
Suppose 2*x + x = 9. Let h be 2/(-6)*(x + -9). Let -v - 1 + v**h - v - 3 + v**2 = 0. Calculate v.
-1, 2
Let y be (-4)/(-26)*(-1)/(-59). Let q = 3078/3835 - y. Factor -2/5*u**4 + 0*u + 0 + q*u**3 - 2/5*u**5 + 0*u**2.
-2*u**3*(u - 1)*(u + 2)/5
Let x(k) be the first derivative of 2*k**5 - 25*k**4/8 - 35*k**3/6 + 5*k**2/2 - 41. Solve x(w) = 0 for w.
-1, 0, 1/4, 2
Let i(u) = -24*u**3 + 9*u**2 + 15*u - 12. Let o(f) = f**3 - f + 1. Let x(p) = i(p) + 12*o(p). What is q in x(q) = 0?
-1/4, 0, 1
Let y(l) be the third derivative of l**5/30 - 5*l**4/12 - 2*l**3 - 29*l**2. Determine n so that y(n) = 0.
-1, 6
Let r(x) = -5 + 1 - 3 + 5. Let a(f) = -f**2 + 19. Let p(d) = 2*a(d) + 18*r(d). Factor p(k).
-2*(k - 1)*(k + 1)
Suppose 0*a - 4*c + 4 = -2*a, 0 = a + 2*c - 6. Factor 9*q**2 - 1 + 0*q + 6*q - 3 + 31*q**a.
2*(4*q - 1)*(5*q + 2)
Let s(v) be the second derivative of v**9/15120 - v**8/4200 + v**7/4200 + v**3/6 + 3*v. Let y(n) be the second derivative of s(n). Factor y(p).
p**3*(p - 1)**2/5
Let s(q) = q**3 + 4*q**2 + 3*q. Let g be s(-3). Let w(m) be the third derivative of 1/42*m**4 + 2*m**2 - 1/21*m**3 + g + 0*m + 1/70*m**5. Factor w(n).
2*(n + 1)*(3*n - 1)/7
Suppose 0 = 2*a - a - 3. Factor -3*m - 3*m**3 + 6*m - m**a - 2*m**3 + 3*m**5.
3*m*(m - 1)**2*(m + 1)**2
Let c = 93 + -88. Let l(k) be the third derivative of 1/360*k**6 + 0 - 1/45*k**c + 5/72*k**4 + k**2 + 0*k - 1/9*k**3. Find v, given that l(v) = 0.
1, 2
Let z(g) be the second derivative of -g**8/448 + g**6/80 - g**4/32 + 5*g**2/2 + g. Let n(f) be the first derivative of z(f). Find w, given that n(w) = 0.
-1, 0, 1
Let b(i) = -3*i**2 + i**2 + 7*i**2 - 5*i**3 + 0*i**2. Let d(t) = t**3 - t**2. Let j(w) = b(w) + 4*d(w). Factor j(n).
-n**2*(n - 1)
Let g = 161 - 643/4. Factor -1/4*n**3 + 1/4*n - 1/4*n**2 + g.
-(n - 1)*(n + 1)**2/4
Let v(m) be the first derivative of -m**4/6 - m**3 - 2*m**2 - 7*m - 2. Let n(g) be the first derivative of v(g). Suppose n(h) = 0. What is h?
-2, -1
Let i(t) be the second derivative of t**6/135 - t**5/90 - t**4/54 + t**3/27 + 7*t. Factor i(l).
2*l*(l - 1)**2*(l + 1)/9
Find i, given that 3 + 9/2*i + 3/2*i**2 = 0.
-2, -1
Let s(r) = -8*r**2 - 10*r**5 - 23*r**2 + 0 + 20*r**4 - r + 11*r**3 + 0. Let h(j) = -2*j**5 + 4*j**4 + 2*j**3 - 6*j**2. Let b(i) = 11*h(i) - 2*s(i). Factor b(u).
-2*u*(u - 1)**3*(u + 1)
Let q(g) be the second derivative of -g**6/15 - 3*g**5/10 + 4*g**3/3 + 35*g. Factor q(n).
-2*n*(n - 1)*(n + 2)**2
Suppose 0 = 4*u - 2*f + 26, -3*u - f = -6*f + 2. Let j be u/(-21)*2/3. What is h in 0*h + j*h**2 + 0 = 0?
0
Let b(n) be the first derivative of -n**9/10584 + n**7/980 + n**6/630 + 11*n**3/3 + 10. Let h(s) be the third derivative of b(s). Factor h(p).
-2*p**2*(p - 2)*(p + 1)**2/7
Let g(h) be the third derivative of h**10/529200 + h**9/211680 - h**5/20 - 2*h**2. Let l(q) be the third derivative of g(q). Factor l(w).
