3*t**3 + 3 - 3 + t.
t*(t + 1)**3
Let m(b) be the third derivative of b**6/300 - b**5/75 - b**4/15 + 8*b**3/15 + 11*b**2. Factor m(p).
2*(p - 2)**2*(p + 2)/5
Suppose 2*o + 0*o = 6. Factor 0*c + 0 - c**o + 1/3*c**2 + 2/3*c**4.
c**2*(c - 1)*(2*c - 1)/3
Let m(v) be the first derivative of -v**6/135 - v**5/45 - v**4/54 + 3*v + 1. Let j(x) be the first derivative of m(x). Determine o so that j(o) = 0.
-1, 0
Let q(v) = 4*v**4 - 123*v**3 + 1541*v**2 - 8192*v + 16389. Let f(i) = -4*i**4 + 124*i**3 - 1540*i**2 + 8192*i - 16388. Let l(h) = 5*f(h) + 4*q(h). Factor l(b).
-4*(b - 8)**4
Let h = -171/25 - -8213/1200. Let p(z) be the third derivative of -1/96*z**4 - h*z**5 + 0*z - z**2 + 1/480*z**6 + 1/24*z**3 + 0. Factor p(x).
(x - 1)**2*(x + 1)/4
Let j(x) = x**2 - 6*x - 2. Let f be j(6). Let z(s) = s**3 + 2*s**2 + 2. Let g be z(f). Factor -2*v - v**4 + 4*v**4 + 8*v**2 - 10*v**3 - v**2 + g*v**3.
v*(v - 1)**2*(3*v - 2)
Find i, given that -12*i + 36*i**2 - 31*i**4 - 27*i**3 + 14*i**4 + 11*i**4 + 9*i**5 = 0.
-2, 0, 2/3, 1
Let y(w) be the third derivative of 0*w - w**2 + 1/1800*w**6 - 1/200*w**5 + 1/6*w**3 + 1/60*w**4 + 0. Let t(x) be the first derivative of y(x). Solve t(p) = 0.
1, 2
Let h(v) be the first derivative of -9*v**4/4 - 8*v**3 - 9*v**2/2 + 6*v - 39. Factor h(q).
-3*(q + 1)*(q + 2)*(3*q - 1)
Suppose -4*s + 14 = -5*w, 0 = s + 5*w + 9. Let n be s - (3 + 3)/(-3). Factor -3/2*f**2 - 1/2 + 3/2*f + 1/2*f**n.
(f - 1)**3/2
Let z(x) = -x**3 + 5*x**2 - 2*x - 1. Let a be z(3). Let m = a + -7. Factor 0 + 0*y**m + 4/7*y**3 - 2/7*y - 2/7*y**5 + 0*y**2.
-2*y*(y - 1)**2*(y + 1)**2/7
Determine m so that -3/5*m**3 - 3/5*m**4 + 18/5*m**2 + 0*m + 0 = 0.
-3, 0, 2
Suppose 5*u - 17 = -2. Let 9*b**2 - 4*b**2 + 2*b**3 - 2*b - 8*b**4 + u*b**2 = 0. Calculate b.
-1, 0, 1/4, 1
Let f = -723/5 - -9409/65. Find x, given that -4/13*x**2 + 0 + 4/13*x**4 - 2/13*x + f*x**5 + 0*x**3 = 0.
-1, 0, 1
Let m(z) be the first derivative of 2*z**5/45 - z**4/6 + 2*z**3/9 - z**2/9 - 16. Find d such that m(d) = 0.
0, 1
Suppose -w = 2*w + 5*m + 79, -77 = 4*w + m. Let p be ((-36)/(-135))/((-4)/w). What is d in -3/5*d**2 - 3/5*d + p = 0?
-2, 1
Let v be ((-9)/12)/(2/24). Let c = -7 - v. Factor 5*n**2 + 2*n + 2*n**4 + n**c + 7*n**3 - n**3.
2*n*(n + 1)**3
What is t in t**5 - 5*t**4 - 4*t**5 - 4*t**4 - 2*t**3 - 4*t**5 = 0?
-1, -2/7, 0
Let a(j) be the first derivative of j**4 + j**3 - 25*j**2/2 + 6*j + 27. Factor a(x).
(x - 2)*(x + 3)*(4*x - 1)
Suppose 0*h = 2*h - 4. Suppose w + 13 = 2*f, 8*w + 45 = 5*f + 3*w. Suppose d**3 + f*d**2 + h*d + 2*d**2 - 3*d**2 = 0. Calculate d.
-2, -1, 0
Suppose 2*o + 2 = 3*o. Factor 4*n - 4*n - 9*n**o + 3*n.
