(l) be the third derivative of l**5/100 - l**3/10 + 4*l**2. Factor a(k).
3*(k - 1)*(k + 1)/5
Find x such that 0 + 2/3*x**2 + 0*x + 0*x**3 - 2/3*x**4 = 0.
-1, 0, 1
Let i(h) be the first derivative of -h**6/33 - 4*h**5/55 + 3*h**4/22 - 5. Factor i(l).
-2*l**3*(l - 1)*(l + 3)/11
Let z(x) be the first derivative of 4*x**5/5 - 6*x**4 + 12*x**3 - 8*x**2 - 23. Solve z(v) = 0.
0, 1, 4
Let v(h) be the second derivative of 5*h**6/7 - 4*h**5/7 - 4*h**4 - 32*h**3/7 - 16*h**2/7 - 3*h. Determine n so that v(n) = 0.
-2/3, -2/5, 2
Suppose 3*b = -n + b + 10, 0 = -3*n + 3*b + 12. Let w(c) be the third derivative of 2/3*c**3 + 7/60*c**n - 1/15*c**5 - 7/12*c**4 - c**2 + 0 + 0*c. Factor w(m).
2*(m - 1)*(m + 1)*(7*m - 2)
Let n(p) = -2*p**4 + 5*p**3 - 4*p**2 + p. Let z(t) = t**4 - 4*t**3 + 4*t**2 - 1. Let w(u) = -2*n(u) - 3*z(u). Factor w(j).
(j - 1)**2*(j + 1)*(j + 3)
Let n = 2 + 3. Suppose -4 = -n*o - 3*k, -2*k = -o + 3*o. Factor 1/2*c**o + 1/4*c**3 + 0 + 0*c.
c**2*(c + 2)/4
Suppose 2*i = 3*g - 25, -5*i = -5*g + 4*g + 17. Let p = g - 29/5. Determine j, given that 2/5*j**5 + 6/5*j**3 + p*j**4 + 2/5*j**2 + 0*j + 0 = 0.
-1, 0
Let r = -3 + 6. Suppose 0 = -4*s + 11 - 3. Factor x**s + 2*x**3 - 6*x**r - 3*x**2.
-2*x**2*(2*x + 1)
Let c be ((-282)/90 - -3)/((-2)/3). Let k(l) be the first derivative of 1/3*l**3 + 1/3*l**6 - c*l**5 + 0*l - 3/4*l**4 - 2 + 1/2*l**2. Factor k(t).
t*(t - 1)**2*(t + 1)*(2*t + 1)
Let q(r) = -r**3 + r**2 + 1. Let x(n) = -n**3 - 17*n**2 - 46*n - 21. Let t(c) = -3*q(c) + x(c). Let t(a) = 0. What is a?
-1, 12
Determine k, given that 9/2 - 21/4*k**2 - 57/4*k = 0.
-3, 2/7
Let s(a) = -11*a**2 - 6*a - 22. Let k(t) = -t**2 - 2. Let f(i) = 18*k(i) - 2*s(i). Suppose f(o) = 0. What is o?
-2, -1
Let s(g) be the third derivative of -g**10/90720 + g**8/10080 - g**6/2160 + 7*g**4/24 + 3*g**2. Let v(j) be the second derivative of s(j). Solve v(b) = 0 for b.
-1, 0, 1
Let s = 9 + -6. Determine j so that -s*j**4 + 24*j**4 - 4*j**2 - 8*j**2 - 6*j**5 - 2*j**3 - j**4 = 0.
-2/3, 0, 1, 3
Let 431*o**3 - o - 427*o**3 - 2*o**5 - o = 0. Calculate o.
-1, 0, 1
Let m be (-5 - -1)*(-11)/(-2). Let y = m + 26. Factor 0*d + 0*d**y + 2/3*d**5 + 0*d**2 + 0 - 2/3*d**3.
2*d**3*(d - 1)*(d + 1)/3
Factor 0*d**4 - 2/13*d**5 + 0 + 0*d + 2/13*d**3 + 0*d**2.
-2*d**3*(d - 1)*(d + 1)/13
Let n(l) be the third derivative of l**7/420 - l**6/96 + l**5/240 + l**4/48 - 7*l**2. Factor n(c).
c*(c - 2)*(c - 1)*(2*c + 1)/4
Let d(k) = -k**2 - 3*k + 4. Let n be d(-3). Suppose -5*c - l - 5 = 0, -5*l - 26 + 1 = 0. Factor -2*r - 6*r**3 + 4*r**2 + n*r + c*r.
-2*r*(r - 1)*(3*r + 1)
Let s(w) be the first derivative of -2*w**5/5 + w**4/2 + 4*w**3/3 - 2. Factor s(f).
-2*f**2*(f - 2)*(f + 1)
Factor -x**3 + 68*x + 3*x**4 - 2*x**4 - x**2 - 67*x.
x*(x - 1)**2*(x + 1)
Let t(n) be the third derivative of 0*n**3 + 1/315*n**7 - 1/180*n**6 - 10*n**2 + 1/36*n**4 + 0 + 0*n - 1/90*n**5. Factor t(y).
