
-25, 0
Let m(b) be the first derivative of b**3 - 135*b**2/2 + 258*b - 354. Suppose m(f) = 0. What is f?
2, 43
Let p(a) be the second derivative of a**7/30 + 41*a**6/75 + 33*a**5/20 - 41*a**4/30 - 122*a**3/15 + 36*a**2/5 - 404*a. Let p(z) = 0. Calculate z.
-9, -2, 2/7, 1
Factor 12/7*w**4 + 2/7*w**5 + 20/7*w**2 + 0 + 24/7*w**3 + 6/7*w.
2*w*(w + 1)**3*(w + 3)/7
Let d(z) = 2. Let j(p) = -2*p**2 + 18*p + 64. Let y(h) = 20*d(h) - 2*j(h). Solve y(t) = 0.
-2, 11
Determine n, given that -2*n**3 + 20/3 + 26*n + 52/3*n**2 = 0.
-1, -1/3, 10
Let x be 1/(-5)*15*(-68)/51. Suppose 0*m - 3/2*m**2 + 0 - 3*m**3 - 3/2*m**x = 0. Calculate m.
-1, 0
Factor -23*f**2 + 3*f**3 + 263*f**2 - 67*f - 176*f.
3*f*(f - 1)*(f + 81)
Determine o so that 0 + 1/4*o - 1/4*o**3 + 0*o**2 = 0.
-1, 0, 1
Let n be (33/(-88)*8)/((-2)/2). Suppose -2/5*t**2 + 1/5*t - 1/5*t**5 + 0*t**n + 2/5*t**4 + 0 = 0. What is t?
-1, 0, 1
Determine h so that -2/9*h**2 + 196/9*h - 4802/9 = 0.
49
Let q = -67 + 70. Factor -s + 20*s**2 + 6*s + s + 16*s**q - 10*s**3.
2*s*(s + 3)*(3*s + 1)
Let k(i) be the first derivative of -20/3*i**3 - 10*i + 25/2*i**2 + 5/4*i**4 + 30. Factor k(y).
5*(y - 2)*(y - 1)**2
Let c(n) be the third derivative of n**9/136080 - n**8/22680 + n**7/11340 + 23*n**5/60 + 19*n**2. Let r(l) be the third derivative of c(l). Factor r(w).
4*w*(w - 1)**2/9
Let q(m) be the second derivative of m**4/3 - 86*m**3/3 + 84*m**2 - 230*m. Factor q(f).
4*(f - 42)*(f - 1)
Let o(h) be the first derivative of 10 + 81/16*h**4 + 0*h - 15/4*h**3 + 3/4*h**2. Suppose o(r) = 0. What is r?
0, 2/9, 1/3
Let y(i) = i**2 + 4*i + 7. Let r be y(-2). Let l be (-1)/3 + (2 - -1). Factor 0*h + 0 + 8*h**r - l*h**2 + 14/3*h**4.
2*h**2*(h + 2)*(7*h - 2)/3
Suppose -52/3 - 134/3*g + 28/3*g**4 + 2/3*g**5 - 88/3*g**2 + 20/3*g**3 = 0. Calculate g.
-13, -1, 2
Let u(o) be the second derivative of -2*o**6/15 - o**5 + 14*o**4 - 152*o**3/3 + 80*o**2 - 2*o - 1. Factor u(r).
-4*(r - 2)**2*(r - 1)*(r + 10)
Let t be (-18)/(-7) - (-6)/14. Factor 7*p**3 + 13*p**t + 4*p**2 - 24*p**3.
-4*p**2*(p - 1)
Let d = 104406/5 + -20881. Factor d*c**2 - 2/5*c**3 + 2/5*c + 0 - 1/5*c**4.
-c*(c - 1)*(c + 1)*(c + 2)/5
Let n(j) be the first derivative of -j**4/16 - j**3/4 + j**2/2 + 3*j - 96. Factor n(r).
-(r - 2)*(r + 2)*(r + 3)/4
Let a be 48 + -36 - (5 + 3). Let p(h) be the second derivative of -5/3*h**3 + 1/12*h**a + 0 + 25/2*h**2 + 8*h. Factor p(f).
(f - 5)**2
Let g(t) = t**3 + 7*t**2 - 2*t - 10. Let l be g(-7). Suppose 8 - 12*j**2 - 20*j - 16 - 3*j**3 + 7*j**3 + l*j**4 = 0. What is j?
-1, 2
Let v(c) be the second derivative of -c**4/14 - 3*c**3/7 - 6*c**2/7 - 80*c. Determine u, given that v(u) = 0.
-2, -1
Suppose 4*u = 5*l + 22, 2*l - 34*u + 36*u - 20 = 0. Let r + 1/2*r**l - 3/2 = 0. What is r?
