. Let d(p) = -2*f(p) - 5*m(p). Let r be d(-7). Solve -2*n**2 + n**3 + 2*n + 0*n**r - n = 0.
0, 1
Find r, given that 2*r**2 + 0*r**2 + 6*r**4 - 6*r**3 + 0*r + 0*r - 2*r**5 = 0.
0, 1
Let r(x) be the first derivative of -1/12*x**4 - 1/2*x**2 - 3*x - 1 + 1/3*x**3. Let n(o) be the first derivative of r(o). Factor n(z).
-(z - 1)**2
Let c = 16 + -13. Let k(z) be the third derivative of -2*z**2 - 1/270*z**5 - 1/108*z**4 + 0*z + 1/27*z**c + 1/540*z**6 + 0. Factor k(j).
2*(j - 1)**2*(j + 1)/9
Suppose 4*a - 2*q - 10 + 4 = 0, -4*q = -2*a. Factor 0 + 0*x + 1/2*x**3 - x**a.
x**2*(x - 2)/2
Determine k, given that -6/5*k**4 + 0*k**3 - 2/5*k**5 + 0*k + 0 + 8/5*k**2 = 0.
-2, 0, 1
Let b(f) be the first derivative of -f**3/6 + 3*f**2/4 + 1. Factor b(s).
-s*(s - 3)/2
Let x(v) be the second derivative of 0 + 0*v**2 + 1/60*v**5 + 5*v + 1/18*v**4 + 1/18*v**3. Find h, given that x(h) = 0.
-1, 0
Let o(k) be the third derivative of -k**5/540 - 27*k**2. Let o(z) = 0. Calculate z.
0
Let h = -8 - -10. Factor -3*q**3 + 2*q**3 - q**3 + 4*q**h - 2*q.
-2*q*(q - 1)**2
Let j(i) = -i**3 + 8*i**2 - 2*i + 16. Let f be j(8). Let 1/2*d + 3/2*d**3 + f + 3/2*d**2 + 1/2*d**4 = 0. What is d?
-1, 0
Let d(p) be the first derivative of -p**4/6 + 10*p**3/9 - 8*p**2/3 + 8*p/3 + 7. Suppose d(i) = 0. Calculate i.
1, 2
Let n(x) be the first derivative of 0*x + 0*x**3 + 1/20*x**4 - 1/30*x**6 + 5 + 0*x**2 + 0*x**5. Let n(a) = 0. Calculate a.
-1, 0, 1
Let r(p) be the third derivative of 5*p**6/24 - 13*p**5/12 - 5*p**4/4 + 22*p**2. Factor r(z).
5*z*(z - 3)*(5*z + 2)
Let t(n) be the first derivative of 8*n**6/9 - 8*n**5/3 - 23*n**4/12 + 61*n**3/9 + 16*n**2/3 + 4*n/3 + 10. Find q, given that t(q) = 0.
-1, -1/4, 2
Suppose -5*r + 37 = 3*u, 3*r - 2 = 4*u - 3. Suppose u*h + 16 = g, -2*g + 5*h = 3*h - 14. Factor -2*y**3 + 1 - 1 + 0 - y**2 - y**g.
-y**2*(y + 1)**2
Let g(k) be the second derivative of -k**10/75600 + k**9/37800 + k**8/16800 - k**7/6300 + k**4/4 + 3*k. Let c(q) be the third derivative of g(q). Factor c(b).
-2*b**2*(b - 1)**2*(b + 1)/5
Suppose 4*o + f - 23 = 0, -4*f - 1 = o - 3. Let p = o - 3. Find i such that -i**2 - i - p*i - i**2 - 2 = 0.
-1
Suppose 0*w = -3*w + 48. Suppose 0 = 3*c - 8*c - x + w, -c = -4*x - 20. Factor -c*p**2 - 2*p**5 + 0*p**5 + 2*p + 3*p**4 + p**4.
-2*p*(p - 1)**3*(p + 1)
Suppose -2*p = -z - 11 + 29, -48 = -4*z + 2*p. Let m be (2 + -3)/((-1)/3). Let -z*w**3 + w**2 - 4 - m*w**2 + 4*w - 2*w**4 - 18*w - 16*w**2 = 0. Calculate w.
-2, -1
Let x = 11 - 1. Let v = x - 7. Factor -v*f**3 + 2*f**3 + 2*f**3 + f**3.
2*f**3
Let v(u) be the first derivative of u**4/4 + 7*u**3/3 + 5*u**2/2 - 6*u - 1. Let j be v(-6). What is c in -2*c - 2*c + 2*c**2 + j*c = 0?
0, 2
Suppose -y - y - 1666 = 0. Let t = 2543/3 + y. Factor -10/3*g**3 + 16/3 + t*g**2 - 56/3*g.
