0 + 2*x**2 + 0*x**4. Let n(z) be the first derivative of c(z). Factor n(b).
-2*(b - 1)*(b + 1)/3
Let h(n) = n**3 + 2*n**2 - 3*n - 3. Let c be h(-2). Find f, given that f**c + 3*f**2 + 7*f - 2*f**2 - 9*f = 0.
-2, 0, 1
Let u(y) be the first derivative of -2/9*y**3 + 3 + 1/18*y**4 - 2/9*y + 1/3*y**2. Determine w, given that u(w) = 0.
1
Let a(q) = 4 + 4*q**3 - q**3 + q**3 + 0*q**2 + 6*q**2. Let v(r) = r**3 + r**2 - r + 1. Let h(l) = -a(l) + 3*v(l). Solve h(c) = 0.
-1
Let t(y) = -y**2 - 32*y - 84. Let k be t(-29). Suppose 8/3*l - 12*l**k + 0 + 28/3*l**5 - 20/3*l**2 + 20/3*l**4 = 0. What is l?
-1, 0, 2/7, 1
Let u = -3 + 2. Let c = u + 3. Suppose -4*j**4 - 5/3*j**5 + 0*j + 0 - 3*j**3 - 2/3*j**c = 0. What is j?
-1, -2/5, 0
Let c be 8/(-98)*(-1 + (-10)/4). Factor 0*w**2 - 4/7*w + 4/7*w**3 + c - 2/7*w**4.
-2*(w - 1)**3*(w + 1)/7
Solve 0 + 0*l**3 + 2/3*l - 2/3*l**5 - 4/3*l**4 + 4/3*l**2 = 0 for l.
-1, 0, 1
Let a(s) = -s**3 - s**2 + s + 3. Let k be a(0). Factor 2/3*w**2 - 4/3*w + 10/3*w**4 + 16/3*w**k + 0.
2*w*(w + 1)**2*(5*w - 2)/3
Let z = 7 + -5. Let h be z - (-1 - 35/45). Factor 22/9*k - 10/9*k**4 - 14/3*k**2 - 4/9 + h*k**3.
-2*(k - 1)**3*(5*k - 2)/9
Let f(j) be the second derivative of -j**4/8 + 7*j**3/2 - 147*j**2/4 + 18*j. Find i, given that f(i) = 0.
7
Let k = 65 - 64. Factor -1/2*q**2 + 3/2*q - k.
-(q - 2)*(q - 1)/2
Let a(z) = -z**3 + 5*z**2 + z - 5. Let l be a(5). Let f = 1/2 - l. Find i such that 1/2*i - f*i**3 + 0*i**2 - 1/4 + 1/4*i**4 = 0.
-1, 1
Let a(g) be the second derivative of -g**8/1680 + g**6/180 - g**4/24 - g**3/3 + g. Let z(x) be the second derivative of a(x). Find v, given that z(v) = 0.
-1, 1
Determine k, given that 4*k - 4*k**4 + 4*k - 8*k**3 + 14*k**2 - 10*k**2 = 0.
-2, -1, 0, 1
Suppose -4*g + 0*l - 2*l = 0, 0 = -g - l - 2. Let s(m) be the first derivative of 2/3*m**4 - 2/3*m - g*m**3 - 2 + 2*m**2. Factor s(o).
2*(o - 1)**2*(4*o - 1)/3
Let 5*u**3 + 5*u**3 - 6*u**3 + 2*u**4 + 4*u**2 - 2*u**2 = 0. What is u?
-1, 0
Let q(a) = 5*a**3 + 20*a**2 - 55*a + 30. Let m(d) = 20*d**3 + 80*d**2 - 220*d + 120. Let r(y) = 2*m(y) - 9*q(y). Suppose r(l) = 0. What is l?
-6, 1
Let h(l) be the second derivative of 0 + l + l**3 - 1/5*l**5 - l**2 + 1/5*l**6 - 1/3*l**4 - 1/21*l**7. Factor h(n).
-2*(n - 1)**4*(n + 1)
Let y(j) = j**4 + 3*j**3 + 7*j**2 - 7*j - 4. Let p(f) = 3*f**4 + 6*f**3 + 15*f**2 - 15*f - 9. Let w(q) = 4*p(q) - 9*y(q). Factor w(d).
3*d*(d - 1)**2*(d + 1)
Let x(j) = 21*j**3 - j**2 - 20*j + 11. Let s(w) = -3*w**3 + 3*w + w - 5 - w**3 + 3. Let q(h) = -11*s(h) - 2*x(h). Factor q(g).
2*g*(g - 1)*(g + 2)
Let n = 3 - -5. Let o = 13 - n. Solve 0*g**4 - g**o - 4*g**2 + 2*g**5 - 7*g**3 + 4*g**4 + 2*g**5 + 4*g = 0.