2*y*(y - 1)**2*(y + 1)/3
Let v(z) be the third derivative of z**6/300 + z**5/150 - z**4/60 - z**3/15 + 8*z**2. Factor v(c).
2*(c - 1)*(c + 1)**2/5
Suppose 9/5*x - 2/5*x**3 + 0 - 4/5*x**4 + 12/5*x**2 + 1/5*x**5 = 0. What is x?
-1, 0, 3
Let w(s) be the first derivative of 2*s**3/57 - 6. Factor w(c).
2*c**2/19
Let b(a) = a**4 - 8*a**3 - 2*a**2 + 2*a - 2. Let m(n) = n**4 - n**3 - n**2 + n - 1. Let h(p) = b(p) - 2*m(p). Solve h(s) = 0.
-6, 0
Let y(f) = 4*f**2 + 4*f + 2. Let l be y(-3). Let -14*m**4 - 17 - 21*m**2 + 2*m**5 - 23*m**2 + 11 + l*m + 36*m**3 = 0. What is m?
1, 3
Let p(i) be the first derivative of 1/10*i**5 - 1/6*i**3 - 2 + 0*i + 0*i**2 - 1/8*i**4 + 1/12*i**6. Determine s so that p(s) = 0.
-1, 0, 1
Let l(j) be the first derivative of -7 + 0*j**3 + 0*j**2 + 0*j**4 - 6/5*j**5 + 0*j - 1/2*j**6. Factor l(y).
-3*y**4*(y + 2)
Let n = -15 - -61/4. Factor 3/4*i**4 + 0*i + 2*i**3 - n + 3/2*i**2.
(i + 1)**3*(3*i - 1)/4
Factor 12*y - 5*y**2 + 2*y**2 + 6*y**2 + 9.
3*(y + 1)*(y + 3)
Let j(d) be the second derivative of -d**10/10080 - d**9/5040 + d**8/1120 - d**4/2 - 4*d. Let v(n) be the third derivative of j(n). Solve v(k) = 0.
-2, 0, 1
Let v(j) = -j**4 + j**3 - j**2 + j + 1. Let i(a) = -a + 0 + a**3 + 0*a + 4 - 5. Let d(n) = -i(n) - v(n). Factor d(f).
f**2*(f - 1)**2
Let i(m) = -11*m**5 - 17*m**4 - 17*m**3 - 5*m**2 + 15*m - 17. Let k(b) = 5*b**5 + 8*b**4 + 8*b**3 + 2*b**2 - 7*b + 8. Let x(s) = 6*i(s) + 13*k(s). Factor x(j).
-(j - 2)*(j - 1)**2*(j + 1)**2
Let m(s) be the first derivative of -8*s**6/21 + 156*s**5/35 - 86*s**4/7 - 256*s**3/21 + 180*s**2/7 + 100*s/7 - 14. Solve m(a) = 0.
-1, -1/4, 1, 5
Let g(f) be the third derivative of -1/60*f**5 + 1/12*f**4 + 0*f**3 + f**2 + 0*f + 0. Factor g(j).
-j*(j - 2)
Factor 3/4*v**2 + 1/4*v**3 + 3/4*v + 1/4.
(v + 1)**3/4
Solve 9/4*t - 1/2 + 7/4*t**4 - 9/4*t**3 - 5/4*t**2 = 0 for t.
-1, 2/7, 1
Let s(c) be the third derivative of -c**5/20 + c**4/4 - c**3/2 - 5*c**2. Factor s(b).
-3*(b - 1)**2
Let q(p) = -p**3 + 11*p**2 - 9*p - 13. Let z be q(10). Let n be ((-2)/4)/(z/102). Find g such that 11*g + 14*g**2 - n*g + 8 - 26*g = 0.
2/7, 2
Let v = -1/8 - -5/8. Find x such that -1/2*x + v*x**3 + 1/2*x**2 - 1/2 = 0.
-1, 1
Let h(j) be the first derivative of j**3 - 9*j**2/2 - 42. What is x in h(x) = 0?
0, 3
Let x(d) = -18*d**4 + 44*d**3 - 32*d**2 + 6*d + 2. Let c(q) = -q**3 + q - 1. Let f(o) = -2*c(o) - x(o). Let f(s) = 0. What is s?
0, 2/3, 1
Let u = 1184/3 - 390. Factor -u*j**2 + 8*j + 8/3.
-2*(j - 2)*(7*j + 2)/3
Factor -13*a**5 - 6*a - a**5 + 15*a**2 - 9*a**3 + 17*a**5 - 3*a**4.
3*a*(a - 1)**3*(a + 2)
Let o = 130 - 128. Solve -1/5*v - 3/5*v**3 - 1/5*v**4 + 0 - 3/5*v**o = 0.