-3*n*(3*n - 1)
Let h(i) be the second derivative of i**6/6 - i**5/2 + 5*i**4/12 - 5*i. Factor h(g).
5*g**2*(g - 1)**2
Let a(b) be the third derivative of b**6/140 - b**5/105 - b**4/28 + 2*b**3/21 + 10*b**2. Suppose a(m) = 0. Calculate m.
-1, 2/3, 1
Let s(i) be the third derivative of i**6/540 + i**3/3 + 3*i**2. Let q(f) be the first derivative of s(f). Factor q(r).
2*r**2/3
Let t(n) be the third derivative of n**7/1365 - n**6/195 - n**5/390 + n**4/39 - 2*n**2 - 5. Factor t(x).
2*x*(x - 4)*(x - 1)*(x + 1)/13
Suppose 3*j - 4 = -10. Let g = -2 - j. Suppose -2/3*i**2 - 1/3*i**3 - 1/3*i + g = 0. Calculate i.
-1, 0
What is b in 4/5 - 2/15*b + 2/15*b**3 + 2/15*b**4 - 14/15*b**2 = 0?
-3, -1, 1, 2
Let s(h) be the third derivative of 0 + 1/42*h**5 + 0*h + 0*h**3 - 1/42*h**4 - 1/140*h**6 + 1/1176*h**8 + 5*h**2 - 1/735*h**7. Determine n so that s(n) = 0.
-2, 0, 1
Let y(l) be the third derivative of l**8/672 - 17*l**7/2100 + l**6/75 - l**5/150 - 21*l**2. Solve y(c) = 0.
0, 2/5, 1, 2
Suppose t - 27 = -5*s, -3*t - s = 2*t - 39. Suppose 0 = t*y - 2*y. Factor 0*a - 2/7*a**2 + y + 4/7*a**3 - 2/7*a**4.
-2*a**2*(a - 1)**2/7
Suppose 0*n + 12 = 3*n. Let d(j) be the first derivative of 1 + 1/18*j**6 + 1/9*j**3 - 1/12*j**n - 1/15*j**5 + 0*j + 0*j**2. Determine r, given that d(r) = 0.
-1, 0, 1
Let l(r) be the third derivative of -r**6/30 + 2*r**5/15 - r**4/6 + 3*r**2. Let l(g) = 0. What is g?
0, 1
Let t = -21 - -26. Let s(x) be the third derivative of 0 + 1/120*x**4 + 1/300*x**t + 0*x**3 - 2*x**2 + 0*x. Factor s(b).
b*(b + 1)/5
Suppose 0 = 3*n + 7 - 13. Find s, given that -5*s**3 + n*s**3 + 4*s**3 - 2*s**3 = 0.
0
Let z(s) be the first derivative of s**9/4536 + s**8/1260 - s**6/270 - s**5/180 - s**3/3 - 2. Let n(i) be the third derivative of z(i). Factor n(o).
2*o*(o - 1)*(o + 1)**3/3
Factor 3*x**5 - 3*x**5 + 2*x**3 - 6*x**3 + 4*x**5.
4*x**3*(x - 1)*(x + 1)
Let a be (-11)/33 - (2 - (-132)/(-45)). Factor 0 - a*n**2 + 3/5*n**4 + 1/5*n**3 - 1/5*n.
n*(n - 1)*(n + 1)*(3*n + 1)/5
Let p be (-3)/6*-4 - 11/22. Suppose 0 + 1/2*t + 1/2*t**4 + 3/2*t**2 + p*t**3 = 0. What is t?
-1, 0
Let p(o) be the first derivative of 1/3*o**3 - 1 + o + 3/4*o**4 - 3/2*o**2 - 2/5*o**5. Determine s so that p(s) = 0.
-1, 1/2, 1
Let i(h) be the second derivative of h**6/45 - h**5/6 + 4*h**4/9 - 4*h**3/9 + 4*h. Suppose i(y) = 0. Calculate y.
0, 1, 2
Find a, given that a**3 + 7*a**2 - 4*a**3 + 3*a**5 - 6*a**2 - a**4 = 0.
-1, 0, 1/3, 1
Let t(g) be the third derivative of g**7/630 + g**6/90 + g**5/60 - g**4/18 - 2*g**3/9 + 19*g**2. Suppose t(o) = 0. Calculate o.
-2, -1, 1
Let w(h) = -h**2 + 9. Let i be w(0). Let x = -7 + i. Determine t, given that -2/11*t + 10/11*t**x + 6/11*t**4 - 14/11*t**3 + 0 = 0.
0, 1/3, 1
Suppose 9*r = 8*r + 2. Factor -r*o**3 + 0 - 4/3*o**2 + 0*o - 2/3*o**4.
