*f - 0. Factor 1/2*o + 1/2*o**f + p.
o*(o + 1)/2
Let p(g) be the third derivative of -g**7/2100 + g**5/300 - 2*g**3/3 - 2*g**2. Let a(r) be the first derivative of p(r). Factor a(c).
-2*c*(c - 1)*(c + 1)/5
Let r(g) be the first derivative of 8/7*g + 1/14*g**4 + 0*g**2 - 2/7*g**3 - 4. Factor r(j).
2*(j - 2)**2*(j + 1)/7
Let r(d) be the first derivative of d**5/20 + d**4/16 - d**3/4 - 5*d**2/8 - d/2 + 2. Determine m so that r(m) = 0.
-1, 2
Let x(w) be the first derivative of w**6/42 - w**5/35 - w**4/14 + 62. Factor x(n).
n**3*(n - 2)*(n + 1)/7
Let v be (-2 - (-1)/1) + (6 - 5). Let k(y) be the first derivative of -1/12*y**3 + v*y**2 + 1/4*y - 2. Solve k(j) = 0.
-1, 1
Factor 0 + 0*l**3 + 0*l - 2/5*l**2 + 2/5*l**4.
2*l**2*(l - 1)*(l + 1)/5
Suppose 2*j = -2*j + 12. Suppose 5*t = t - 4*d + 16, -t + 2 = j*d. Determine l so that 0*l + 0 + 0*l**2 - 2/3*l**3 + l**t + 1/3*l**4 = 0.
-1, 0, 2/3
Let p = 8/7 - -5/14. Let s = -22 - -53/2. Find r, given that -9/2*r**4 + 3/2*r - p*r**3 + 0 + s*r**2 = 0.
-1, -1/3, 0, 1
Factor -c**3 + 1/2 - 1/2*c**2 + c.
-(c - 1)*(c + 1)*(2*c + 1)/2
Let a(z) = z**3 + 9*z**2 - 9*z + 14. Let u be ((-1 - -1) + 10)/(-1). Let f be a(u). Factor -4/3*q**f + 0*q + 1/3*q**5 + 5/3*q**3 - 2/3*q**2 + 0.
q**2*(q - 2)*(q - 1)**2/3
Let t be 2/(-5) - 51/(-15). Let g be (-2)/(-4) + (-6)/(-4). Factor 7*w**t + 0*w**4 - w**3 - 8*w - g*w**4.
-2*w*(w - 2)**2*(w + 1)
Let i be (((-8)/1)/(-2))/((-28)/(-6)). Find f, given that 2/7*f**5 + 2/7*f**2 - 2/7*f**4 + 0 + 4/7*f - i*f**3 = 0.
-1, 0, 1, 2
Let s be 1 - 2*2/(-4). Factor -4*x**3 + 3*x**s + 5*x - 4*x - 2*x + x**2.
-x*(2*x - 1)**2
Factor 0 + 2/3*k**2 - 2*k.
2*k*(k - 3)/3
Let x(b) be the first derivative of -b**5/30 + b**3/9 + b - 1. Let l(h) be the first derivative of x(h). Factor l(d).
-2*d*(d - 1)*(d + 1)/3
Let k(y) be the third derivative of y**5/20 - 2*y**3 - 6*y**2. Factor k(m).
3*(m - 2)*(m + 2)
Suppose -2*o = 2*b - 4*o - 74, 3*o + 31 = b. Suppose b = l + l. Find s, given that -2*s**4 + l*s**3 + 21*s**2 + 4 - 20*s - 9*s**4 - 14*s**4 = 0.
-1, 2/5, 1
Let z(f) = -23*f**4 - 2*f**3 - 3*f**2 + 11*f + 17. Let u(m) = -8*m**4 - m**3 - m**2 + 4*m + 6. Let n(g) = 17*u(g) - 6*z(g). Factor n(t).
t*(t - 2)*(t - 1)*(2*t + 1)
Suppose 0 = 4*l + 3*c + 11, 6*c - c + 7 = -l. Let z be 6/(-10) - 2/l. Factor -2/5*x**4 + 2/5*x**2 + 2/5*x - z*x**3 + 0.
-2*x*(x - 1)*(x + 1)**2/5
Let x(c) be the third derivative of c**3 + 0 - 3*c**2 - 3/8*c**4 + 1/20*c**5 + 0*c. Factor x(o).
3*(o - 2)*(o - 1)
Let r(u) be the second derivative of 0*u**2 + 0*u**4 + 1/70*u**7 + 0*u**5 + 1/50*u**6 + 0 + 0*u**3 + 5*u. Factor r(l).
3*l**4*(l + 1)/5
Suppose 8 = -5*x + 28. Let p(u) be the third derivative of 0*u + 2/27*u**3 + 1/270*u**5 + 2*u**2 + 1/36*u**x + 0. Factor p(l).
