1, 3, 5
Let s(b) = b**2 + 6*b + 10. Let a be s(-4). Let x(m) = -2*m - 18. Let q be x(-10). Determine l so that a*l + 4/3*l**2 - 4/3 - q*l**3 = 0.
-1, 2/3, 1
Let p(z) = z**2 + 19*z + 20. Let w be p(-18). Determine k so that -k + k - 4*k - 2*k**w + 4*k**2 = 0.
0, 2
Determine y so that -3/2*y + y**3 + 0 - 2*y**2 + 2*y**4 + 1/2*y**5 = 0.
-3, -1, 0, 1
Let x(s) be the second derivative of -s**6/225 - s**5/50 - s**4/90 + s**3/15 + 2*s**2/15 + 28*s. Determine o so that x(o) = 0.
-2, -1, 1
Suppose 50 - 134 = -2*u. Suppose u*s + 10 = 47*s. Find j such that 2/7 - 2/7*j**s + 6/7*j**4 - j + 13/7*j**3 = 0.
-2, -1, 1/3, 1/2
Let r(u) be the first derivative of 2*u**5/5 + 3*u**4/2 + 2*u**3 + u**2 - 103. Factor r(a).
2*a*(a + 1)**3
Let c(x) be the second derivative of -3*x**7/7 + 4*x**6/3 + x**5/2 - 10*x**4/3 + 4*x**3/3 - x + 28. Determine n so that c(n) = 0.
-1, 0, 2/9, 1, 2
Suppose 6*w - 54 = -12*w. Let l(a) be the second derivative of 1/6*a**4 - 3*a**2 + 0 + 2/3*a**w + a. Factor l(d).
2*(d - 1)*(d + 3)
Let o be (-79)/(-4) - 1/(-4). Let l = 24 - o. Solve 8*s**4 + s**l - 9*s**4 - 2*s**5 = 0.
0
Let j be 9/(-18)*8/(-5). Let d = 362 + -360. Factor -1/5*z**3 - 3/5*z**d + 0*z + j.
-(z - 1)*(z + 2)**2/5
Let d(p) be the third derivative of 4*p**3 + 0 - 1/3*p**4 + 0*p + 1/90*p**5 + 2*p**2. Factor d(j).
2*(j - 6)**2/3
Let g(j) be the first derivative of 3*j**4/2 - 17*j**3/3 - 13*j**2/2 + 10*j - 94. Let g(i) = 0. What is i?
-1, 1/2, 10/3
Let v(f) = -f**3 + f**2 - f - 1. Let q(y) = 1991 + y - 1987 + 3*y**3 - 15*y**2 + 5*y**2. Let z(h) = -2*q(h) - 10*v(h). Solve z(m) = 0.
-1, -1/2
Let -2/5*q**5 + 8/5*q**2 + 4/5*q**3 - 4/5 - 4/5*q**4 - 2/5*q = 0. What is q?
-2, -1, 1
Let m(q) be the second derivative of 5*q**8/336 - 3*q**7/56 + q**6/24 + q**5/24 + q**3/2 + 21*q. Let l(r) be the second derivative of m(r). Factor l(w).
5*w*(w - 1)**2*(5*w + 1)
Let d(o) = o**4 + 34*o**3 + 125*o**2 + 92*o. Let z(g) = 3*g**4 + 135*g**3 + 501*g**2 + 369*g. Let y(f) = -9*d(f) + 2*z(f). Factor y(k).
-3*k*(k + 1)*(k + 5)*(k + 6)
Let l(c) be the second derivative of 2*c**7/105 + 19*c**6/90 - c**5/6 - 8*c**3/3 - 18*c. Let n(x) be the second derivative of l(x). Factor n(v).
4*v*(v + 5)*(4*v - 1)
Let m(n) = n. Let a(v) = -5*v - 22. Let l(o) = 2*a(o) + 4*m(o). Let c be l(-8). Suppose -4/3*t + 0 + 3*t**3 - t**5 + 0*t**2 - 2/3*t**c = 0. Calculate t.
-2, -2/3, 0, 1
Let h(v) be the third derivative of 2*v**2 - 1/20*v**5 + 0 + 0*v**3 + 1/24*v**4 + 0*v. Factor h(i).
-i*(3*i - 1)
Let p(v) = v**2 + 8*v + 16. Let m be p(-4). Suppose 4*z = -9*q + 4*q - 20, -q - 4*z - 20 = 0. Find o such that m + 3/2*o**3 - o**2 + q*o = 0.
0, 2/3
Let -22/19*c + 20/19*c**2 + 2/19 = 0. What is c?