-2, -1, 0, 2/3, 1
Let n(t) = 5*t**3 - 7*t**2 + 7*t - 5. Let w(v) = -9*v**3 + 13*v**2 - 13*v + 9. Let h(i) = -7*n(i) - 4*w(i). Factor h(r).
(r - 1)**3
Let p(m) be the first derivative of 4*m**5/5 + 4*m**4 - 4*m**3/3 - 8*m**2 + 6. Factor p(k).
4*k*(k - 1)*(k + 1)*(k + 4)
Let s = -16 + 32. Let u = 20 - s. Factor 0*d + 4/5*d**3 + 0 + 2/5*d**2 + 2/5*d**u.
2*d**2*(d + 1)**2/5
Let 8/11*x**2 + 12/11*x**3 - 10/11 + 2/11*x**4 - 12/11*x = 0. Calculate x.
-5, -1, 1
Let s(n) be the third derivative of -n**8/3192 + 2*n**7/1995 - n**5/285 + n**4/228 + 8*n**2. Factor s(i).
-2*i*(i - 1)**3*(i + 1)/19
Let r(m) be the first derivative of m**4/6 + 4*m**3/9 + m**2/3 + 3. What is n in r(n) = 0?
-1, 0
Let q(o) be the second derivative of -o**5/60 + 5*o**4/36 + 13*o**3/18 + 7*o**2/6 - 3*o - 1. Factor q(k).
-(k - 7)*(k + 1)**2/3
Suppose -2*z - z - d = -11, -3*z + 1 = -d. Find a, given that -1/5*a**z + 0 + 1/5*a**4 + 1/5*a - 1/5*a**3 = 0.
-1, 0, 1
Let g = 151 - 151. Let g - 2/7*c**2 - 2/7*c = 0. Calculate c.
-1, 0
Let q(o) be the first derivative of -1/13*o**6 + 0*o + 6 + 2/13*o**2 + 2/13*o**5 - 10/39*o**3 + 1/26*o**4. Find t such that q(t) = 0.
-1, 0, 2/3, 1
Suppose 2*g**3 + 4*g**5 - 2*g**3 - 5*g**5 + g**3 = 0. Calculate g.
-1, 0, 1
Determine t so that -2/5*t - 2/5*t**2 + 4/5 = 0.
-2, 1
Let h be 51/17 - 106/36. Let s(q) be the second derivative of 5/18*q**3 + 3*q + 0 + h*q**4 - 1/12*q**5 - 1/3*q**2. Factor s(b).
-(b - 1)*(b + 1)*(5*b - 2)/3
Let b(d) = -d**2 + 5*d - 4. Suppose 4 = 3*r - 8. Let f be b(r). Factor -6*u**4 + f*u**4 + 2 - 21*u**2 - 3*u - 3*u**4 - 25*u**3.
-(u + 1)**3*(9*u - 2)
Solve -70*l - 138*l**2 + 163*l**2 + 30*l + 20 - 5*l**3 = 0 for l.
1, 2
Let v(l) be the second derivative of -19*l**4/4 + l**3 - 15*l. Determine x, given that v(x) = 0.
0, 2/19
Let o(p) = -2*p**3 + 2*p**2 - 2*p + 2. Let x(m) = m**2 - m + 1. Let c(g) = o(g) - 2*x(g). Determine h, given that c(h) = 0.
0
Let y(d) be the third derivative of d**5/90 - d**4/12 - 4*d**3/9 - 11*d**2. Determine j so that y(j) = 0.
-1, 4
Factor 1/5*u**2 - 1/5*u**3 + 3/5 + u.
-(u - 3)*(u + 1)**2/5
Find d, given that -8/13*d**2 + 0 - 8/13*d - 2/13*d**3 = 0.
-2, 0
Let b(h) be the first derivative of h**4 - 8*h**3/3 + 2*h**2 + 9. Factor b(n).
4*n*(n - 1)**2
Let a(r) be the second derivative of r**6/600 - r**5/150 + 5*r**2/2 - 3*r. Let p(d) be the first derivative of a(d). Factor p(z).
z**2*(z - 2)/5
Factor -1/2*x**3 - 1/2*x**4 + 1/2*x + 1/2*x**2 + 0.
-x*(x - 1)*(x + 1)**2/2
Determine s so that -4/7*s**3 + 0*s**2 - 2/7*s**4 + 4/7*s + 2/7 = 0.
-1, 1
Suppose 0 = -7*k + 2*k. Let x(b) be the second derivative of 0*b**2 - 7/30*b**4 + 2*b - 1/25*b**6 + k + 4/25*b**5 + 2/15*b**3. Factor x(y).
-2*y*(y - 1)**2*(3*y - 2)/5
Let t(p) = p. Let w(z) = -2*z**2 - 3*z. Suppose m = 3*m - 4. Let h = -3 - m. Let b(f) = h*t(f) - w(f). Factor b(l).