2*w**3*(w + 1)/7
Let l(k) be the second derivative of k**7/483 - k**5/230 - 8*k. Factor l(a).
2*a**3*(a - 1)*(a + 1)/23
Let v be (-226)/(-10) + (-14)/(-35). Suppose -5*u + 38 = 5*q + 3, -u + v = 5*q. Suppose 7*g - g**2 - g**5 + u*g**4 - 7*g + 2*g**2 - 3*g**3 = 0. What is g?
0, 1
Let a(f) = f**4 - f**3 + f + 1. Let u(h) = -9*h**4 - 4*h**3 - 51*h**2 - 96*h - 56. Let l(g) = 24*a(g) + 3*u(g). Factor l(z).
-3*(z + 1)*(z + 3)*(z + 4)**2
Factor 1/2*c**4 - 2*c + 2*c**3 - 3/2 + c**2.
(c - 1)*(c + 1)**2*(c + 3)/2
Let u be (1*(4 + -4))/2. Let g(h) be the third derivative of 0 + 0*h + 1/96*h**4 + 2*h**2 + u*h**3 + 1/240*h**5. Factor g(r).
r*(r + 1)/4
Let q(k) be the second derivative of k**4/72 + k**3/36 - k**2/6 + 7*k. Factor q(g).
(g - 1)*(g + 2)/6
Let j be -3*((-16)/(-120))/((-16)/5). Let z(n) be the first derivative of -3/4*n**2 - 1/2*n - 1/2*n**3 + 1 - j*n**4. Suppose z(p) = 0. What is p?
-1
Let g(m) be the second derivative of -m**4/12 - m**3/2 - 40*m. Suppose g(z) = 0. What is z?
-3, 0
Suppose -9 = -4*z + 39. Let u be (-3)/2*(-16)/z. Find q, given that -5*q - 2*q**4 + 3*q - 1 - q**4 + 2*q**3 + 4*q**u = 0.
-1, -1/3, 1
Let g(r) = 6*r**2 + 45*r - 33. Let v(a) = a**2 - a - 1. Let h(x) = -g(x) + 18*v(x). Suppose h(k) = 0. Calculate k.
1/4, 5
Let u(j) be the first derivative of j**4/10 + 2*j**3/5 - 8*j/5 + 5. Determine r so that u(r) = 0.
-2, 1
What is u in -6*u**2 + 7 - 5 + 2*u**4 + 2*u**2 = 0?
-1, 1
Suppose 2/9*f**3 - 4/9*f**2 + 0 + 0*f = 0. Calculate f.
0, 2
Let f(r) be the third derivative of 0*r - 1/4*r**4 - 1/20*r**6 + 1/28*r**8 + 0 + 1/2*r**3 - 2/5*r**5 - 8*r**2 + 1/10*r**7. Solve f(c) = 0 for c.
-1, 1/4, 1
Let k(c) be the second derivative of c**4/6 + 4*c**3 + 36*c**2 + 27*c. Solve k(p) = 0.
-6
Let l(o) be the second derivative of o**7/126 - o**5/30 + o**3/18 - 5*o. Factor l(d).
d*(d - 1)**2*(d + 1)**2/3
Let z(m) be the second derivative of 1/3*m**3 + 1/3*m**4 + 2*m - m**2 - 1/5*m**5 + 1/21*m**7 - 1/15*m**6 + 0. What is l in z(l) = 0?
-1, 1
Let r(d) be the first derivative of -4/7*d**3 - 2/7*d - 2 - 4/7*d**2 - 2/7*d**4 - 2/35*d**5. What is j in r(j) = 0?
-1
Let 3/5*c**4 + 24/5 - 21/5*c**3 + 54/5*c**2 - 12*c = 0. What is c?
1, 2
Suppose 2*n + 3*n = -5. Let j = 1 + n. Factor -1/2*c**2 + 1/2*c**3 + j + 0*c.
c**2*(c - 1)/2
Solve 5*m**3 - 8*m**5 + 10*m**2 + 3*m**5 + 34*m**4 - 44*m**4 = 0.
-2, -1, 0, 1
Let o = 22 + -12. Let s = o - 10. Find y, given that s*y - 2/5*y**2 + 2/5 = 0.
-1, 1
Let c(j) be the first derivative of -j**6/1260 - j**5/210 - 5*j**3/3 + 1. Let s(o) be the third derivative of c(o). Determine n, given that s(n) = 0.
-2, 0
Let t be 3 + 1 + (-30)/8. Find p, given that -5/4*p - p**2 - t = 0.
-1, -1/4
Factor 11*k + 0*k**2 - 2*k**2 - 18 + 9*k.