1/10, 1
Let i(p) be the third derivative of 0*p**4 + 2/21*p**7 + 0*p**3 - 4*p**2 + 0*p + 0 - 3/5*p**5 - 1/10*p**6 - 1/84*p**8. Factor i(b).
-4*b**2*(b - 3)**2*(b + 1)
Let l(g) be the second derivative of -g**5/110 - 4*g**4/33 - 7*g**3/33 - 89*g. Factor l(h).
-2*h*(h + 1)*(h + 7)/11
Let n = 402 - 402. Let s(z) be the first derivative of 4 + 0*z + n*z**3 + 1/9*z**2 - 1/18*z**4. Determine y so that s(y) = 0.
-1, 0, 1
Factor 2/5*v**2 - 2/5*v**3 + 16/5*v - 24/5.
-2*(v - 2)**2*(v + 3)/5
Let c(a) be the first derivative of a**6/120 + a**5/40 - 31*a - 32. Let o(i) be the first derivative of c(i). Factor o(g).
g**3*(g + 2)/4
Determine w, given that 29*w**4 + 92*w**2 + 7*w**4 - 33*w + 61*w**2 - 3*w**5 + 3*w**2 - 126*w**3 - 30*w = 0.
0, 1, 3, 7
Suppose 1/3*q**3 - 17/3*q**2 + 25*q - 33 = 0. Calculate q.
3, 11
Let n(r) be the second derivative of -r**7/42 + r**6/30 + 9*r**5/20 - 5*r**4/12 - 8*r**3/3 + 6*r**2 - 91*r. Suppose n(d) = 0. Calculate d.
-2, 1, 3
Let f(v) be the third derivative of -v**6/24 - 7*v**5/12 - 5*v**4/3 + 40*v**3/3 + v**2 + 47*v. Suppose f(s) = 0. What is s?
-4, 1
Let i(u) be the third derivative of -u**8/336 - u**7/15 - 3*u**6/8 - 13*u**5/15 - 5*u**4/6 - 2*u**2 - 23. Suppose i(n) = 0. What is n?
-10, -2, -1, 0
Suppose 0 = -2*r + o + 9, o = 3*r - o - 12. Let m(b) be the first derivative of 0*b + 0*b**3 + 7/40*b**5 - 1/16*b**4 + 0*b**2 - 3 - 5/48*b**r. Factor m(d).
-d**3*(d - 1)*(5*d - 2)/8
Let f(p) be the second derivative of p**6/540 + p**5/270 + 9*p**2/2 + 2*p. Let a(n) be the first derivative of f(n). Solve a(d) = 0 for d.
-1, 0
Factor -200*x**3 - 10*x**2 - 36*x + 133*x - 100 + 110*x**4 + 108*x - 5*x**5.
-5*(x - 20)*(x - 1)**3*(x + 1)
Let y(j) be the first derivative of 0*j + 0*j**3 - 5 + j**2 + 0*j**5 + 0*j**4 - 1/40*j**6. Let h(t) be the second derivative of y(t). Factor h(u).
-3*u**3
Let m(r) be the first derivative of -400/3*r - 4/9*r**3 - 46 - 40/3*r**2. Factor m(w).
-4*(w + 10)**2/3
Let f(q) be the second derivative of q**4/28 - 3*q**3/7 + 27*q**2/14 + 9*q + 10. Factor f(k).
3*(k - 3)**2/7
Suppose 0 = 225*n - 249*n + 72. Let r(y) be the first derivative of -1/9*y**n + 9 + 0*y + 0*y**2. Let r(g) = 0. What is g?
0
Suppose -4*j + 6 = -6. Suppose 3 = -j*o - 24. Let k(h) = 4*h**2. Let b(q) = -8*q**2 - q. Let z(i) = o*k(i) - 4*b(i). Find m such that z(m) = 0.
0, 1
Let v(b) be the second derivative of -b**4/4 + 65*b**3 - 12675*b**2/2 + 9*b - 22. Suppose v(w) = 0. What is w?
65
Factor 1/7*h**3 + 7*h + 0 + 2*h**2.
h*(h + 7)**2/7
Let h(v) be the third derivative of 5*v**8/84 + 32*v**7/105 + 17*v**6/30 + 2*v**5/5 - 67*v**2. Factor h(l).
4*l**2*(l + 1)**2*(5*l + 6)
Let k = 37/125 - -14/375. Factor -1/3*g**3 + 1/3*g**4 + k*g + 0 - 1/3*g**2.
g*(g - 1)**2*(g + 1)/3
Let y(g) = 75*g**4 + 427*g**3 + 588*g**2 + 270*g + 31. Let d(m) = 150*m**4 + 855*m**3 + 1175*m**2 + 540*m + 65. Let u(r) = -3*d(r) + 5*y(r). Solve u(v) = 0.
