) = 0?
0, 1
Let x(a) be the third derivative of a**4/24 - a**3/2 - 3*a**2. Let p be x(5). Solve -2/3*h**3 + 2*h**p + 2/3 - 2*h = 0.
1
Let a(p) = -100*p**4 + 304*p**3 - 276*p**2 + 136*p - 40. Let k(v) = v**3 + v - 1. Let m(x) = a(x) - 24*k(x). Factor m(j).
-4*(j - 1)**2*(5*j - 2)**2
Suppose -7*q = -4*q. Let l = 2 - q. Factor 0*b - 1/2*b**l + 1/2.
-(b - 1)*(b + 1)/2
Suppose 4*c + 11 = 19. Let u(b) be the first derivative of -5/14*b**4 + c - 8/21*b**3 + 0*b - 1/7*b**2 - 4/35*b**5. Solve u(p) = 0.
-1, -1/2, 0
Suppose -2*d = -15*d + 52. Factor 0*a + 2/3*a**3 - 1/3*a**2 - 1/3*a**d + 0.
-a**2*(a - 1)**2/3
Let u(c) be the second derivative of c**4/42 - c**3/21 + c - 32. Suppose u(t) = 0. What is t?
0, 1
Let c = -43 + 46. Let r(m) be the second derivative of 1/33*m**c + 1/66*m**4 + m + 0*m**2 + 0. Solve r(x) = 0 for x.
-1, 0
Let h(k) = -k**3 + k**2 + k + 2. Let s be h(2). Suppose 3*c = -s*c. Find r such that c*r**2 + r**2 - 3*r**2 = 0.
0
Factor -3/5*t + 2/5*t**2 + 1/5.
(t - 1)*(2*t - 1)/5
Let f(k) be the second derivative of -2*k + 1/6*k**4 - k**2 - 1/20*k**5 + 1/6*k**3 + 0. Factor f(r).
-(r - 2)*(r - 1)*(r + 1)
Let d(k) be the second derivative of -k**5/180 + k**4/36 - k**3/18 + k**2 + k. Let m(r) be the first derivative of d(r). Factor m(z).
-(z - 1)**2/3
Let t(q) be the third derivative of q**7/1260 - q**6/90 + q**5/15 - q**4/24 - 3*q**2. Let x(o) be the second derivative of t(o). What is z in x(z) = 0?
2
Let l(u) be the second derivative of u**4/18 - u**2/3 - 11*u. Find y such that l(y) = 0.
-1, 1
Let a(q) = q**2 - 13*q + 44. Let g be a(5). Factor 0 + 5/4*o**3 + 1/4*o**g + o + 2*o**2.
o*(o + 1)*(o + 2)**2/4
Solve 14*h**5 + 15*h**2 - 8*h**5 - 15*h**4 + 4*h - 10*h = 0.
-1, 0, 1/2, 1, 2
Let a(k) be the second derivative of k**4/30 - 28*k**3/15 + 196*k**2/5 - k + 7. Let a(x) = 0. What is x?
14
Let p(c) be the second derivative of -7*c**6/1080 + 23*c**5/360 - c**4/12 - c**3/3 + 3*c. Let w(s) be the second derivative of p(s). Find h such that w(h) = 0.
2/7, 3
Solve 4/9*x**4 + 0 + 4/9*x - 4/9*x**2 - 1/3*x**3 - 1/9*x**5 = 0 for x.
-1, 0, 1, 2
Let n(d) be the second derivative of -11/2*d**3 - 2*d + 0 - 3/5*d**5 - 13/4*d**4 - 3*d**2. Factor n(i).
-3*(i + 1)*(i + 2)*(4*i + 1)
Let n(f) be the first derivative of -3/2*f**4 + 3 - 4/3*f**3 + f**2 + 0*f. Find k, given that n(k) = 0.
-1, 0, 1/3
Let o(x) = -x + 5. Let a be o(5). Let i = -37/6 + 20/3. What is p in i*p**2 + a + 1/2*p = 0?
-1, 0
Let i(t) be the second derivative of 3*t - 1/50*t**5 + 0*t**3 + 0*t**2 + 0*t**4 + 0. Let i(n) = 0. Calculate n.
0
Let o(g) = 2*g**2 - 5*g. Let z(q) = 10*q**2 - 26*q. Let j(w) = 10*w**2 - 26*w. Let s(v) = 6*j(v) - 5*z(v). Let p(c) = -16*o(c) + 3*s(c). Factor p(x).
-2*x*(x - 1)
Let r(s) be the first derivative of 2*s**3/9 - s**2 - 8*s/3 - 3. Find p such that r(p) = 0.
-1, 4
Solve 3/4*s**4 + 0*s**3 + 0*s - s**2 + 1/4*s**5 + 0 = 0 for s.