-1, 0
Suppose -z + 1 = -1. Let m**2 - 2*m**4 - m + m**2 + 0*m**z - m**5 + 2*m = 0. Calculate m.
-1, 0, 1
Suppose -4*u - t + 8 = -u, -2*u + 4*t - 4 = 0. Factor 2/7*y - u*y**5 - 4/7 + 52/7*y**4 - 68/7*y**3 + 32/7*y**2.
-2*(y - 1)**4*(7*y + 2)/7
Factor 16/7 - 100/7*x**2 - 36/7*x**3 - 48/7*x.
-4*(x + 1)*(x + 2)*(9*x - 2)/7
Factor 5 + 1 - 6 + 5*v - 4*v**2 + v**3 - 2.
(v - 2)*(v - 1)**2
Suppose -67*m = -71*m + 12. What is i in 1/5*i**4 + 0*i + 0 + 0*i**2 - 1/5*i**m = 0?
0, 1
Let a(z) be the first derivative of -z**3/3 - 9*z**2/2 + 10*z - 3. Let j be a(-10). Suppose j - w**3 - w + 2*w**3 - w**2 + 1 = 0. What is w?
-1, 1
Let f(n) be the second derivative of -4*n + 0*n**2 + 0 - 1/24*n**3 + 0*n**4 + 1/80*n**5. Factor f(c).
c*(c - 1)*(c + 1)/4
Factor 80*y + 37*y**3 + 92*y**2 + 16 - 12*y**3 + 3*y**3.
4*(y + 1)*(y + 2)*(7*y + 2)
Let b(n) be the first derivative of -7*n**4/8 - 5*n**3/6 + n**2/2 - 6. Factor b(x).
-x*(x + 1)*(7*x - 2)/2
Let t = -4/131 - -370/3537. Let f(r) be the first derivative of t*r**3 + 0*r**2 + 0*r + 1 + 2/15*r**5 + 1/27*r**6 + 1/6*r**4. Factor f(h).
2*h**2*(h + 1)**3/9
Let w be 6/(-10) + (-6)/15. Let a be -3*w*(-2)/(-2). Factor -1/2*y**2 + 1/4*y**4 + 0*y**a + 1/4 + 0*y.
(y - 1)**2*(y + 1)**2/4
Solve 4*g**2 - 158*g + 86 + 126*g - 22 = 0 for g.
4
Let p(i) = -i**3 - 15*i**2 - 9*i + 72. Let z be p(-14). Factor 4/7 - 4*q + 7*q**z.
(7*q - 2)**2/7
Suppose -15 = -685*x + 680*x. Suppose -3*z**2 - x*z - 3/4*z**3 + 0 = 0. What is z?
-2, 0
Find h, given that 0 + 6/7*h + 2/7*h**3 - 8/7*h**2 = 0.
0, 1, 3
Let t be (-1 - (-2 - -1)) + 3. Let i be 1/t - 10/(-6). Let -1/4*g**i + g - g**3 + 1/4 = 0. What is g?
-1, -1/4, 1
Factor 5 - 15*d - 5 - 3*d**2 - 18.
-3*(d + 2)*(d + 3)
Let u be (-2)/4*(-24)/4. Let f be u/3 - (-3)/9. Factor 2/3*a**2 + 0*a + f*a**3 + 2/3*a**4 + 0.
2*a**2*(a + 1)**2/3
Let o be (-4)/((0 - -1)/(-1)). Let y be (-2*1)/(-1 - (-5)/15). Factor -g**5 + 0*g**3 - 3*g**o - y*g**3 + g**4 + 2*g**3.
-g**3*(g + 1)**2
What is d in -3*d**2 + d**4 + 5*d**2 + 3*d**3 - 6*d**3 = 0?
0, 1, 2
Suppose -q + 3 = 2*t, 3*q = 5*t + 12 - 36. Factor 0*x + 1/2*x**2 - 1/2*x**t + 0.
-x**2*(x - 1)/2
Let f(r) be the third derivative of r**7/42 + r**6/8 + r**5/12 - 5*r**4/8 - 5*r**3/3 + 27*r**2. Find n such that f(n) = 0.
-2, -1, 1
Let z = 5/7 - 1/21. Solve -2*k + 4/3 + z*k**2 = 0 for k.
1, 2
Let h(x) = -x**4 + 7*x**3 + 11*x**2 + 5*x. Let z = -11 + 17. Let i(d) = 3*d**3 + 6*d**2 + 3*d. Let v(c) = z*h(c) - 11*i(c). Let v(y) = 0. Calculate y.
-1/2, 0, 1
Let i(g) be the third derivative of -g**6/240 - 8*g**2. Factor i(x).
-x**3/2
Suppose 0 = 12*a - 17*a + 55. Suppose 0*n + 5*y - a = -2*n, n + y = 4. Find g such that 1/2*g - 1/2*g**n + 0*g**2 - 1/4 + 1/4*g**4 = 0.
-