ve of 5/24*d**4 + 0 + 2*d**2 + 0*d + 11/6*d**3 + 1/12*d**5. Let n(a) = -4*b(a) - 22*f(a). Factor n(r).
2*r*(r + 1)
Let g(d) be the third derivative of d**7/735 + 11*d**6/840 + 19*d**5/420 + 13*d**4/168 + d**3/14 - 11*d**2. Factor g(p).
(p + 1)**2*(p + 3)*(2*p + 1)/7
Let m(x) = 11*x**3 + 19*x**2 + 24*x - 5. Let f(t) = 39*t**3 + 66*t**2 + 84*t - 18. Let n(y) = 5*f(y) - 18*m(y). Solve n(u) = 0.
-2, 0
Suppose 4*o - 5*d - 33 = 0, -2*o + 1 + 8 = -d. Suppose -2*s = o*s, -s = 4*l. Factor l*x + 0 + 0*x**2 + 1/3*x**3.
x**3/3
Suppose 2*b = 5*r - 47 - 25, -3*r + 2*b + 44 = 0. Factor 35*u**3 + 3*u + 10*u**3 + r*u**2 + 27*u**4 + 7*u**2.
3*u*(u + 1)*(3*u + 1)**2
Let z = -33 - -34. Let d be 0/4 - z/(-2). Determine l so that -1/4*l**2 - 3/4*l - d = 0.
-2, -1
Let q be -2*3*(-7)/21. Suppose -3 = m - q*m. Find h, given that -2/7*h + 0*h**2 + 0 - 2/7*h**5 + 0*h**4 + 4/7*h**m = 0.
-1, 0, 1
Let a be (-2 - -7)*6/(-10). Let h be 0*((-1)/a + 0). Suppose 2/9*m - 2/9*m**2 + h = 0. Calculate m.
0, 1
Let c(q) be the first derivative of q**9/16632 - q**8/4620 + q**6/990 - q**5/660 - 4*q**3/3 - 4. Let y(v) be the third derivative of c(v). Factor y(w).
2*w*(w - 1)**3*(w + 1)/11
Factor 9*n**2 - n**3 - 4*n - 3*n + 6*n - 11*n**2.
-n*(n + 1)**2
Let r(s) be the second derivative of s**8/1680 - s**7/630 - 2*s**4/3 + s. Let v(p) be the third derivative of r(p). Find n such that v(n) = 0.
0, 1
Let 6/5 + 2/5*b**3 + 2*b**2 + 14/5*b = 0. What is b?
-3, -1
Let s = -8 - -11. Determine q so that 5 + s*q - 1 - 2*q**2 - q**2 + 2 = 0.
-1, 2
Let d = 457/6 - 76. Let g(f) be the second derivative of 0 + 1/10*f**5 - d*f**4 + 0*f**2 - 1/3*f**3 + 2*f + 1/15*f**6. Factor g(v).
2*v*(v - 1)*(v + 1)**2
Suppose 0 = 2*s - m - m, 4*m = 12. Factor 3*y**s - y**2 + 2*y**2 - y**4 - 4*y**3 + y.
-y*(y - 1)*(y + 1)**2
Suppose 0 = -3*n - 2*n - 20. Let h(a) = 15*a**3 - 21*a**2 + 15*a - 9. Let x(q) = 7*q**3 - 10*q**2 + 7*q - 4. Let k(p) = n*h(p) + 9*x(p). Factor k(g).
3*g*(g - 1)**2
Let p(n) = -5*n**2 + 2*n - 1. Let a be p(1). Let c be 4/(-10) - a/10. Find i, given that -8/11*i - 90/11*i**3 + 50/11*i**4 + 48/11*i**2 + c = 0.
0, 2/5, 1
Factor 2*m**4 + 0*m**3 - 12 - 2*m**5 + 3*m**3 + 14 - 4*m**2 + m**3 - 2*m.
-2*(m - 1)**3*(m + 1)**2
Factor 167*d - 472*d**2 - 36 - 407*d - 240*d**3 - 15*d**4 - 21*d**4.
-4*(d + 3)**2*(3*d + 1)**2
Let y(w) = -w**4 - w**3 + w + 1. Let h(a) = 5*a**5 + 45*a**4 + 80*a**3 + 60*a**2 + 5*a - 15. Let p(t) = h(t) + 15*y(t). Solve p(i) = 0.
-2, -1, 0
Let m(o) be the first derivative of o**6/18 + 3*o**5/5 + 7*o**4/6 - 2*o**3/9 - 5*o**2/2 - 7*o/3 + 8. Suppose m(r) = 0. What is r?
-7, -1, 1
Find w such that 0*w + 1/9*w**2 + 0 = 0.
0
Find m such that -m**2 + 1/5*m**3 + 8/5*m - 4/5 = 0.