-2, 0, 1
Let z(l) = -2*l**3 - 4*l**2 + 4*l + 2. Let c(b) = -3*b**3 + 12*b**2 + 9*b**2 + 13*b**3 - 20*b - 11. Let x(p) = -2*c(p) - 11*z(p). What is d in x(d) = 0?
-2, 0, 1
Let r(w) be the third derivative of w**6/120 + 2*w**5/5 + 8*w**4 + 256*w**3/3 + 27*w**2. Suppose r(b) = 0. What is b?
-8
Let f(g) be the third derivative of g**7/945 - g**5/270 - 6*g**2. Factor f(u).
2*u**2*(u - 1)*(u + 1)/9
Suppose 3*u + 0*a - 22 = a, 0 = -2*u - 4*a + 10. Let z = 12 - u. Factor 2*p**4 - 22*p**2 + 5*p**z + 22*p**2.
p**4*(5*p + 2)
Let q(a) be the first derivative of a**6/60 + a**5/20 - a**3/6 - a**2/4 - 3*a + 2. Let h(z) be the first derivative of q(z). Suppose h(o) = 0. Calculate o.
-1, 1
Suppose -7 = -2*w + 2*n + 9, -2*w - 5*n - 12 = 0. Let k(i) be the second derivative of -2*i + 0*i**3 + 0*i**2 + 0 + 1/30*i**w. Suppose k(b) = 0. What is b?
0
Let h(u) be the third derivative of 3/100*u**5 - 9/40*u**4 + 9/10*u**3 - u**2 + 0*u - 1/600*u**6 + 0. Factor h(b).
-(b - 3)**3/5
Let a(k) be the second derivative of k**4/36 + 2*k**3/9 + k**2/2 + 2*k. Factor a(q).
(q + 1)*(q + 3)/3
Let w(o) be the first derivative of 0*o**4 - 1/2*o**2 + 0*o + 1/90*o**5 - 2 - 1/9*o**3. Let j(t) be the second derivative of w(t). Factor j(n).
2*(n - 1)*(n + 1)/3
Let p be (-4 - 4/(-1)) + 3. Let o be (-2)/(-9)*(p - 0). Factor -o*r + 2/3*r**3 + 1/3 - 1/3*r**4 + 0*r**2.
-(r - 1)**3*(r + 1)/3
Let g(f) = -f**3 + 5*f**2 + 0 + 7*f + 0*f**3 - 3 - 1. Let m be g(6). Let -6*k - k**3 - m*k**2 - k**3 - 2 - 4*k**2 = 0. Calculate k.
-1
Factor 2/13 + 2/13*o**2 + 4/13*o.
2*(o + 1)**2/13
Let f(z) be the first derivative of z**3/9 - z**2/6 - 2*z/3 - 3. Factor f(o).
(o - 2)*(o + 1)/3
Let a(o) = -o + 5. Let r be a(3). Let p(t) be the first derivative of -2/21*t**3 - 2/7*t + 2/7*t**r - 2. Factor p(f).
-2*(f - 1)**2/7
Let q(g) be the first derivative of -2 + 0*g + 2/5*g**5 + 2/3*g**3 + g**4 + 0*g**2. Determine v so that q(v) = 0.
-1, 0
Let c(h) be the first derivative of -h**6/6 - 2*h**5/5 + h**4 + 2*h**3/3 - 3*h**2/2 - 19. Factor c(f).
-f*(f - 1)**2*(f + 1)*(f + 3)
Factor -254*i**2 - 2*i + 4*i + 252*i**2.
-2*i*(i - 1)
Let w be (10*10/125)/(8/20). Suppose 16/3*r**w - 4/3 + 2/3*r + 10/3*r**3 = 0. What is r?
-1, 2/5
Let g(n) = 2*n**5 - 2*n**4 - 4*n**3 - 3. Let o(w) = -2*w**5 + w**4 + 3*w**3 + 2. Let u(z) = -2*g(z) - 3*o(z). Find b such that u(b) = 0.
-1, 0, 1/2
Let w = 4 + 1. Suppose 0*u = w*u - 40. Suppose -18/5*t**5 - 4/5*t**2 - 12/5*t**4 - u*t + 16/5 + 58/5*t**3 = 0. Calculate t.
-2, -1, 2/3, 1
Let n(m) be the first derivative of -m**9/1848 - m**8/770 - m**7/1155 - m**3 - 6. Let f(i) be the third derivative of n(i). Factor f(r).
-2*r**3*(3*r + 2)**2/11
Suppose 3*u + a = 25, 12 = 4*u - 3*a - 4. Factor 3*s + 9*s**2 - s + 0*s - u*s**2.