2*(l + 1)*(l + 2)/9
Let z(i) be the third derivative of i**7/280 - i**6/160 - i**5/80 + i**4/32 + 6*i**2. What is m in z(m) = 0?
-1, 0, 1
Let g(u) be the first derivative of -3*u**5/5 + 3*u**4/4 + 3*u**3 - 3*u**2/2 - 6*u - 2. Factor g(j).
-3*(j - 2)*(j - 1)*(j + 1)**2
Let h be (-5)/30 - (-37)/6. Let g = h + -11. Let x(k) = -k**5 + k**3 - 5*k. Let n(p) = 3*p. Let q(s) = g*n(s) - 3*x(s). Let q(d) = 0. What is d?
-1, 0, 1
Let w(t) be the first derivative of -t**7/1680 - t**6/720 + 5*t**3/3 + 1. Let l(o) be the third derivative of w(o). Determine s so that l(s) = 0.
-1, 0
Let v(y) = -5*y**3 + 243*y**2 - 3840*y + 20477. Let r(s) = 5*s**3 - 242*s**2 + 3840*s - 20478. Let c(d) = 3*r(d) + 2*v(d). What is u in c(u) = 0?
16
Let q be (3 + -6 + 1)*-1. Factor 6/7*m**3 - 22/7*m**q + 24/7*m - 8/7.
2*(m - 2)*(m - 1)*(3*m - 2)/7
Let p(c) be the second derivative of -7*c**6/30 - 3*c**5/20 + 2*c**4/7 - 2*c**3/21 + 15*c. Determine u so that p(u) = 0.
-1, 0, 2/7
Let a(s) be the third derivative of -s**7/40 + 9*s**6/160 - s**5/40 + 4*s**2. Suppose a(g) = 0. What is g?
0, 2/7, 1
Let x(u) = u - 1. Let l(h) = -h**2 - 22*h - 202. Let q(d) = l(d) - 6*x(d). Find c such that q(c) = 0.
-14
Let p(w) be the first derivative of 2*w**5/75 + 7*w**4/60 - 2*w**3/15 - 3*w**2/2 + 1. Let a(j) be the second derivative of p(j). Solve a(g) = 0 for g.
-2, 1/4
Let f(j) be the second derivative of j**6/80 - j**5/80 - j**4/24 + j**3/24 + j**2/16 - 9*j. Suppose f(l) = 0. What is l?
-1, -1/3, 1
Suppose 3*p - 55*t = -59*t, -2*p + 3*t = 0. Factor 0 + p*k - 4/3*k**5 + 0*k**4 + 4/3*k**3 + 0*k**2.
-4*k**3*(k - 1)*(k + 1)/3
Let q(k) = -25*k**2 - 10*k - 4. Let f(x) = 350*x**2 + 140*x + 55. Let d(b) = 4*f(b) + 55*q(b). Find p, given that d(p) = 0.
-2/5, 0
Let k(r) = 4*r**2 - 20. Let x(g) = 3*g**2 + 4*g. Let m be x(-2). Let y(n) = 8*n**2 - 39. Let o(u) = m*y(u) - 7*k(u). Factor o(w).
4*(w - 2)*(w + 2)
Let u(c) be the first derivative of 0*c - 1/2*c**4 + 4 + 0*c**3 + 0*c**2 - 1/3*c**6 - 4/5*c**5. Factor u(i).
-2*i**3*(i + 1)**2
Suppose 0 = -6*u + 24 - 18. Let d(m) be the first derivative of -1/6*m**3 + 0*m**2 - u + 0*m. Factor d(z).
-z**2/2
Let a(h) be the third derivative of 0 + 5*h**2 + 1/12*h**4 + 1/50*h**5 - 2/15*h**3 + 0*h. Factor a(f).
2*(f + 2)*(3*f - 1)/5
Let d(j) be the second derivative of -j**7/336 - j**6/40 - 13*j**5/160 - j**4/8 - j**3/12 - 4*j. Solve d(f) = 0.
-2, -1, 0
Let n = 194 - 189. Let x(d) be the third derivative of 1/2*d**3 + 0*d + 0 + 1/12*d**4 - 1/60*d**n - 4*d**2. Factor x(h).
-(h - 3)*(h + 1)
Let u(m) = 5*m**2 - 25*m - 25. Let p(y) = y**2 - 6*y - 6. Let v be (3/(-6) + 1)*22. Let f be -1 + 0 + v - 1. Let t(k) = f*p(k) - 2*u(k). Factor t(l).
-(l + 2)**2
Suppose -2*w + 27 = 21. Factor 2/9*f**2 + 0 - 2/9*f**w + 0*f.
