2*g**2 = 0.
-1/24
Let m(p) be the second derivative of -p**5/40 + 7*p**4/24 - p**3/3 - 3*p**2 + 2*p + 54. Factor m(g).
-(g - 6)*(g - 2)*(g + 1)/2
Suppose -3*v = 5*l - 3 + 1, 0 = 2*v + l - 6. Factor -92*n - 30 + 67*n - v*n**2 - n**2.
-5*(n + 2)*(n + 3)
Suppose 74*o - 32 = 66*o. Suppose 0*k - 3*k = -6. Suppose -3*l + k*l**2 + 3*l + 2 - o*l = 0. What is l?
1
Let p(y) = 5*y**2 + 61*y + 125. Let q(b) = b**2 + 12*b + 25. Let l be (-11)/(-5 - (-3 - 1)). Let v(z) = l*q(z) - 2*p(z). Factor v(g).
(g + 5)**2
Let f = -34315/48 - -715. Let s(d) be the first derivative of 0*d**3 + 1/20*d**5 + 10 + 0*d**2 + 0*d**4 + 0*d + f*d**6. Solve s(u) = 0.
-2/5, 0
Let v = -28981 - -231849/8. Find z, given that -v*z**2 - 5/8*z + 7/4 = 0.
-7, 2
Suppose o = -g - 7, -127*o + 129*o - 7 = g. Factor 0*s - 1/6*s**2 - 1/6*s**4 + o + 1/3*s**3.
-s**2*(s - 1)**2/6
Let g = 17746/45 + -3542/9. Let k be (-1 - 5)*(-4)/6. Solve -4/5*j**2 + 4/5*j**k + g*j - 4/5*j**3 + 0 = 0 for j.
-1, 0, 1
Find o, given that 13/3*o + 5/3*o**2 + 7/3 - 1/3*o**3 = 0.
-1, 7
Let u(r) be the second derivative of -r**4/32 - r**3/16 + 84*r. Factor u(z).
-3*z*(z + 1)/8
Let x = 2/13517 - -11584/13517. Solve -x - 9/7*z**4 - 3/7*z + 3/7*z**3 + 15/7*z**2 = 0 for z.
-1, -2/3, 1
Let w = -5 + 4. Let v be 2 + (-1 + 1 - w). Determine p so that -v*p**5 + 0*p**4 - 5*p**3 + 6*p**4 - p**3 + 3*p**3 = 0.
0, 1
Let z(l) be the first derivative of l**4/5 + 4*l**3/15 + 98. Factor z(d).
4*d**2*(d + 1)/5
Determine r, given that -7/2*r - 11/2*r**2 + 3 + r**3 = 0.
-1, 1/2, 6
Let c(a) be the second derivative of -3*a**5/20 + 3*a**4/4 + 2*a**3 + a + 18. Factor c(m).
-3*m*(m - 4)*(m + 1)
Let q(c) be the second derivative of -c**4/9 - 2*c**3/3 + 5*c + 7. Solve q(h) = 0.
-3, 0
Let a(p) = 2*p**4 + p**3 - p**2 + p - 1. Let c(k) = -5*k**5 - 36*k**4 + 82*k**3 + 33*k**2 - 83*k + 3. Let q(r) = 3*a(r) + c(r). Solve q(y) = 0.
-8, -1, 0, 1, 2
Suppose 8 - 2 = -d - 2*z, d + z = -2. Suppose 4*l - 3*p + 6 = -5*p, -6 = -l + d*p. Let l - 2/5*a**2 + 2/5*a = 0. What is a?
0, 1
Let y(s) be the first derivative of -s**4/4 - s**3/3 + 3*s**2 + 35. Factor y(h).
-h*(h - 2)*(h + 3)
Factor 0 + 2/9*g**4 + 2/3*g**2 + 2/3*g**3 + 2/9*g.
2*g*(g + 1)**3/9
Let b(a) be the second derivative of -a**5/150 - a**4/10 - 8*a**3/15 - 16*a**2/15 + 23*a. Factor b(t).
-2*(t + 1)*(t + 4)**2/15
Let i be (1/9 - (-91)/(-819))/2. Determine a, given that 3/2*a**2 - 3/2*a + i = 0.
0, 1
Let m = -23844 - -23846. Find k such that -2/3*k + 2 - 8/3*k**m = 0.
-1, 3/4
Let f = 697/13020 + -8/217. Let c(w) be the third derivative of -1/12*w**4 + 0*w - 4*w**2 - 1/3*w**3 + 1/30*w**5 + 0 + f*w**6. Solve c(v) = 0 for v.
-1, 1
Suppose m = 4*m - 6. Let r(h) = -h**3 - 18*h**2 - 17*h + 3. Let l be r(-17). Suppose -2*x + 3*x**3 - x**4 + 14*x**m - 17*x**2 + l*x = 0. What is x?