2*l*(l - 1)
Let x(p) = 25*p**3 - 5*p**2 + 15*p. Let b(w) = w**4 - w**3 - w. Let k(y) = -15*b(y) - x(y). Factor k(h).
-5*h**2*(h + 1)*(3*h - 1)
Let c(w) be the first derivative of -w**3 - 6*w - 9/2*w**2 - 2. Factor c(b).
-3*(b + 1)*(b + 2)
Let n = 26 + -29. Let b be (0 + (-3 - n))/(-2). Factor 0*l + 1/2*l**2 + b.
l**2/2
Let q be 2/(-5) - 21/(-15). Let d be (1 - q - -3)/1. Factor 2/5*z**2 + 2/5*z**d + 0 + 0*z.
2*z**2*(z + 1)/5
Let f(d) = 8*d**3 + 6*d**2 + 6*d - 6. Let z(w) = 23*w**3 + 17*w**2 + 17*w - 17. Suppose -2*i - 18 = i. Let o(s) = i*z(s) + 17*f(s). Find y, given that o(y) = 0.
0
Let j(q) = -5*q**5 + 9*q**4 - 4*q**3 - 9*q**2 + 9*q - 9. Let k(x) = 2*x**5 - 4*x**4 + 2*x**3 + 4*x**2 - 4*x + 4. Let r(n) = 4*j(n) + 9*k(n). Factor r(h).
-2*h**3*(h - 1)*(h + 1)
Let l(d) be the third derivative of -2*d**7/315 + d**5/45 - 6*d**2. What is p in l(p) = 0?
-1, 0, 1
Let a be -1 - (-69)/21 - (3 + -1). Factor a*w**2 + 2/7*w + 0.
2*w*(w + 1)/7
Let d be 10/(-25) + (-1)/(-15) + 1. Solve 2/3*m**2 + 2/3*m - d - 2/3*m**3 = 0 for m.
-1, 1
Suppose 0*k + 4 = 2*o + 2*k, -2*k - 20 = -4*o. Let f = 6 + -3. Factor -9*u**4 - 3*u**f + o*u - 2*u + 2*u + 14*u**2 - 6*u**2.
-u*(u - 1)*(3*u + 2)**2
Let z = 1/16 + 13/48. Let f(l) be the first derivative of -2/3*l + 1/6*l**4 - z*l**2 - 1 + 2/9*l**3. Suppose f(r) = 0. Calculate r.
-1, 1
Let m(f) be the second derivative of 1/6*f**2 - 1/9*f**3 + 1/36*f**4 + 3*f + 0. Factor m(q).
(q - 1)**2/3
Factor -1/5*s**2 + 0 + 2/5*s - 1/5*s**3.
-s*(s - 1)*(s + 2)/5
Let p(z) be the second derivative of 0*z**2 + 0 - 2/3*z**3 + 1/6*z**4 + 1/10*z**5 + 2*z. Let p(i) = 0. Calculate i.
-2, 0, 1
Let x(h) be the second derivative of -h**5/20 - h**4/12 - h**2/2 + h. Let b(l) = l**3 + l**2 + l + 3. Let t(v) = b(v) + 2*x(v). Factor t(k).
-(k - 1)*(k + 1)**2
Find d, given that 5*d**2 - 9*d**2 + 6 - 6*d - 2*d + 6*d**2 = 0.
1, 3
Let g(l) = -l**5 - l**4 - l. Let s(m) = 4*m**5 + 3*m**4 - m**3 + 5*m. Let u(c) = -5*g(c) - s(c). Factor u(p).
p**3*(p + 1)**2
Solve 0 - 4/7*f + 4/7*f**2 = 0 for f.
0, 1
Let i(d) be the third derivative of d**6/780 + d**5/195 + d**4/156 - 15*d**2. Let i(f) = 0. What is f?
-1, 0
Let o(v) be the third derivative of -5*v**8/336 + v**7/7 - v**6/6 - v**5/2 + 25*v**4/24 + v**2. Find m, given that o(m) = 0.
-1, 0, 1, 5
Let x(t) be the first derivative of 0*t**2 - 2/3*t**4 + 4/15*t**5 + 0*t - 9 + 4/9*t**3. Solve x(p) = 0.
0, 1
Let v = 26 - 26. Let k(o) be the first derivative of -2/3*o**2 - 1 + 2/9*o**3 + v*o. Determine b, given that k(b) = 0.
0, 2
Factor 12*h**4 - 2*h**3 + 1226 - 14*h**3 - 1226 + 4*h**2.
4*h**2*(h - 1)*(3*h - 1)
Let o(u) be the first derivative of -5*u**6/6 + 5*u**5 - 45*u**4/4 + 35*u**3/3 - 5*u**2 - 19. Factor o(k).
-5*k*(k - 2)*(k - 1)**3
Suppose -5*x + 3*x = -