-2*(g - 2)**2*(5*g - 2)/3
Let s(p) be the second derivative of -p**5/4 + 5*p**4/4 + p. Factor s(o).
-5*o**2*(o - 3)
Factor 219*g**2 + 4*g**5 - 112*g**2 - 107*g**2 + 8*g**4.
4*g**4*(g + 2)
Let r(y) be the first derivative of y**6/90 - y**5/60 - y**4/36 + y**3/18 - 2*y + 4. Let j(h) be the first derivative of r(h). What is z in j(z) = 0?
-1, 0, 1
Suppose 13 = b + 5*d, -2*b + 3*b - 2*d - 6 = 0. Let u be -3 + (26/b - 0). Determine j, given that u*j**2 - 1/2*j + 1/4 = 0.
1
Suppose 5*x = 2*a - 2, -2*x = 10*a - 5*a - 5. Factor -2/5*d**3 + 4/5*d**2 - 2/5*d + x.
-2*d*(d - 1)**2/5
Suppose -8 = -c - 5*l - 4, 2*c = 5*l - 67. Let t = -187/9 - c. Factor -4/9*j - 2/9*j**2 - t.
-2*(j + 1)**2/9
Let c(x) = 2*x - 14. Let y be c(8). Factor -2/9*l**y + 2/9*l**3 + 2/9 - 2/9*l.
2*(l - 1)**2*(l + 1)/9
Let p = 64 + -319/5. Factor -k - p*k**3 + 4/5*k**2 + 2/5.
-(k - 2)*(k - 1)**2/5
Let v(m) = -5*m**4 - 7*m**3 + m**2 - 3. Let f(p) = 4*p**4 + 6*p**3 + 2. Let b(k) = 3*f(k) + 2*v(k). Factor b(z).
2*z**2*(z + 1)**2
Suppose 0*l = 2*l + 54. Let u = 27 + l. Factor 2/3*i**4 + u - 2/3*i**3 + 0*i + 2/3*i**5 - 2/3*i**2.
2*i**2*(i - 1)*(i + 1)**2/3
Let m be 19049/77 + 18/99. Let j = -247 + m. Suppose -2/7*z**3 - 2/7*z - j*z**2 + 0 = 0. What is z?
-1, 0
Let n = 1/16 - -1/16. Let a(r) be the first derivative of 0*r**3 + 1/8*r**4 + 0*r - 1/24*r**6 - 2 - n*r**2 + 0*r**5. Determine h so that a(h) = 0.
-1, 0, 1
Let l(n) be the second derivative of -n**6/195 - n**5/130 + n**4/39 - n. Factor l(y).
-2*y**2*(y - 1)*(y + 2)/13
Factor -2/3*d**2 - 2/3*d**5 + 0 + 0*d + 2/3*d**3 + 2/3*d**4.
-2*d**2*(d - 1)**2*(d + 1)/3
Let o(d) = -d - 7. Let x be o(-9). Solve -4*y**x - 2*y**3 - y**2 + 0*y**2 + 7*y**2 + 4*y = 0 for y.
-1, 0, 2
Let g(w) be the first derivative of -1 + w - 4/5*w**2 + 4/15*w**3 - 1/30*w**4. Let t(h) be the first derivative of g(h). Factor t(q).
-2*(q - 2)**2/5
Let z(y) = -5*y**4 - 4*y**3 + 7*y**2 + 2*y + 2. Let t(i) = -14*i**4 - 13*i**3 + 21*i**2 + 6*i + 7. Let a(w) = 2*t(w) - 7*z(w). Factor a(l).
l*(l - 1)*(l + 1)*(7*l + 2)
Factor 28*b**2 - 22*b**4 + 28*b**3 + 4*b**2 + 2*b**4 - 21*b + 5*b.
-4*b*(b - 2)*(b + 1)*(5*b - 2)
Let b be 10/(300/(-9))*-10. Suppose 4/13*n + 0 - 2/13*n**2 - 2/13*n**b = 0. What is n?
-2, 0, 1
Let m = 1 - 3. Let s be ((-17)/102)/(m/8). Factor -2/3*l - 1/6*l**4 + 1/3*l**3 + 1/2*l**2 - s.
-(l - 2)**2*(l + 1)**2/6
Determine d, given that -4/3*d**2 + 2/3*d + 4/3 - 2/3*d**3 = 0.
-2, -1, 1
Let m(v) = -v + 2. Let q be m(2). Factor -6*b**3 + 5*b**3 + q*b**3.
-b**3
Let p(f) be the first derivative of 4*f**5/5 + 4*f**4 + 20*f**3/3 + 4*f**2 + 2. Determine x so that p(x) = 0.
-2, -1, 0
Let n(x) = -x**3 - x**2 + 4*x. Let o be n(-3). Suppose -3*u + o*u**5 - 4*u**5 + u**5 + 6*u**4 - 6*u**2 = 0. What is u?