0, 1
Let i(y) be the second derivative of -7/6*y**4 + 1/2*y**5 + 0 - 1/15*y**6 + 48*y + 0*y**2 + y**3. Factor i(g).
-2*g*(g - 3)*(g - 1)**2
Find x such that -30/19*x + 32/19 - 2/19*x**2 = 0.
-16, 1
Factor 4/3 + 4/3*o + 1/3*o**2.
(o + 2)**2/3
Factor 52/3*d**2 - 2/3*d**5 + 0 + 6*d + 4*d**4 + 16*d**3.
-2*d*(d - 9)*(d + 1)**3/3
Find d, given that 10*d - 6*d**3 - 35*d**4 + 36*d**3 - 1064*d**2 + 1139*d**2 = 0.
-1, -1/7, 0, 2
Let q(v) = -14*v + 146. Let k be q(10). Let x(f) be the first derivative of 0*f + 2/15*f**5 - 2/9*f**3 - 1/2*f**4 + 1/9*f**k + 1 + 2/3*f**2. Solve x(y) = 0.
-2, -1, 0, 1
Let l(d) be the first derivative of -3*d**6/14 + 191*d**5/35 - 561*d**4/14 + 380*d**3/7 - 100*d**2/7 + 220. Find f such that l(f) = 0.
0, 2/9, 1, 10
Let c(a) = -2*a**2 + 7*a. Let z(s) = 17*s**2 - 11*s**2 - 7*s**2 - s + 7*s. Let l(g) = 4*c(g) - 3*z(g). Factor l(u).
-5*u*(u - 2)
Let o(s) = s**2 + 4*s + 33. Let v(q) = 3*q - 1. Let j(a) = -2*o(a) - 6*v(a). Find f, given that j(f) = 0.
-10, -3
Let f = 13 + -10. Suppose 28 - 135 = -f*i - y, i + y - 37 = 0. Find n, given that 22*n**3 + i*n**4 + 24*n**5 - 6*n**2 + 10*n**2 + 5*n**4 = 0.
-2/3, -1/2, 0
Factor 3/5*o**3 + 0 + 0*o + 21/5*o**2.
3*o**2*(o + 7)/5
Let s(u) = 6*u**3 - 317*u**2 + 28*u + 334. Let f(p) = -p**3 + 53*p**2 - 5*p - 56. Let q(k) = -34*f(k) - 6*s(k). Factor q(h).
-2*(h - 50)*(h - 1)*(h + 1)
Let c(j) be the first derivative of j**3/3 + j + 44. Let y(s) = -10*s**2 - 51*s - 17. Let u(m) = 3*c(m) + y(m). Factor u(o).
-(o + 7)*(7*o + 2)
Let d(b) be the second derivative of b**4/66 + 9*b**3/11 + 50*b**2/11 + 419*b. Suppose d(v) = 0. What is v?
-25, -2
Let o = 4161/140 + -207/7. Let q(s) be the first derivative of -9/10*s**2 - o*s**4 + 3/5*s + 3/5*s**3 + 7. Solve q(b) = 0 for b.
1
Let v(g) = -37*g + 12 + 32 + 35*g. Let r be v(22). Solve -4/5*x**2 + r*x + 4/5 = 0.
-1, 1
Solve -1035*t**2 + 71415*t - 26*t**3 + 7*t**3 - 1642545 + 14*t**3 + 10*t**3 = 0 for t.
69
Let w(c) be the third derivative of 0*c + 1/180*c**5 + 0 + 0*c**3 + 1/36*c**4 - 10*c**2. What is n in w(n) = 0?
-2, 0
Let k(c) = 2*c**2 - 3*c. Let l = 0 + 2. Let g be k(l). Let -4*d**2 - 3*d**2 + 2*d + 0*d**g + 5*d**2 = 0. Calculate d.
0, 1
Let i(a) be the second derivative of a**6/10 - 3*a**5/20 - a**4 + 2*a**3 - 60*a. What is b in i(b) = 0?
-2, 0, 1, 2
Solve 20*w**2 - 10*w**4 - w**5 - 6*w**4 + 25*w**4 + 21*w**3 - 9*w**4 = 0.
-4, -1, 0, 5
Let r(z) be the first derivative of -z**5/140 + z**4/42 + 2*z**3/21 - 4*z**2/7 + 10*z - 8. Let m(l) be the first derivative of r(l). Factor m(t).
-(t - 2)**2*(t + 2)/7
Suppose -3*v + 30 = 2*l - 0*v, 0 = 3*v. Factor -n**2 - l*n**2 + 6*n**2 + 5*n**3.
5*n**2*(n - 2)
Let r(n) be the third derivative of n**6/15 - 47*n**5/30 + 8*n**4/3 + 11*n**3/3 + 6*n**2 + 2. Let r(x) = 0. What is x?