-2*o**2*(o + 1)*(o + 2)/3
Let s(h) = h**2 - h. Let u(p) = 8*p**2 - 8*p + 4. Let o(z) = 20*s(z) - 2*u(z). Factor o(v).
4*(v - 2)*(v + 1)
Let w(g) be the first derivative of g**9/18144 - g**8/10080 - g**7/5040 + g**6/2160 + 2*g**3/3 - 7. Let z(t) be the third derivative of w(t). Factor z(i).
i**2*(i - 1)**2*(i + 1)/6
Let j(o) be the first derivative of 0*o + 0*o**3 + 3/2*o**2 - 4 - 3/4*o**4. Factor j(g).
-3*g*(g - 1)*(g + 1)
Let a(y) be the third derivative of -y**8/1344 + y**6/480 - 10*y**2. Factor a(g).
-g**3*(g - 1)*(g + 1)/4
Let j(n) be the first derivative of n**6/1440 - n**5/160 + n**4/48 + n**3/3 - 4. Let x(w) be the third derivative of j(w). Factor x(t).
(t - 2)*(t - 1)/4
Suppose 1/2 - 1/4*i - 1/4*i**2 = 0. Calculate i.
-2, 1
Let r be (-25 - -22)/((-2)/7). Find j such that 0*j - 3*j**4 + 3*j**2 - r*j**5 + 0 + 21/2*j**3 = 0.
-1, -2/7, 0, 1
Let q be (-4)/(-8)*6/9. Let v(g) be the first derivative of 3 - g**2 + g + q*g**3. Let v(f) = 0. Calculate f.
1
Suppose 36 = -3*l + 12. Let j = -5 - l. What is a in -4*a**2 + 11*a**2 + 0*a**j - 2*a - 8*a**3 + 3*a**4 = 0?
0, 2/3, 1
Factor 0 - 3/2*a**3 - 9*a - 21/2*a**2.
-3*a*(a + 1)*(a + 6)/2
Let h(w) be the third derivative of -w**8/10080 - w**7/1260 - w**6/540 - w**4/8 - w**2. Let n(f) be the second derivative of h(f). Factor n(c).
-2*c*(c + 1)*(c + 2)/3
Let g(w) be the first derivative of w**5/20 - w**4/6 + w**3/6 - 3*w + 1. Let k(s) be the first derivative of g(s). Factor k(b).
b*(b - 1)**2
Let s(m) be the third derivative of 0*m - 1/1050*m**7 + 0 + 1/120*m**6 - 5*m**2 - 3/100*m**5 - 1/15*m**3 + 7/120*m**4. Factor s(j).
-(j - 2)*(j - 1)**3/5
Let l be (-10)/(-2)*(1 - 0). Let d(g) = -6*g**2 - 6*g - 5. Let k(m) = -7*m**2 - 7*m - 6. Let p(a) = l*k(a) - 6*d(a). Solve p(s) = 0.
-1, 0
Suppose 4/9*h**2 + 0*h + 2/9*h**3 + 0 = 0. What is h?
-2, 0
Solve -k - 1/2*k**2 + 0 + 1/2*k**4 + k**3 = 0.
-2, -1, 0, 1
Let x(k) be the second derivative of -k**6/105 - k**5/35 + k**4/14 + 4*k**3/21 - 4*k**2/7 - 27*k. Determine t so that x(t) = 0.
-2, 1
Let z(y) = 3*y - 10. Let q be 38/8 - (-13)/52. Let o be z(q). Suppose 2/7*t + 12/7*t**3 + 8/7*t**4 + 8/7*t**2 + 2/7*t**o + 0 = 0. Calculate t.
-1, 0
Factor 48*k + 20*k**2 - 88*k - 15*k**2.
5*k*(k - 8)
Let k(u) be the third derivative of u**6/420 + u**5/210 - u**4/84 - u**3/21 + 7*u**2. Factor k(p).
2*(p - 1)*(p + 1)**2/7
Suppose a - 3 + 5 = 0. Let u be a - -3*(-8)/(-6). Factor -2*j + 3 + 1 - 4*j + u*j**2.
2*(j - 2)*(j - 1)
Let h be (31/2 - -1)/(-9). Let o = h + 5/2. Suppose 0 + o*i**3 + 4/3*i + 2*i**2 = 0. What is i?
-2, -1, 0
Let l(i) be the second derivative of 0*i**2 - 1/18*i**4 + 0*i**5 - i - 2/27*i**3 + 1/135*i**6 + 0. Let l(r) = 0. Calculate r.
-1, 0, 2
Let y(n) = -8*n**2 - 8*n - 5. Let o(r) = 9*r**2 + 9*r + 6. Let v(f) = 5*o(f) + 6*y(f). Factor v(t).
-3*t*(t + 1)
Let a(k) be the thi