2*a**2.
-2*a**2*(a + 1)**2
Let y(f) = 135*f**4 + 80*f**3 - 80*f**2 - 190*f. Let n(g) = 5*g**4 + 3*g**3 - 3*g**2 - 7*g. Let o(k) = -55*n(k) + 2*y(k). Factor o(h).
-5*h*(h - 1)*(h + 1)**2
Suppose 5*m**2 - 4*m**3 - 1 + 6 - m**4 - 5 = 0. Calculate m.
-5, 0, 1
Let a(o) be the first derivative of -o + 1/2*o**3 - 4 + 0*o**2 - 1/2*o**4 + 3/20*o**5. Let k(z) be the first derivative of a(z). Factor k(w).
3*w*(w - 1)**2
Let d = -11 - -14. Suppose 3*w = -5*h + 16, 4*h = -d*w + 5*w + 4. Find g such that 4*g**w - 5*g**2 - 2*g**2 + 3*g**3 + g - g**4 = 0.
0, 1
Let k = 113/5 - 22. Determine c so that 3/5*c + 0*c**2 - k*c**3 + 0 = 0.
-1, 0, 1
Let n = 10 - -5. Suppose -4*l = l - n. Solve 8*w**4 + 2*w**4 - 20*w**l + 2 - 10*w - 9*w**2 + 14*w**2 - 2*w**5 + 15*w**2 = 0.
1
Let x(z) be the third derivative of -z**5/80 + 7*z**4/32 - 5*z**3/4 + 30*z**2. Solve x(m) = 0 for m.
2, 5
Let s(k) = -k + 1. Let d be s(-5). Let i(j) be the second derivative of 1/5*j**5 - 1/2*j**2 + 0 - 1/2*j**4 + j - 1/30*j**d + 2/3*j**3. What is n in i(n) = 0?
1
Suppose 8 = 5*q + 8. Suppose 3*d - 2 = 5*c - 1, d - 2*c = 0. Determine t, given that 0*t**3 - 1/4*t**4 + 1/4*t**d + 0*t + q = 0.
-1, 0, 1
Let l be (-3)/6 - (-3567)/(-30). Let r = l + 120. Determine q, given that 3/5*q - r*q**2 - 1/5 + 1/5*q**3 = 0.
1
Let w(a) be the first derivative of 3*a**5/10 + a**4/2 + a**3/3 + 2*a**2 + 3. Let d(h) be the second derivative of w(h). Factor d(m).
2*(3*m + 1)**2
Let t be (4 - -4) + (-7 - 1). Find o such that -1/6*o + t - 1/6*o**3 - 1/3*o**2 = 0.
-1, 0
Let g(u) = -u**3 - 7*u**2 - 6*u + 2. Let p be 6/(-4 + 5 + -2). Let w be g(p). Determine z so that -1/2 - 1/2*z**w - z = 0.
-1
Let f be 228/252 - 3/(-7). Factor f*w**2 - w**3 + 0 - 1/3*w.
-w*(w - 1)*(3*w - 1)/3
Let g(f) be the second derivative of 0*f**4 - 1/40*f**5 + 0*f**3 - 2*f - 1/60*f**6 + 0*f**2 + 0. Factor g(w).
-w**3*(w + 1)/2
Suppose 4*i - 5*g = 7, g = 2*i - 3*g - 2. Let r(n) be the first derivative of -1/22*n**4 + 0*n - 2 + 4/33*n**i - 1/11*n**2. Let r(v) = 0. What is v?
0, 1
Let i = -37/4 + 113/12. Let z(f) be the second derivative of -9*f**2 - i*f**4 - 4*f + 2*f**3 + 0. Factor z(t).
-2*(t - 3)**2
Let c(m) be the second derivative of m**6/30 - m**5/20 - m**4/4 + 5*m**3/6 - m**2 - 7*m. Factor c(h).
(h - 1)**3*(h + 2)
Let k = 1019/7 + -145. Solve 8/7*h**2 + 2*h + k - 8/7*h**3 = 0.
-1/2, 2
Let b(l) be the third derivative of -l**8/1512 + l**7/945 + l**6/540 - l**5/270 + 5*l**2. Let b(v) = 0. Calculate v.
-1, 0, 1
Suppose 5*h + 35 = -4*t - 13, -t - 12 = -4*h. Let f be t/27*(-30)/4. What is c in f*c + 8/3*c**3 + 16/3*c**2 + 2/3 = 0?
-1, -1/2
Suppose -p + 0*p - 4*r = 14, 0 = -3*r - 15. Let f be 16/p*(-15)/(-10). Determine u so that -2/7 + 0*u**3 + 0*u + 4/7*u**2 - 2/7*u**f = 0.
-1, 1
Let c(q) = q**2 + 8*q + 10. Let x be c(-7). Suppose -v = v. Factor v*o**3 + o + 5*o**x - 6*o**3.