-1/4, 1, 11
Let b(f) = -19*f + 515. Let u be b(27). Let s(w) be the first derivative of 2/45*w**3 + 1/30*w**4 - 8 + 0*w + 0*w**u. Find v such that s(v) = 0.
-1, 0
Solve -10*a**4 + a**5 - 3*a**3 + 825*a - 8*a**2 - 629*a + 148*a**2 = 0.
-2, 0, 7
Let j be (4/7)/(10/70). Let n be (18/15)/(j/10). Suppose 3*l**5 - 3*l**n + 0 + 0*l + 3/2*l**2 - 3/2*l**4 = 0. What is l?
-1, 0, 1/2, 1
Let l(n) = 5*n**3 - 9*n**2 + 3*n - 17. Suppose -5 = -4*v - 21. Let z(h) = 4*h**2 + 1 - 2*h + 6 + 1 - 2*h**3. Let m(x) = v*l(x) - 9*z(x). Factor m(s).
-2*(s - 1)**2*(s + 2)
Let -9*j**5 - 139*j**3 - 180 + 10980*j + 417*j**4 - 396*j**3 - 237*j**2 - 10436*j = 0. Calculate j.
-1, 2/3, 1, 45
Let g(u) = -2*u**3 - 2*u**2 - u + 1. Let r(p) = -2*p**3 + 6*p**2 - 18*p - 22. Let d(i) = -4*g(i) + 2*r(i). Factor d(a).
4*(a - 2)*(a + 1)*(a + 6)
Let l(m) be the second derivative of -25*m**4/96 + 5*m**3/8 - 9*m**2/16 - 50*m + 2. Find a, given that l(a) = 0.
3/5
Let c(x) = -4*x**4 + 32*x**3 - 132*x**2 + 200*x - 72. Let w(b) = b**4 - b**3 - b**2 - b - 1. Let d(g) = c(g) + 8*w(g). Factor d(p).
4*(p - 2)*(p - 1)**2*(p + 10)
Let c(g) be the third derivative of g**5/480 + 5*g**4/6 + 400*g**3/3 + 2*g**2 - 54*g. Factor c(b).
(b + 80)**2/8
Let -98/11 - 70/11*u - 2/11*u**3 + 26/11*u**2 = 0. What is u?
-1, 7
Let f(i) be the second derivative of 0*i**2 + 1/900*i**6 - i**3 + 0*i**4 + 0 - 7*i - 1/300*i**5. Let p(r) be the second derivative of f(r). Factor p(v).
2*v*(v - 1)/5
Let i(v) = -v - 7. Let a be i(-8). Factor f**4 + 0*f**5 - 2*f**5 + f - 2*f**2 + a + 3*f**5 + f**3 - 3*f**3.
(f - 1)**2*(f + 1)**3
Let s(b) = -10*b**2 - 1436*b + 133956. Let d(o) = -6*o**2 - 716*o + 66978. Let p(l) = 7*d(l) - 4*s(l). Find i such that p(i) = 0.
183
Let 7/2*m**3 + 79/2*m**2 + 11*m + 0 = 0. What is m?
-11, -2/7, 0
Let a(x) = -x**3 - 19*x**2 - 21*x - 14. Let s be a(-18). Factor -23*q**2 - 16 + s*q + 14*q**3 - 25*q**2 - 2*q**4 + 12*q**2.
-2*(q - 2)**3*(q - 1)
Let l be -1 + 9 - -1*287/(-42). Factor 8/3*w - l*w**2 - 2 + 1/6*w**3.
(w - 3)*(w - 2)**2/6
Determine h, given that 0 + 2/11*h**5 - 14/11*h**3 - 24/11*h - 4/11*h**4 + 40/11*h**2 = 0.
-3, 0, 1, 2
Let t be 13/26 - 6/(-4). Let n(a) be the second derivative of -1/36*a**4 + 0*a**t + 1/6*a**3 - 4*a + 0. Factor n(d).
-d*(d - 3)/3
Let n(r) = -11*r**2 - 29*r + 6. Let b(m) = 5 - m**2 + 14*m**2 - 30*m - 23*m**2. Let k(i) = 6*b(i) - 5*n(i). Let k(l) = 0. Calculate l.
-7, 0
Let j(b) = b**4 + b**3 + 2*b**2 - b - 1. Let y(t) = 28*t**4 + 83*t**3 - 79*t**2 - 23*t - 3. Let g(a) = 3*j(a) - y(a). Factor g(z).
-5*z*(z - 1)*(z + 4)*(5*z + 1)
Let k(r) be the first derivative of r**5/10 - r**4/8 - r**3/2 + r**2/4 + r - 23. What is i in k(i) = 0?
-1, 1, 2
Let p = 6/839 + 1660/2517. Wh