-3, 1
Let n(q) be the first derivative of -q**6/24 + q**5/20 + 3*q**4/8 + q**3/6 - 5*q**2/8 - 3*q/4 + 184. Factor n(l).
-(l - 3)*(l - 1)*(l + 1)**3/4
Let g(z) be the third derivative of z**6/600 + 11*z**5/150 - 23*z**4/120 + 70*z**2 + 3. Find d such that g(d) = 0.
-23, 0, 1
Let b(m) = -5*m**4 - 22*m**3 - 53*m**2 - 28*m - 2. Let r(p) = 6*p**4 + 21*p**3 + 54*p**2 + 27*p + 3. Let n(s) = 3*b(s) + 2*r(s). Determine c so that n(c) = 0.
-5, -2, -1, 0
Let y(x) = 18*x**5 + 8*x**4 + 52*x**3 - 94*x**2 + 90*x - 34. Let l(u) = -2*u**5 - u**4 - u**3 - u + 1. Let i(a) = 10*l(a) + y(a). Factor i(m).
-2*(m - 2)*(m - 1)**3*(m + 6)
Let r(h) be the third derivative of -h**8/672 - h**7/210 + 7*h**6/240 + h**5/6 + h**4/4 - 8*h**2 - 4. Suppose r(y) = 0. Calculate y.
-2, -1, 0, 3
Let k(f) be the third derivative of -f**8/1008 + 13*f**7/315 - 7*f**6/15 - 13*f**5/90 + 169*f**4/72 - 46*f**2 - 6. Determine z, given that k(z) = 0.
-1, 0, 1, 13
Let w(k) = -k**2 - 17*k - 33. Let n be w(-14). Suppose -d + n*d - 24 = 0. Factor 0 + 2/11*i**d + 2/11*i - 4/11*i**2.
2*i*(i - 1)**2/11
Let q be (4/(-10))/(3/(-45)). Let g be 12/(-3) + 7 - -2 - -1. Factor -4*d**5 - g - d**3 + 5*d**4 + q.
-d**3*(d - 1)*(4*d - 1)
Factor 1/3*q**2 + 0 + 9*q.
q*(q + 27)/3
Suppose 4*f = -f - 35. Let l(s) = -s - 5. Let m be l(f). Factor i**m - 3*i**5 + 9*i**3 + 0*i**2 + 5*i**2.
-3*i**2*(i - 2)*(i + 1)**2
Let f be 8/44 + ((-304)/(-132))/2. Let 0*a + 0 + 5/3*a**4 + f*a**5 - 1/6*a**2 + 1/6*a**3 = 0. What is a?
-1, -1/2, 0, 1/4
Solve -4/7 - 18/7*h - 30/7*h**2 - 6/7*h**4 - 22/7*h**3 = 0 for h.
-1, -2/3
Find x such that -127*x**2 + 32*x + 11*x**3 + 2*x**4 + x**5 - 13*x**4 + 63*x**2 + 31*x**3 = 0.
0, 1, 2, 4
Let k be (-2)/(3 - 57/18). Suppose 2*l - 6 = 0, -5*o - k = 5*l - 57. Factor -2*a**5 - 17*a**2 + 8*a**3 - 3 + 7 - o*a + 13*a**2.
-2*(a - 1)**3*(a + 1)*(a + 2)
Let p(r) be the first derivative of r**3/15 + 77*r**2/5 + 5929*r/5 - 178. Suppose p(x) = 0. What is x?
-77
Let q(b) = -6*b**3 - 2*b**2 - 2*b + 2. Let g = 34 + -32. Let s(t) = 19*t**3 + 5*t**2 + 7*t - 7. Let c(m) = g*s(m) + 7*q(m). Factor c(i).
-4*i**2*(i + 1)
Let x(o) = o**2 - o + 1. Let f(a) = 7*a**2 - 8*a + 3. Let v(d) = 5*f(d) - 30*x(d). Factor v(n).
5*(n - 3)*(n + 1)
Let f be 9/8*-32*13/(-260). Find q, given that f*q + 0 - 3/5*q**2 = 0.
0, 3
Let i(t) be the second derivative of t**9/6048 + t**8/3360 - t**7/1680 - t**6/720 + 17*t**3/6 - 12*t. Let d(v) be the second derivative of i(v). Factor d(u).
u**2*(u - 1)*(u + 1)**2/2
Suppose -2 = 31*p - 32*p. Factor 2*i**2 - 15*i**4 - 12*i**2 + p*i**3 - 20*i**3 - 7*i**3.
-5*i**2*(i + 1)*(3*i + 2)
Let c(z) be the first derivative of -4*z**5/5 + 9*z**4 + 4*z**3/3 - 18*z**2 - 334. Factor c(f).
-4*f*(f - 9)*(f - 1)*(f + 1)
Let v(h) = h**2 - 10*h + 2. Let l be v(10). Factor 5*b - 4*b + 2*b - l*b**2 - 5*b.