-2*f**2*(f - 1)/9
Factor 6/11*s**3 + 2/11*s**2 + 0 - 4/11*s.
2*s*(s + 1)*(3*s - 2)/11
Let m(j) be the third derivative of 5*j**8/336 - 3*j**7/14 + 31*j**6/24 - 17*j**5/4 + 25*j**4/3 - 10*j**3 - 14*j**2. Determine o so that m(o) = 0.
1, 2, 3
Let y(p) be the second derivative of -p**4/3 - 2*p**3/3 + 4*p**2 - 23*p. Find i such that y(i) = 0.
-2, 1
Let v(x) be the third derivative of 0*x - 1/120*x**5 - 1/96*x**6 + x**2 + 0*x**4 + 0 + 0*x**3. Factor v(s).
-s**2*(5*s + 2)/4
Let g(b) = b**4 - b**3 - b - 1. Let s(m) = -12*m**3 + 3*m**4 + 0*m**3 + 8*m**2 - 8*m - 10 - m**4. Let l(x) = -10*g(x) + s(x). Solve l(o) = 0 for o.
-1, -1/4, 0, 1
Let z(i) be the third derivative of -i**8/168 + i**7/105 + i**6/60 - i**5/30 - 5*i**2. Factor z(o).
-2*o**2*(o - 1)**2*(o + 1)
Let p be (4/(-14))/(10/(-210)). Let q(h) = -10*h**3 + 14*h**2 - 28*h + 18. Let f(n) = -9*n**3 + 15*n**2 - 28*n + 17. Let a(w) = p*f(w) - 5*q(w). Factor a(v).
-4*(v - 3)*(v - 1)**2
Let n be (3 + 15/(-5))/(-5 + 4). What is l in n*l + 1/3 - 1/3*l**2 = 0?
-1, 1
Suppose j + 0*j - 4 = 0. What is z in -2*z**j + 0*z**4 + 3*z**3 + z**3 - 2*z**2 = 0?
0, 1
Let i be 2*2/2*1. Let z be (-28)/(-6) + 4/(-6). Let -z*x - 3*x**2 - 4 + 0 + 2*x**i = 0. Calculate x.
-2
Let o(u) be the first derivative of u**6/21 + 2*u**5/35 - 3*u**4/14 - 10*u**3/21 - 2*u**2/7 + 17. Determine z so that o(z) = 0.
-1, 0, 2
Let a(g) be the third derivative of -5*g**8/224 + g**7/21 + g**6/24 - g**5/6 + 5*g**4/48 + 16*g**2. Suppose a(o) = 0. What is o?
-1, 0, 1/3, 1
Let q(n) be the first derivative of -n**8/3360 - n**7/420 - n**6/144 - n**5/120 - 7*n**3/3 - 5. Let a(b) be the third derivative of q(b). Factor a(y).
-y*(y + 1)**2*(y + 2)/2
Let f be (-1 - 801)*(-1)/(-6). Let b = f + 135. Factor 1/3*w**2 + b*w + 4/3.
(w + 2)**2/3
Factor -2/5*q**5 - 6/5*q**2 - 2/5*q**4 + 0*q + 2*q**3 + 0.
-2*q**2*(q - 1)**2*(q + 3)/5
Let f(g) be the second derivative of g**4/4 - 3*g**3/2 - 6*g. Factor f(i).
3*i*(i - 3)
Let q = -12 - -25. Suppose 4*c + 1 - q = 0. Suppose 6*t**2 + 6/7*t - 4/7 + 50/7*t**c + 18/7*t**4 = 0. What is t?
-1, 2/9
Let k(d) be the third derivative of -5*d**8/336 + d**6/12 - 5*d**4/24 + 6*d**2. Suppose k(j) = 0. What is j?
-1, 0, 1
Factor -5*q**3 - 4 + 2 - 9*q**2 - q**4 - 7*q + 0*q**4.
-(q + 1)**3*(q + 2)
Let y(i) be the second derivative of i**4/6 - i**3/2 + 2*i**2 + 4*i. Let b(h) = -h**2 + 2*h - 3. Let z(q) = -3*b(q) - 2*y(q). Factor z(m).
-(m - 1)*(m + 1)
Factor -12*m**5 + 9*m**3 - 25*m**4 - 8*m**3 - 9*m**3 + 5*m**4.
-4*m**3*(m + 1)*(3*m + 2)
Suppose -7 = -5*c - 2. Let m be 2/(-8)*(c + -2). Factor 1/2*v**2 + 1/4*v + m*v**3 + 0.
v*(v + 1)**2/4
Let y(w) = 4*w**3 + 20*w**2 - 5*w - 23. Let j be y(-5). Factor -2/5*n**j - 8/5 + 8/5*n.
-2*(n - 2)**2/5
Let r(z) be the first derivative of 1/15*z**3 -