + 602/(-10). Let a be (-1025)/z - 3/(-18). Let a*x**2 + 35/2*x**3 + 7*x + 25/4*x**4 + 1 = 0. Calculate x.
-1, -2/5
Let t(g) be the first derivative of -2*g**5/65 + 2*g**3/13 + 2*g**2/13 - 15. Factor t(b).
-2*b*(b - 2)*(b + 1)**2/13
Let r be (-47)/5 + (-6)/10. Let k = -7 - r. Determine b so that 0 - 2/7*b**2 + 2/7*b**4 + 0*b - 2/7*b**5 + 2/7*b**k = 0.
-1, 0, 1
Let -5*h**4 - 3 - 17 - 30*h**3 + 2*h**4 - 65*h**2 - 2*h**4 - 60*h = 0. Calculate h.
-2, -1
Suppose -4*r + 2*l - 3 - 3 = 0, -23 = -3*r - 4*l. Let w be 3 + 1 + (-1 - r). Factor 2/9*z**3 + 0*z + 0*z**w + 0.
2*z**3/9
Let t(w) be the first derivative of w**6/21 + 2*w**5/7 + w**4/7 - 4*w**3/3 - 3*w**2/7 + 18*w/7 - 36. Solve t(z) = 0.
-3, -1, 1
Let r = 443 - 440. Suppose 0*s**2 + 0*s + 0 + 0*s**4 - 1/4*s**5 + 1/4*s**r = 0. Calculate s.
-1, 0, 1
Suppose 4*m - 7*j - 13 = -6*j, -2*m + 8 = -2*j. Factor 0 + 8/3*p**2 + 16/3*p**m + 1/3*p.
p*(4*p + 1)**2/3
Let k(c) = -5*c**2 + 3*c - 1. Let n(m) = -14*m**2 + 8*m - 2. Let g(x) = x + 2. Let y be g(10). Let w be (-32)/y*1*-3. Let p(r) = w*k(r) - 3*n(r). Factor p(j).
2*(j - 1)*(j + 1)
Let c(g) be the third derivative of g**7/210 + g**6/60 + 3*g**2. Find n such that c(n) = 0.
-2, 0
Suppose 3*v - q = 12, 3*v = -2*v + q + 20. What is x in 0*x**3 - 2*x**v - x**5 + 8*x**2 + 2*x**3 + 7*x + 1 + 1 = 0?
-1, 2
Let b(x) be the third derivative of x**7/840 - x**6/360 - x**5/60 + x**3/2 - x**2. Let t(u) be the first derivative of b(u). Determine l so that t(l) = 0.
-1, 0, 2
Let h(a) be the first derivative of 1/3*a - 5/6*a**4 - 3 + 1/5*a**5 + 4/3*a**3 - a**2. Factor h(b).
(b - 1)**3*(3*b - 1)/3
Let g(z) be the third derivative of z**8/1176 - z**7/245 + z**6/210 + 17*z**2. Factor g(o).
2*o**3*(o - 2)*(o - 1)/7
Determine r, given that -4*r**4 - 3*r**5 + r**3 + 2*r**3 - 2*r**4 - 6*r**5 = 0.
-1, 0, 1/3
Factor -5*r + 5*r**2 - 25*r + 129 - 10*r - 49.
5*(r - 4)**2
Suppose -4*f + 2 + 14 = 0. What is x in -f*x + x**3 + x**3 + 2*x - 4*x - 4 = 0?
-1, 2
Factor -8/7 + 2/7*g**2 + 0*g.
2*(g - 2)*(g + 2)/7
Suppose z + 192 = 4*z. Suppose -3*c**2 + 5*c**2 - 6*c**2 - z - 32*c = 0. Calculate c.
-4
Suppose -3*i = 2*i - 15. Suppose 4*r - 9 = i. Factor 1/4*x**5 + x**2 + x**4 + 1/4*x + 3/2*x**r + 0.
x*(x + 1)**4/4
Let r(h) be the second derivative of -5*h**4/4 + 4*h**3 + 6*h**2 - 11*h + 3. Solve r(s) = 0 for s.
-2/5, 2
Let q(i) be the second derivative of 0 - 1/20*i**4 + 3/100*i**5 + 0*i**3 - 4*i + 0*i**2. Factor q(f).