-o*(o - 1)*(o + 1)
Let u = -6 + 14. Suppose u = -3*z - 2*v, 5*v = -0*z + 2*z - 20. Solve r**2 + z*r**2 - 2*r**2 + 2*r**3 - r**4 = 0.
0, 1
Suppose 125/3*o**5 - 8/3*o + 52/3*o**2 - 30*o**3 - 25/3*o**4 + 0 = 0. Calculate o.
-1, 0, 2/5
Let o(y) be the third derivative of 7/240*y**6 + 0*y - 1/4*y**4 - 3/40*y**5 + 1/3*y**3 + 0 - 7*y**2. Factor o(i).
(i - 2)*(i + 1)*(7*i - 2)/2
Let h(x) = x - 11. Let j be h(9). Let g be (j/(-3))/((-1)/(-6)). Let 0 - 2/9*m**g - 2/3*m**2 - 2/9*m - 2/3*m**3 = 0. Calculate m.
-1, 0
Let q(c) be the first derivative of -1/75*c**6 - 1/10*c**5 - 4/15*c**3 + c + 0*c**2 - 1 - 4/15*c**4. Let r(a) be the first derivative of q(a). Factor r(w).
-2*w*(w + 1)*(w + 2)**2/5
Suppose 0 = -4*n + 2 + 6. Solve -9*z**n - 4*z + 3*z**2 - 3*z**3 + 4*z = 0.
-2, 0
Let z = -8 + 11. Suppose 6 = 5*y - z*k - 13, k + 13 = 3*y. What is b in -2/5*b**y + 0*b**3 + 2/5*b**4 + 0*b + 0 + 0*b**2 = 0?
0, 1
Let a(w) be the first derivative of -1/6*w**3 + 2 - 3/4*w**2 - w. Factor a(p).
-(p + 1)*(p + 2)/2
Suppose -2*o + f + 8 = -0*o, -4*f - 5 = o. Let m(p) be the second derivative of 2/9*p**o + 1/6*p**4 + 3*p + 1/9*p**2 + 0. Factor m(n).
2*(3*n + 1)**2/9
Solve 0*k - 2/5*k**5 + 0*k**2 + 0 + 0*k**3 - 4/5*k**4 = 0.
-2, 0
Determine v so that 36/5*v + 16/5*v**3 + 8/5 + 48/5*v**2 = 0.
-2, -1/2
Let 8/5*m**2 + 2/5*m**5 - 4/5*m**3 + 2/5*m - 4/5*m**4 - 4/5 = 0. What is m?
-1, 1, 2
Let h(a) be the first derivative of 0*a + 0*a**3 + 1/30*a**4 - 1 - 1/15*a**2. Find l such that h(l) = 0.
-1, 0, 1
Let v be (6 + -4)*2 - 34/9. Let -v*k**2 - 4/3*k - 2 = 0. Calculate k.
-3
Let d = 92 - 92. Let r(i) be the third derivative of 0 + 1/180*i**6 + i**2 + 0*i**4 + 1/90*i**5 + d*i + 0*i**3. Factor r(w).
2*w**2*(w + 1)/3
Let k(n) be the second derivative of -n**7/56 + 3*n**5/80 - 14*n. Solve k(a) = 0 for a.
-1, 0, 1
Suppose 0 = 7*d - 2*d - 2*w - 15, 0 = -3*d - 4*w + 9. Solve 2*k + 7*k**2 + 0*k**2 - 2*k**d - 4*k**2 + k**4 - 4*k**2 = 0.
-1, 0, 1, 2
Let p(t) be the third derivative of -t**2 - 1/4*t**4 + 2/3*t**3 + 1/30*t**5 + 0 + 0*t. Suppose p(i) = 0. Calculate i.
1, 2
Let j(f) = -15*f**3 + 76*f**2 - 91*f + 19. Let i(t) = 46*t**3 - 228*t**2 + 272*t - 56. Let c(u) = 3*i(u) + 8*j(u). Find k such that c(k) = 0.
2/9, 2
Let o(s) be the first derivative of s**3 - 36*s**2 + 432*s - 8. Find p, given that o(p) = 0.
12
Let m(f) be the first derivative of -f**6/39 - 4*f**5/65 - f**4/26 - 10. Factor m(u).
-2*u**3*(u + 1)**2/13
Let c = -6 + 6. Let s = c + 4. Let -1/5*d**2 - 1/5*d**s + 3/5*d - 3/5*d**3 + 2/5 = 0. What is d?
-2, -1, 1
Factor -6*p**4 + 2*p + 2*p**5 - 2*p**2 - p**5 + 8 + 11*p**3 - 14*p.
(p - 2)**3*(p - 1)*(p + 1)
Let u = -1/26 + 55/78. Let k(p) be the first derivative of 0*p - u*p**3 + p**2 + 2. Factor k(v).