-1, 0, 1
Let u(v) = 6*v**2 + 4*v - 2. Let i(z) be the second derivative of 1/12*z**4 + 1/6*z**3 + 0*z**2 + 4*z + 0. Let m(l) = 4*i(l) - u(l). Solve m(s) = 0 for s.
-1, 1
Let j(y) be the first derivative of 5*y**5/3 - 95*y**4/12 + 38*y**3/3 - 26*y**2/3 + 8*y/3 - 2. Factor j(i).
(i - 2)*(i - 1)*(5*i - 2)**2/3
Let h be -1*10/(-12)*48/60. Let x be (2/(-9))/((-3)/9). Let x*k**2 + h*k + 0 = 0. Calculate k.
-1, 0
Let i be (-10)/(-15)*(-3)/2. Let y be i - -7 - (0 + 0). What is f in -y*f**4 - 2*f**5 + 2*f**4 + 4*f**3 + 2*f**4 = 0?
-2, 0, 1
Let i(m) = m**3 + 1. Let b(y) = -15*y**3 - 3*y**2 + 3*y - 9. Let t(z) = -b(z) - 12*i(z). Factor t(u).
3*(u - 1)*(u + 1)**2
Let w be (3 + 44/(-12))/(-2). Let s(p) be the first derivative of 2 + 1/9*p**3 + 0*p - w*p**2. Factor s(y).
y*(y - 2)/3
Let n be 2 - 2*1/(-2). Suppose 9 = -5*x + n*d, 3*x - 5*d + 15 = x. Suppose -1/3*s**4 + 0*s**2 + 0*s - 1/3*s**3 + x = 0. Calculate s.
-1, 0
Let r = -7 - -12. Solve 0*t**4 + 2*t**4 - r*t**4 - 3*t**2 + 6*t**2 = 0 for t.
-1, 0, 1
Suppose -2*i = -0*i - 5*b - 15, -3*b = -2*i + 9. Factor -3/2*p**2 + i + 1/2*p + 3/2*p**3 - 1/2*p**4.
-p*(p - 1)**3/2
Let c(d) = -3*d**3 + 5*d**2 - 7*d + 5. Let l(m) be the third derivative of m**6/30 - m**5/10 + m**4/3 - m**3 + m**2. Let b(a) = 6*c(a) + 5*l(a). Factor b(w).
2*w*(w - 1)*(w + 1)
Let d = 20/69 - -1/23. Let p(c) be the first derivative of -d*c**2 + 2 + 0*c + 2/9*c**3. Let p(g) = 0. What is g?
0, 1
Let y = 25 + -149/6. Let o(u) be the second derivative of -u + 0 + 1/10*u**5 + 0*u**3 + y*u**4 + 0*u**2. Suppose o(a) = 0. What is a?
-1, 0
Let n(i) be the third derivative of -7*i**6/120 + i**5/30 + 7*i**4/24 - i**3/3 + 12*i**2. Factor n(y).
-(y - 1)*(y + 1)*(7*y - 2)
Let c(w) = -6*w**2 - 3*w - 3. Let g(f) = -f**2 - f - 1. Let y(s) = 4*c(s) - 28*g(s). What is h in y(h) = 0?
-2
Let w(k) = 9*k**2 - k + 3. Let l(r) = -5*r**2 - 2. Let a(q) = 11*l(q) + 6*w(q). Let b be a(-4). Factor 3/2*z**b - 3/2*z - z**2 - 1/2 + z**3 + 1/2*z**5.
(z - 1)*(z + 1)**4/2
Suppose 15 - 5 = 5*f. Factor 0 + 1/3*w**f + 0*w.
w**2/3
Let u(t) be the third derivative of -t**7/2520 + t**6/360 - t**5/120 + t**4/24 - t**2. Let z(c) be the second derivative of u(c). Factor z(n).
-(n - 1)**2
Factor 0*h**2 + 0*h - 1/2*h**5 + 0*h**3 + 0 + h**4.
-h**4*(h - 2)/2
Let f(k) be the second derivative of -1/3*k**4 + 4*k**2 + 9*k + 0 + 2/3*k**3. Find b such that f(b) = 0.
-1, 2
Suppose -3*p = -8*p. Let u(h) be the third derivative of 0*h**5 + 0 + 0*h**6 - 1/504*h**8 + p*h**4 - 1/315*h**7 - h**2 + 0*h + 0*h**3. Factor u(w).
-2*w**4*(w + 1)/3
Suppose -j + 4*j - 18 = 0. Let p be ((-2)/j)/(6/(-6)). Suppose -p*c**4 - 1/6*c**5 + 1/3*c**2 + 0 + 0*c**3 + 1/6*c = 0. Calculate c.
-1, 0, 1
Let j = 16 + -12. Factor -3*n**2 + 4*n**2 + 