3*f**2*(f - 1)/5
Suppose -5*j - 12 + 52 = 0. Let r = -8 + j. Factor -1/3*s**3 + r*s**2 + 1/3*s + 0.
-s*(s - 1)*(s + 1)/3
Let p(a) be the third derivative of a**8/36960 - a**7/4620 + a**5/165 - 5*a**4/24 - 4*a**2. Let i(k) be the second derivative of p(k). Solve i(r) = 0 for r.
-1, 2
Let v(s) be the first derivative of -s**4/5 + 38*s**3/15 - 8*s**2 - 10*s + 6. Factor v(x).
-2*(x - 5)**2*(2*x + 1)/5
Let r(b) = -3*b**3 - b**2 - b. Let s be r(-2). Let i = s - 65/3. Factor -i*q**2 + 0 + 1/3*q.
-q*(q - 1)/3
Let k(i) be the second derivative of 0 + 2*i**2 + 9*i + 8/3*i**3 + 2*i**4 + 2/15*i**6 + 4/5*i**5. Suppose k(a) = 0. Calculate a.
-1
Let a be (-7)/(-24) + 11/(1408/(-16)). Let -1/3*h**3 - a*h**4 + 0*h + 0*h**2 + 0 = 0. Calculate h.
-2, 0
Let z(u) be the first derivative of -u**5/60 - u**4/36 - 3*u - 1. Let p(n) be the first derivative of z(n). Factor p(l).
-l**2*(l + 1)/3
Let j(c) be the first derivative of 0*c**2 + 2/27*c**3 + 1/18*c**4 + 0*c + 2. Factor j(u).
2*u**2*(u + 1)/9
Let j = 8 - 7. Suppose -b + 6 - j = 0. Let g(m) = 18*m**2 - 10*m + 12. Let w(x) = -7*x**2 + 4*x - 5. Let k(v) = b*g(v) + 12*w(v). Factor k(l).
2*l*(3*l - 1)
Let s = 1150/3 + -390. Let p = s - -41/6. Factor 0 - 1/6*x + p*x**2.
x*(x - 1)/6
Let f be ((69/(-6))/23)/(2/(-14)). Suppose -f*a**2 + 0 - 2*a**3 + a = 0. What is a?
-2, 0, 1/4
Let l be (-53)/(-30) - 2/9. Let p = 1/18 + l. Determine q so that p*q + 8/5 + 2/5*q**2 = 0.
-2
Let d(x) be the first derivative of 2*x + 0*x**4 - 1/60*x**6 - 4 + 0*x**3 + 0*x**5 + 0*x**2. Let l(n) be the first derivative of d(n). Factor l(q).
-q**4/2
Let x = -368 + 370. Suppose 0*o - 1/2*o**3 + 0 - 1/2*o**x = 0. What is o?
-1, 0
Let i(p) = p - 2. Let d be i(0). Let m(x) = x**4 + x**3 - x**2 + x + 2. Let q(w) = 3*w**4 + 3*w**3 - 3*w**2 + 2*w + 5. Let r(g) = d*q(g) + 5*m(g). Factor r(k).
-k*(k - 1)*(k + 1)**2
Let l(c) be the second derivative of 0 - 1/20*c**5 - c + 2/3*c**3 + 4*c**2 - 1/6*c**4. Let l(u) = 0. What is u?
-2, 2
Let b(h) = -5*h**2 - h - 3. Let z be 2/(-4)*0/(-2). Let w(r) = 1 + r + z - 2*r + r**2. Let f(a) = b(a) + 3*w(a). Solve f(q) = 0.
-2, 0
Let j(p) be the third derivative of p**7/210 - p**6/60 - p**5/15 + p**4/3 + 9*p**2. Factor j(t).
t*(t - 2)**2*(t + 2)
Let f(w) be the third derivative of w**8/672 - w**7/140 + w**6/80 - w**5/120 + 15*w**2. Factor f(p).
p**2*(p - 1)**3/2
Let v(w) be the third derivative of -w**8/16800 - w**7/3150 - w**4/8 + 4*w**2. Let m(u) be the second derivative of v(u). What is t in m(t) = 0?
-2, 0
Suppose 5*c - 16 = 2*y, -5*y = 5*c - 29 - 1. Let -168 - i**y + 168 - i = 0. What is i?
-1, 0
Let x(b) = -b**4 - 3*b**3 + 5*b**2 - 7*b. Let v(r) = -r**4 - 3*r**3 + 4*r**2 - 6*r. Let o(g) = -7*v(g) + 6*x(g). Determine k so that o(k) = 0.