1, 2
Let r(j) be the third derivative of j**8/168 - j**7/21 + j**6/10 + j**5/15 - 7*j**4/12 + j**3 - 23*j**2. Let r(g) = 0. Calculate g.
-1, 1, 3
Let o(d) = -5*d**3 - d**2 + 17*d. Let z(h) = -2*h**3 + 8*h. Let i(k) = 6*o(k) - 13*z(k). Factor i(q).
-2*q*(q + 1)*(2*q + 1)
Suppose 5*j = -5*t + 30, 3*t + j = 4 + 12. Find a, given that -15/2*a**3 + 0 - 6*a**4 - 3/2*a**t - 3*a**2 + 0*a = 0.
-2, -1, 0
Let u(t) be the third derivative of -t**9/60480 + t**8/20160 + t**7/5040 - t**6/720 - t**5/30 - 4*t**2. Let g(v) be the third derivative of u(v). Factor g(q).
-(q - 1)**2*(q + 1)
Find f, given that -15/4*f**3 + 3/4*f**4 - 3*f + 6*f**2 + 0 = 0.
0, 1, 2
Let a be (-24)/(-108)*(-2 + 11). Let 0 + 0*r**a + 0*r + 0*r**3 - 3/2*r**5 - r**4 = 0. What is r?
-2/3, 0
Factor 27/8 - 9/4*c + 3/8*c**2.
3*(c - 3)**2/8
Let b(a) be the first derivative of -a**3/2 - 15*a**2/4 - 9*a - 31. Factor b(h).
-3*(h + 2)*(h + 3)/2
Suppose -13 + 4 = 3*r. Let v be (-3)/(r/(-6)*-3). Determine b so that -4 - 2*b + 4 - b**v - 1 = 0.
-1
Let h(l) be the first derivative of -5*l**3/6 + 15*l**2 - 90*l + 20. Suppose h(g) = 0. Calculate g.
6
Let d(j) be the second derivative of -j**4/48 + j**3/24 + j**2/4 - 5*j. Factor d(p).
-(p - 2)*(p + 1)/4
Let t = -9 - -11. Suppose t*m**2 - 9 + 6 - 4*m + 5 = 0. Calculate m.
1
Factor 3/4*d**4 + 0 + 0*d - 9/4*d**3 + 3/2*d**2.
3*d**2*(d - 2)*(d - 1)/4
Let g(h) be the first derivative of -3*h**4/10 + 4*h**3/15 + 4. Solve g(v) = 0 for v.
0, 2/3
Let o(t) = -9*t**5 - 13*t**4 - 22*t**3 + 8*t - 5. Let w(r) = -4*r**5 - 7*r**4 - 11*r**3 + 4*r - 2. Let g(l) = 2*o(l) - 5*w(l). Solve g(u) = 0.
-2, -1, 0, 1/2
Let y(d) be the third derivative of 3*d**6/80 - d**5/10 + d**4/16 - 4*d**2. Factor y(s).
3*s*(s - 1)*(3*s - 1)/2
Let t(q) be the second derivative of -1/2*q**4 + 0 - 2*q - q**2 - q**3 - 1/10*q**5. Determine o so that t(o) = 0.
-1
Let h(a) be the second derivative of -a**7/945 - a**6/360 + a**5/180 + a**4/12 + 3*a. Let j(p) be the third derivative of h(p). Let j(n) = 0. What is n?
-1, 1/4
Let s(u) be the third derivative of 2*u**6/75 - 7*u**5/75 - u**4/15 + u**2. Suppose s(a) = 0. What is a?
-1/4, 0, 2
Let w(x) be the second derivative of -x**4/36 - x**3/6 - x**2/3 - 31*x. Factor w(d).
-(d + 1)*(d + 2)/3
Suppose -l + 23*l**2 - 3 + 1 + 1 - 1 - 20*l**3 = 0. Calculate l.
-1/4, 2/5, 1
Let a be 1/(2 + (-38)/20). Suppose 3*z + 14 = 4*p, -3*p + 2*z + 0*z = -a. Find s, given that 0 + 1/3*s + 1/3*s**p = 0.
-1, 0
Suppose 13*v - 15*v**2 - 14*v - 5*v = 0. What is v?
-2/5, 0
Let v(x) = -x**3 + 7*x**2 + x. Let k be v(7). Suppose 2*m + 15 = k*m. Let -18*y**2 - 1 - 132*y**2 - 30*y - 1 - 250*y**m = 0. What is y?
-1/5
Factor -50/3 - 2/3*k**2 + 20/3*k.
-2*(k - 5)**2/3
Factor 1/2 - 1/8*w**2 + 0*w.
-(w - 2)*(w + 2)/8
Factor -245*i - 12*i**3 - 20*i**2 + 0*i**4 + 237*i + 4*i**5 + 4*i**4.