-2*b*(b + 1)
Factor -1000/3 - 10*m**2 + 100*m + 1/3*m**3.
(m - 10)**3/3
Let i = -3/2905 - -1663/2905. What is y in -i*y**3 + 4/7*y + 0*y**2 - 2/7 + 2/7*y**4 = 0?
-1, 1
Suppose -2*b - 4 = 0, b + 9 = k - 2*b. Factor 0 - 20*z + 4*z**k - 12*z**2 - 8 + 3 + 4*z**4 - 3.
4*(z - 2)*(z + 1)**3
Factor -4*n**5 + 193314*n**2 + 49843*n**2 - 1607200*n + 732058 + 2011942 + 52663*n**2 + 452*n**4 - 18124*n**3.
-4*(n - 35)**3*(n - 4)**2
Let w(r) be the second derivative of 5/3*r**3 + 1/4*r**5 + 0 + 0*r**2 - 21*r + 5/4*r**4. Let w(y) = 0. Calculate y.
-2, -1, 0
Let c(r) be the second derivative of 1/60*r**4 + 2/15*r**3 + 0 + 0*r**2 - 14*r. Suppose c(x) = 0. Calculate x.
-4, 0
Let b(m) be the third derivative of m**7/42 + m**6/24 - m**5/3 - 5*m**4/6 - 18*m**2. Factor b(t).
5*t*(t - 2)*(t + 1)*(t + 2)
Suppose 0 = 115*n - 152*n. Suppose 3/5*c**3 + n + 0*c**2 - 3/5*c = 0. What is c?
-1, 0, 1
Let a = -54 - -57. Suppose p = -9*p + a*p. Factor 0*s**2 + 2/15*s**3 - 2/15*s + p.
2*s*(s - 1)*(s + 1)/15
Let o(p) be the second derivative of 1/3*p**4 + 14*p - 1 - 32/3*p**3 + 128*p**2. Suppose o(l) = 0. Calculate l.
8
Let j(m) be the first derivative of -1/15*m**2 - 4/15*m + 1/30*m**4 + 4/45*m**3 + 11. Factor j(h).
2*(h - 1)*(h + 1)*(h + 2)/15
Determine u so that -2*u**2 + 1/3*u**3 - 16/3*u + 0 = 0.
-2, 0, 8
Determine j so that -55*j**2 - 20 - 1070*j**4 + 113*j**3 + 47*j**3 - 160*j + 1145*j**4 = 0.
-2, -1, -2/15, 1
Suppose -4*g = 2*s - 6, -3*s + 7 = 3*g - 4*s. Solve -31*y - g*y**2 + 6*y**2 + y - 9*y**2 + 35 = 0 for y.
-7, 1
Let -10*h**2 - 80 - 65*h**2 - 10*h**3 - 10*h**2 - 200*h = 0. What is h?
-4, -1/2
Let w be (2 + 5/(-10))/((-9)/32). Let u = -3 - w. Solve 0 - 20/3*y**2 + 5/3*y**4 + 10*y**3 - u*y**5 - 8/3*y = 0 for y.
-2, -2/7, 0, 1, 2
Factor 32/3*y + 2/3*y**3 + 2/3*y**5 + 0 - 4*y**4 + 16*y**2.
2*y*(y - 4)**2*(y + 1)**2/3
Suppose -35*b + 104 = -9*b. Let g(h) be the third derivative of -3/20*h**5 + 1/4*h**b + 0 + 0*h**3 + 0*h - 5*h**2 + 1/40*h**6. Suppose g(j) = 0. What is j?
0, 1, 2
Suppose 5*h = 13 + 22. Factor h*u**2 - 3*u**2 + 3 - 11 + 0*u - 4*u.
4*(u - 2)*(u + 1)
Let r = -339/59 - -5589/295. Find z, given that -18/5 + 24/5*z**2 + r*z = 0.
-3, 1/4
Let f(g) = g + 3. Let d be f(0). Factor 5 + 30*s**2 + 7 + 7*s**d - 2*s**3 + 18 + 55*s.
5*(s + 1)*(s + 2)*(s + 3)
Let x be 3/5 + (-8)/(-20). Suppose 2*l + 5*c = -15, -c = -l - x + 11. Find y such that l*y - 15 - 3*y - y**2 + 5 + 9 = 0.
1
Let s = 60 + -60. Let -4*f**5 - 19*f + 24*f - 7*f**2 + s*f**3 - 1 + 8*f**4 - f**3 = 0. Calculate f.
-1, 1/2, 1
Let k(n) be the first derivative of -n**3/6 - 115*n**2/16 + 29*n/8 + 20. Suppose k(x) = 0. What is x?
-29, 1/4
Suppose 252*f = 273*f - 63. Let h(g) be the second derivative of -