-2*(k - 9)*(k - 1)
Let t(x) be the second derivative of x**7/14 + x**6/2 + 9*x**5/20 - 9*x**4/4 + 61*x. Let t(i) = 0. What is i?
-3, 0, 1
Let g = -47/24 - -549/280. Let y(c) be the third derivative of 0*c - 1/60*c**6 - 1/12*c**3 - 1/20*c**5 + 0 + 2*c**2 - 1/12*c**4 - g*c**7. Factor y(t).
-(t + 1)**4/2
Let s(m) be the third derivative of m**7/35 + m**6/60 - 4*m**5/15 + m**4/3 + 6*m**2. Factor s(a).
2*a*(a - 1)*(a + 2)*(3*a - 2)
Let z be ((-5)/(-10))/(1/6). Let j(w) be the third derivative of 0*w + 0*w**z + 0*w**5 + 1/420*w**6 + 0*w**4 + 0 - w**2. Determine a, given that j(a) = 0.
0
Let n(v) be the second derivative of 3*v**5/40 - 5*v**4/8 + v**3 - 25*v. Let n(q) = 0. Calculate q.
0, 1, 4
Let u(r) = 8*r**2 + 5*r + 3. Let c(z) = 15*z**2 + 10*z + 5. Let p(l) = 3*c(l) - 5*u(l). Factor p(t).
5*t*(t + 1)
Let f(w) be the second derivative of -w**4/24 - w**3/4 + 12*w. Find c, given that f(c) = 0.
-3, 0
Let c(i) = -i**2. Let p(q) = -17*q**2 - 13*q**2 + 44*q**2 - 18*q**2 - 6*q + 9. Let k = -4 + 3. Let f(b) = k*p(b) + 5*c(b). Factor f(u).
-(u - 3)**2
Suppose -7*p = -3*p - 16. Suppose -10 = -p*i - 2*r, -5*i + 12 = 4*r - 2*r. Factor -z**i - z**5 + 3*z**4 - 2*z**4 + 0*z**3 + z**3.
-z**2*(z - 1)**2*(z + 1)
Suppose -3*k + 63 - 3 = 0. Suppose 0 = -f - 2*f + 5*p + 20, k = -5*p. Factor 2/3*v**3 + 0 + f*v**2 - 2/3*v.
2*v*(v - 1)*(v + 1)/3
Suppose 0 = 12*z - 14*z + 6. Find w, given that -4/9*w - 10/9*w**4 + 0 + 2*w**z - 14/9*w**5 + 10/9*w**2 = 0.
-1, 0, 2/7, 1
Suppose -2*f + 6*f = 5*n + 28, -2*f - 4 = 2*n. Let p(y) be the first derivative of 0*y**f - 2/5*y**5 + 0*y - 2/3*y**3 - y**4 + 1. Suppose p(i) = 0. Calculate i.
-1, 0
Suppose 5*q = -5*p + 2*p - 15, 4*p - 12 = 4*q. Suppose 3*k - 15 = -p*k. Determine v so that 0 - 2*v**3 + 2*v**k + 0*v + 2/3*v**2 - 2/3*v**4 = 0.
-1, 0, 1/3, 1
Let z be 40/(-8) - 48/(-9). Let -1/3*m**5 + 0 - z*m**3 - 2/3*m**4 + 0*m**2 + 0*m = 0. Calculate m.
-1, 0
Let r be (4 + 44/(-12))*15. Let x(v) be the first derivative of 0*v**4 - 1/3*v**6 + 0*v + 1 + 4/5*v**r + v**2 - 4/3*v**3. Solve x(q) = 0 for q.
-1, 0, 1
Let h(c) be the first derivative of -c**6/60 + c**5/30 + c**4/12 - c**3/3 + c**2/2 - 1. Let y(d) be the second derivative of h(d). Factor y(w).
-2*(w - 1)**2*(w + 1)
Let r(a) = -2*a**2 - 13*a + 10. Let i be r(-10). Let o be (45/(-75))/(2/i). Find z, given that o*z**2 + 8/9 - 8*z = 0.
2/9
Let k(p) be the third derivative of 3*p**2 - 1/18*p**3 + 1/360*p**6 + 0 - 1/60*p**5 + 1/24*p**4 + 0*p. Factor k(l).
(l - 1)**3/3
Let i(v) be the second derivative of v**7/63 + 2*v**6/135 - 2*v**5/45 - v**4/27 + v**3/27 - 7*v. Solve i(o) = 0.
-1, 0, 1/3, 1
Suppose 2*z + 7 = 4*p - 45, 0 = -4*p - 3*z + 42. Let -8 - 1 + 3*n**2 + 