4*i*(i - 2)*(i + 1)**3
Suppose z - 1 = w + 2, -5*w + 2*z - 6 = 0. Let l be w + -1 - 8/(-6). Factor m**3 - l - 1/3*m**2 - m + 2/3*m**4.
(m - 1)*(m + 1)**2*(2*m + 1)/3
Suppose -2*f - 2*f + 3*u + 9 = 0, 4*f + 12 = -4*u. Solve f*p**3 - 1/2*p**4 + 0*p - 1/2*p**5 + 0 + 0*p**2 = 0.
-1, 0
Suppose -4*l = -3*d + 6, 2*l = 2*d - 2*l. Suppose 4*s - 5*m - 31 = 0, 3*m - d - 5 = -5*s. Solve 0*v + 0*v**s + 0*v**2 + 0 - 1/3*v**5 + 1/3*v**3 = 0 for v.
-1, 0, 1
Suppose 0 = 5*a - 3*a + 3*t - 20, 5*a - 5*t = 0. Suppose 10 - 2 = a*c. Factor 3*z**2 + 3*z**c - 2*z**2 - 2*z - 2*z**2.
2*z*(z - 1)
Suppose -5*p = -2*k + 25 + 18, -5*p = -3*k + 57. Let b be (-17)/14 - (-21)/k. Factor 2/7*t**3 - b*t + 0 + 0*t**2.
2*t*(t - 1)*(t + 1)/7
Let r(h) = -13*h**2 + 8*h + 1. Let w(f) = -25*f**2 + 17*f + 1. Let l(j) = 7*r(j) - 4*w(j). Solve l(o) = 0 for o.
1/3, 1
Factor 86*d + 36*d + 5*d**3 + 45*d**2 + 13*d + 135.
5*(d + 3)**3
Factor -40/3*u - 2/3*u**4 - 12*u**2 - 14/3*u**3 - 16/3.
-2*(u + 1)*(u + 2)**3/3
Let d(b) be the first derivative of b**5/110 + b**4/66 - b**3/33 - b**2/11 + 3*b + 1. Let r(c) be the first derivative of d(c). Factor r(w).
2*(w - 1)*(w + 1)**2/11
Let w(j) be the second derivative of -j**6/660 + j**4/44 + 2*j**3/33 + 3*j**2/2 + 8*j. Let c(g) be the first derivative of w(g). Find o, given that c(o) = 0.
-1, 2
Let r(s) be the second derivative of 1/25*s**6 - 1/105*s**7 - 1/15*s**3 + 1/25*s**5 - 1/5*s**4 + 0 + 4*s + 3/5*s**2. Find g, given that r(g) = 0.
-1, 1, 3
Let f(r) be the third derivative of -r**6/540 - 2*r**5/135 - r**4/36 - 12*r**2. Solve f(d) = 0 for d.
-3, -1, 0
Let t(d) be the first derivative of 2*d**3/21 + 2*d**2/7 + 2*d/7 + 12. Factor t(u).
2*(u + 1)**2/7
Let z(d) = -2*d + 5. Suppose -a + 6*a = 5*y - 20, 5*y + 5*a = -20. Let u be z(y). Let 0 + 0*q**4 + 0*q**2 + 0*q**3 - 1/4*q**u + 0*q = 0. Calculate q.
0
Let c be 0/(2/(-2) - -2). Let f(w) be the first derivative of c*w + 0*w**3 + 0*w**2 + 2 - 1/6*w**4. Factor f(l).
-2*l**3/3
Let p(k) be the second derivative of k**8/33600 - k**6/3600 - k**4/2 + 2*k. Let v(o) be the third derivative of p(o). Factor v(m).
m*(m - 1)*(m + 1)/5
Let t(p) be the third derivative of p**5/30 - p**4/12 - 5*p**2. What is s in t(s) = 0?
0, 1
Suppose x - s - 12 = 0, 3*s + s + 62 = 5*x. Let u be (-6)/x*4 + 2. Factor 4/7*y**2 - 2/7*y + 0 - u*y**3.
-2*y*(y - 1)**2/7
Solve 8/7*g**3 + 0 - 8/7*g**2 + 0*g - 2/7*g**4 = 0 for g.
0, 2
Let o(i) be the second derivative of 2*i + 1/3*i**3 - 1/15*i**6 + 0 + 1/6*i**4 - 1/10*i**5 + 0*i**2. Factor o(b).
-2*b*(b - 1)*(b + 1)**2
Let k(h) be the second derivative of -h**8/560 + h**6/60 - h**4/8 + 2*h**3/3 - h. Let f(w) be the second derivative of k(w). Let f(s) = 0. Calculate s.
-1, 1
Let w(n) = -n**2 - 17*n + 5. Let u(z) = -3*z**2 - 42*