-4, -1, -2/5, -1/3
Determine c so that 0 - 3/8*c**5 - 15/8*c**4 - 15/4*c + 39/8*c**2 + 9/8*c**3 = 0.
-5, -2, 0, 1
Let n(k) = k**2 - 17*k - 18. Let i be n(11). Let m be (2/(-8) + 91/i)/(-2). Factor 0 + m*r - 2/3*r**4 + 2/3*r**2 - 2/3*r**3.
-2*r*(r - 1)*(r + 1)**2/3
Factor 0*a**2 - 9/2*a**3 + 3/2*a**4 + 6*a + 0.
3*a*(a - 2)**2*(a + 1)/2
Let l = -42 - -27. Let v = 28 + l. Factor -15*r**2 - v*r**3 + 27*r - r**3 - 30*r + 2*r**3.
-3*r*(r + 1)*(4*r + 1)
Let r(v) be the second derivative of 0*v**3 - 2*v + 0*v**2 + 1/30*v**4 - 9/100*v**5 + 0 + 7/150*v**6. Factor r(j).
j**2*(j - 1)*(7*j - 2)/5
Let g be (60/(-300))/(1/(-20)). Let b(z) be the second derivative of 1/3*z**2 + 4/9*z**3 - 9*z + 1/6*z**g + 0. Determine i so that b(i) = 0.
-1, -1/3
Determine d so that -18/7 - 9/7*d**3 - 6*d**2 + 69/7*d = 0.
-6, 1/3, 1
Let u(v) be the first derivative of -1/2*v**4 - 6*v - 3/20*v**5 + 1 - 1/2*v**3 + 0*v**2. Let w(r) be the first derivative of u(r). Factor w(l).
-3*l*(l + 1)**2
Let t(v) be the second derivative of -v**8/504 + v**6/90 - v**4/36 - 11*v**2/2 - 14*v. Let g(q) be the first derivative of t(q). Find m such that g(m) = 0.
-1, 0, 1
Let u be 5/(75/(-27))*(-10)/3. Let f(n) be the second derivative of -8/5*n**2 + 1/5*n**4 + 0 + 1/10*n**5 + 1/75*n**u - 4/15*n**3 - 3*n. Factor f(x).
2*(x - 1)*(x + 2)**3/5
Let b(q) be the second derivative of 2*q**6/15 + q**5 + 3*q**4 + 14*q**3/3 + 4*q**2 + 14*q - 4. Find t such that b(t) = 0.
-2, -1
Suppose -2*r + 0*q + 8 = -4*q, -3*r + 2*q = -12. Suppose b + 3 = 2*o, -b - 3*b + 48 = r*o. Factor -h**3 + 2*h**3 - h**4 + 5*h**5 + 0*h**3 - b*h**5.
-h**3*(h + 1)*(2*h - 1)
Suppose 36 + i**4 + 56*i - 18*i**3 + 57*i**2 + i**2 - 134*i + i**4 = 0. Calculate i.
1, 2, 3
Let i(p) be the first derivative of -p**7/6 + 5*p**6/24 + p**5/6 + 3*p**2/2 - 4. Let c(s) be the second derivative of i(s). Factor c(d).
-5*d**2*(d - 1)*(7*d + 2)
Let h(y) be the second derivative of y**5/4 + 5*y**4/4 - 10*y. Factor h(q).
5*q**2*(q + 3)
Let g = -2027/1221 + 265/111. Factor 0 - 4/11*o**2 + 0*o + 2/11*o**5 - g*o**4 + 10/11*o**3.
2*o**2*(o - 2)*(o - 1)**2/11
Let o be ((-18)/(-15))/(320/(-78900)). Let f = o + 296. Factor -3/8*s - 1/8*s**2 + 1/4 + 3/8*s**3 - f*s**4.
-(s - 2)*(s - 1)**2*(s + 1)/8
Suppose -3*z + 2 = -5*i - 3, 0 = 3*i + 2*z - 16. Factor -4*f**2 + 6*f**i - 18*f + 16*f.
2*f*(f - 1)
Let f(k) be the first derivative of -4*k**5/5 - 16*k**4 - 284*k**3/3 - 112*k**2 + 576*k - 441. Suppose f(b) = 0. What is b?
-9, -4, 1
Let n be (-271)/(-45) - (-12)/(-2). Let d(q) be the third derivative of q**2 + n*q**6 - 13/90*q**5 + 0*q - 2/9*q**3 + 0 + 11/36*q**4. Factor d(h).
2*(h - 2)*(h - 1)*(4*h - 1)/3
Let d be ((-32)/5)/(18/(-45)). Let g be 