2*s*(s + 1)
Let l = 563 + -563. Factor 2/11 - 2/11*q**2 + l*q.
-2*(q - 1)*(q + 1)/11
Suppose i - 4*i + 2*m - 8 = 0, i + m = 4. Suppose 5 = 2*x - x + 3*d, -5*x + 3*d = -7. Factor -3*j**x + 5*j**2 - 2*j + i*j.
2*j*(j - 1)
Let i(t) be the third derivative of -t**8/7560 + t**7/945 - t**6/405 - 2*t**3/3 + 6*t**2. Let r(b) be the first derivative of i(b). Factor r(y).
-2*y**2*(y - 2)**2/9
Factor -2/7*a**4 + 2/7*a**2 - 2/7*a**5 + 0*a + 2/7*a**3 + 0.
-2*a**2*(a - 1)*(a + 1)**2/7
Let f = 1962/5 - 388. Factor 2/5*j - 2/5*j**2 - 8/5*j**5 - f*j**4 + 0 - 18/5*j**3.
-2*j*(j + 1)**3*(4*j - 1)/5
Suppose -5*u = -2*w + 7, 2*w - w = -4. Let n be u*(2 - 8/3). Solve 77*f**5 + 10*f**2 - n*f**2 + 4*f + 119*f**5 - 75*f**3 - 133*f**4 = 0.
-2/7, 0, 1/4, 1
Let t(o) be the second derivative of 0*o**3 + 3*o - 1/200*o**6 + 0 - 1/40*o**4 + 3/2*o**2 - 1/50*o**5. Let l(v) be the first derivative of t(v). Factor l(s).
-3*s*(s + 1)**2/5
Let g(q) = -q**2 + 3*q. Let j be g(2). Suppose 2*m - 18 = -7*m. Factor n**4 - 3*n**4 + 10*n - m*n**4 - j - 18*n**2 + 14*n**3.
-2*(n - 1)**3*(2*n - 1)
Let m be 3/((-72)/(-80)) + 7. Determine p so that 43/3*p**3 - 35/3*p**2 + m*p**4 - 8/3*p + 4/3 - 35/3*p**5 = 0.
-1, -2/5, 2/7, 1
Solve -1/6*j**3 - 1/2*j**2 - 1/3*j + 0 = 0.
-2, -1, 0
Let t be 1*11 + (6 - 7). Let u be 4/10 - 4/t. Solve 0*a**3 + 2/7*a**4 + u*a + 0 - 2/7*a**2 = 0 for a.
-1, 0, 1
Let m(d) be the third derivative of d**7/13860 - d**5/660 - 3*d**4/8 - 5*d**2. Let s(l) be the second derivative of m(l). Factor s(a).
2*(a - 1)*(a + 1)/11
Factor 4*p + 0*p - 9 - 4*p + 3*p**2 - 6*p.
3*(p - 3)*(p + 1)
Let p(j) = -3*j**2 + 0*j**3 - 4*j**2 + 0*j**2 - 3*j**3. Let h(q) = -q**3 - 3*q**2. Let b(y) = -7*h(y) + 3*p(y). Factor b(u).
-2*u**3
Suppose -4*m + 4*r = 2*r - 16, 9 = 5*m + 3*r. Factor 2/3*i**5 + 4/3*i**4 + 0 - 2/3*i - 4/3*i**2 + 0*i**m.
2*i*(i - 1)*(i + 1)**3/3
Let o(i) be the first derivative of 2*i**3/9 + 2*i**2/3 + 2. Factor o(u).
2*u*(u + 2)/3
Let s(h) = -7*h + 7*h - 7*h - 5. Let n = 1 + -2. Let f(c) = -c**2 - c - 1. Let d(p) = n*s(p) + 5*f(p). Factor d(u).
-u*(5*u - 2)
Suppose 3*h = 2*h + 3. Let v(z) = 8*z**4 - 2*z**5 + 2*z**2 - 3*z - 7*z**3 - z**5 + 0*z**3. Let p(q) = q. Let t(u) = h*p(u) + v(u). What is l in t(l) = 0?
0, 2/3, 1
Let n(a) be the third derivative of -2*a**7/105 - a**6/15 + a**5/15 + a**4/3 - 4*a**2. Factor n(u).
-4*u*(u - 1)*(u + 1)*(u + 2)
Let x(b) = -b**2 - 7*b + 14. Let r be x(-8). Suppose 6 + r = 4*a. Determine u so that 2/5*u**4 + 0 + 6/5*u**a + 0*u + 4/5*u**2 = 0.
-2, -1, 0
Determine z so that 21/4*z + 3/2 + 9/4*z**2 = 0.
-2, -1/3
Let n = -479/110 + 49/10. Suppose -2/11 + 2/11*i**3 - n*i**2 + 6/11*i = 0. What