-2*v*(v - 1)
Find z, given that 54/7*z + 2/21*z**5 + 54/7 + 2/21*z**4 - 12/7*z**2 - 12/7*z**3 = 0.
-3, -1, 3
Let h(u) be the third derivative of -u**6/40 + 3*u**5/20 - u**4/4 + 3*u**2. Determine d, given that h(d) = 0.
0, 1, 2
Let q = -353 + 353. Suppose q*a + 0 - 3/2*a**3 + 1/2*a**4 + a**2 = 0. Calculate a.
0, 1, 2
Let v(y) be the third derivative of -y**6/540 + y**5/54 - 2*y**4/27 + 4*y**3/27 - 5*y**2. Factor v(p).
-2*(p - 2)**2*(p - 1)/9
Let o(w) = -28*w**2 + 76*w - 12. Let a(g) = g**2. Let y(r) = 4*a(r) + o(r). Factor y(s).
-4*(s - 3)*(6*s - 1)
Let m(o) be the first derivative of -o**4/14 + 8*o**3/21 - 5*o**2/7 + 4*o/7 - 35. Factor m(k).
-2*(k - 2)*(k - 1)**2/7
Suppose -4*g + g = -6, 4*u - 34 = -3*g. Suppose u + x**2 - 7 + 4*x + 0 + 4 = 0. Calculate x.
-2
Let y = 35 - 31. Factor 0 + y*x**2 - 2/3*x - 6*x**3.
-2*x*(3*x - 1)**2/3
Let c = 29 - 25. Factor -4*z**3 - z**3 + z**c - z**2 + 3*z**2 + 2*z**3.
z**2*(z - 2)*(z - 1)
Suppose -64 + 36 = -7*y. Let p(v) be the third derivative of 0*v - 1/240*v**5 - 1/12*v**4 + 0 - 1/6*v**3 - y*v**2 + 1/160*v**6. Let p(r) = 0. Calculate r.
-1, -2/3, 2
What is u in -64*u**2 + 69*u**2 + 2*u + 13*u = 0?
-3, 0
Suppose h + b = -4*h - 5, 0 = -2*h + 2*b - 2. Let x(s) = s**2 + 1. Let m be x(h). Suppose -2*o**3 + 5*o**2 - 2*o**2 - 5*o**m = 0. What is o?
-1, 0
Solve -2*s**3 + 2 - 4*s**2 + 2*s - s**2 + 3*s**2 = 0.
-1, 1
Factor -47 + 47 + 3*c**3 - 3*c**2.
3*c**2*(c - 1)
Factor -2/5*o**5 - 6/5*o**3 + 0 + 6/5*o**4 + 0*o + 2/5*o**2.
-2*o**2*(o - 1)**3/5
Let f(v) be the first derivative of -4 - 1/4*v**4 - 8*v + 2/3*v**3 + 2*v**2. Suppose f(n) = 0. What is n?
-2, 2
Let p(i) be the first derivative of -i**4/5 - 2*i**3/5 + 2*i/5 - 6. Factor p(m).
-2*(m + 1)**2*(2*m - 1)/5
Suppose 5*x + 15 = 3*o, 0 = 4*o - 0*x + x + 3. Let -5/2*j**2 + o - 1/2*j = 0. Calculate j.
-1/5, 0
Let f be (-27)/(-3) - (-2)/2. Let l(k) = k**3 - 10*k**2 + 2. Let j be l(f). Find c such that -2/5*c + 0 + 2/5*c**j = 0.
0, 1
Let a(n) be the first derivative of -n**5/15 - n**4/4 - n**3/9 + n**2/2 + 2*n/3 - 19. Find u such that a(u) = 0.
-2, -1, 1
Let l = 370/497 + 8/71. Solve 2/7*y - l*y**2 + 0 = 0.
0, 1/3
Let h = 192/455 + -2/91. Solve 0 - 2/5*y**2 + 2/5*y**3 - h*y + 2/5*y**4 = 0.
-1, 0, 1
Suppose 4*j = 2 + 6, 0 = 5*a + 5*j + 30. Let i be ((-2)/a)/(35/56). Factor i*l**2 + 4/5*l + 2/5.
2*(l + 1)**2/5
Let x(d) = d - 9. Let m be x(10). Let -6*k + 0*k + 2*k**2 + k**2 - m + 4 = 0. Calculate k.
1
Let s(w) = 135*w**2 + 540*w - 620. Let v(o) = 5*o**2 + 20*o - 23. Let i(f) = 2*s(f) - 55*v(f). Factor i(m).
-5*(m - 1)*(m + 5)
Let w be (-3 + 2)*3 + 5. Factor -4 - 2*o**w - 6*o + 3 + 1 - 4.
-2*(o + 1)*(o + 2)
Suppose 0 = 28*p - 31*p. Let n = 6 - 4.