-2, -1, 0
Let y be (3/(-6))/(7/(-42)). Solve -16*p**2 + 0*p**2 + 20*p + 4*p**3 + 0 - y - 5 = 0 for p.
1, 2
Suppose 33 = 10*v + 13. Find u, given that 1/2*u**v - 1/2 + 0*u = 0.
-1, 1
Let t(y) = 3*y - 18. Let o be t(6). Let q(x) be the second derivative of 0*x**5 + 1/24*x**4 + 0*x**2 + 1/168*x**7 - 1/60*x**6 + x + o - 1/24*x**3. Factor q(s).
s*(s - 1)**3*(s + 1)/4
Suppose 46*p - 6 = -4*f + 44*p, f + 4*p = -9. Factor -2/11*w**f - 16/11*w + 8/11 + 10/11*w**2.
-2*(w - 2)**2*(w - 1)/11
Let u(t) be the first derivative of t**6/15 - 12*t**5/25 + 11*t**4/10 - 4*t**3/15 - 12*t**2/5 + 16*t/5 + 9. Solve u(z) = 0 for z.
-1, 1, 2
Let m(h) = -h**3 + 8*h**2 - 7*h - 6. Let a be m(7). Let d be 4/a - 28/(-6). Factor 0*c**2 - 2*c**2 + d*c - 2 + 0.
-2*(c - 1)**2
Let y(b) be the first derivative of -b**3/3 - b**2/2 + 5. Let u(r) = -8*r**3 + 24*r**2 + 26*r - 6. Let g(m) = u(m) + 6*y(m). Factor g(x).
-2*(x - 3)*(x + 1)*(4*x - 1)
Let n(s) be the first derivative of -s**3/4 - 15*s**2/8 - 3*s + 11. What is r in n(r) = 0?
-4, -1
Suppose 14*z - b = 18*z - 3, 3*z + 5*b + 19 = 0. Let -2/5*y**5 - 2/5*y**4 + 0 + 2/5*y**z + 0*y + 2/5*y**3 = 0. Calculate y.
-1, 0, 1
Let l(t) be the second derivative of 2*t**7/7 - 14*t**6/15 + 3*t**5/5 + t**4 - 4*t**3/3 - 56*t. Factor l(x).
4*x*(x - 1)**3*(3*x + 2)
Let z = 9320/9 - 270052/261. Let w = z - 6/29. Factor 1/3*a**2 - w*a + 1/3.
(a - 1)**2/3
Solve -1/9*n - 1/9*n**2 + 1/9*n**3 + 1/9 = 0 for n.
-1, 1
Let n(h) be the first derivative of -h**3 - h**2 - 5*h + 3. Let t(s) = s**2 + 1. Let l(w) = -n(w) - 5*t(w). Factor l(y).
-2*y*(y - 1)
Let c = 3 + 2. Let h(z) = z**3 - 6*z**2 + 6*z - 3. Let n be h(c). Factor i + i + 3*i**n - i**2.
2*i*(i + 1)
Let h(o) be the third derivative of o**5/180 - o**4/72 - o**3/9 + 3*o**2. Factor h(v).
(v - 2)*(v + 1)/3
Let x(h) be the first derivative of -2*h**5/15 + 7*h**4/6 - 16*h**3/9 - 16*h**2/3 + 2. Factor x(j).
-2*j*(j - 4)**2*(j + 1)/3
Let s be (-68)/(-20) - (-3)/5. Suppose -3*z = 4*n - 10, -z = -s*n + 8 + 10. Suppose -q**2 - 3 - 15*q - 6*q**n - 21*q**3 + 3*q**2 - 29*q**2 = 0. What is q?
-1, -1/2
Let g be 19/3 + (-5)/15. Let k be g/27 - (-32)/18. Determine r so that 3*r**2 + k*r**3 - 3*r**2 + 5*r**2 - 3*r**2 = 0.
-1, 0
Let s(z) be the first derivative of -5*z**3/12 + 25*z**2/4 - 45*z/4 - 19. Find t, given that s(t) = 0.
1, 9
Let f(u) be the second derivative of 0*u**3 + 6*u - 1/72*u**4 + 0*u**2 - 1/120*u**5 + 0. Factor f(v).
-v**2*(v + 1)/6
Let t(