, -1
Let y = 2 - -10. Suppose -4*s = 2*g - 16, -3*g + y = 2*s - 0*s. Factor n**2 + g - n + 6*n - 2*n.
(n + 1)*(n + 2)
Let t(u) be the third derivative of 1/25*u**5 + 1/200*u**6 + 0 + 4*u**2 + 1/5*u**3 + 1/8*u**4 + 0*u. Factor t(y).
3*(y + 1)**2*(y + 2)/5
Let d(o) be the third derivative of -6*o**2 + 1/4*o**4 + 1/8*o**6 + 9/20*o**5 + 0*o + 0*o**3 - 1/16*o**8 + 0 - 9/70*o**7. Suppose d(j) = 0. Calculate j.
-1, -2/7, 0, 1
Suppose 218*m - 468 = 101*m. Factor 2/7*j**2 + 14 - m*j.
2*(j - 7)**2/7
Let d be ((-2)/14)/(116/(-203)). Factor -d*t**2 - 1/4 + 1/2*t.
-(t - 1)**2/4
Let x be (1/(-12))/((-29)/116). Solve 2/3*t + x + 1/3*t**2 = 0 for t.
-1
Let z(x) = -6*x**3 - 64*x**2 + 22*x + 2. Let b be z(-11). Determine n so that -9/7*n**4 + 0*n + 3/7*n**5 + 0 + 9/7*n**3 - 3/7*n**b = 0.
0, 1
Let d = -42 + 48. Let a(r) be the second derivative of -r - 1/12*r**4 - 1/42*r**7 + 0 + 1/20*r**5 + 0*r**3 + 0*r**2 + 1/30*r**d. Suppose a(g) = 0. What is g?
-1, 0, 1
Let b be 42/49 - 4/7. Let o be ((-20)/(-8))/(3/(12/5)). Determine z, given that 0 - b*z**o - 4/7*z = 0.
-2, 0
Solve 0*u + 3/5*u**3 + 0 + 6/5*u**2 - 3/5*u**4 = 0.
-1, 0, 2
Let w(a) be the first derivative of -a**5/12 + 5*a**4/12 - 5*a**3/6 - 8*a**2 - 13. Let p(s) be the second derivative of w(s). Factor p(t).
-5*(t - 1)**2
Let v(q) = -q**3 - q**2 + q + 1. Let k(j) = -j**3 - 2*j**2 - j. Let d = 77 + -79. Let m(s) = d*v(s) + k(s). Factor m(r).
(r - 2)*(r + 1)**2
Let h(p) be the second derivative of -5*p**7/42 - 32*p**6/3 - 184*p**5 + 3840*p**4 - 17280*p**3 - 768*p. Factor h(l).
-5*l*(l - 4)**2*(l + 36)**2
Let x(m) be the first derivative of 12*m - 8*m**2 + 4/3*m**3 - 27. Let x(n) = 0. Calculate n.
1, 3
Find l, given that 102/11 - 100/11*l - 2/11*l**2 = 0.
-51, 1
Let m be 1/((-182)/317 - 0)*-2. Let i = 3/182 + m. Determine v, given that -1 + i*v - v**2 - 3/2*v**3 = 0.
-2, 1/3, 1
Let m(f) be the first derivative of -1/3*f**3 + 0*f + 5/16*f**4 + 0*f**2 - 13 - 1/20*f**5. Let m(h) = 0. Calculate h.
0, 1, 4
Suppose 6 = -4*q + p - 14, 4*p + 34 = -3*q. Let w be (7/(-42))/(4/q). Factor -3/4*c**4 + 0 - 1/2*c + w*c**5 + 3/4*c**2 + 1/4*c**3.
c*(c - 2)*(c - 1)**2*(c + 1)/4
Let b(l) = -37*l - 50*l + 69*l. Let y(n) = n**2 - n. Let i(z) = -b(z) + 3*y(z). Factor i(p).
3*p*(p + 5)
Factor 5/4*r**4 + 5*r**3 + 0 - 5/4*r**2 - 5*r.
5*r*(r - 1)*(r + 1)*(r + 4)/4
Let y(c) = -2*c**4 + 13*c**3 + 4*c**2 - 14*c - 18. Let n(a) = -2*a**4 + 12*a**3 + 4*a**2 - 16*a - 18. Let v(z) = 5*n(z) - 4*y(z). Factor v(u).
-2*(u - 3)**2*(u + 1)**2
Let 2/13*d - 6/13*d**4 - 6/13 + 2/13*d**5 - 4/13*d**3 + 12/13*d**2 = 0. Calculate d.
-1, 1, 3
Let s(w) be the second derivative of 0*w**4 + 0 - 1/100*w**5 + 1/30*w**3 - 21*w + 0*w**2. Factor s(n).
-n*(n - 1)*(n + 1)/5
Solve 14/5*p**2 - 32/5 - 2/5*p**5 - 46/5*p**3 + 18/5*p**4 + 48/5*p = 0.
-1, 1, 4
Let a(h) = 2*h**2 + 2*h - 2. Let c be a(-2). Let g(v) be the second derivative of -5/6*v**4 + 1/5*v**5 - 4/3*v**3 + 3*v**c - 2*v + 0. Factor g(o).
2*(o - 3)*(o + 1)*(2*o - 1)
Let t(u) be the first derivative of -u**6/3 + 12*u**5/5 - 2*u**4 - 4*u**3 + 5*u**2 - 334. Let t(j) = 0. What is j?
-1, 0, 1, 5
Let a(i) be the third derivative of i**7/630 + 7*i**6/540 + i**5/60 - i**3/3 + 6*i**2. Let m(u) be the first derivative of a(u). Factor m(d).
2*d*(d + 3)*(2*d + 1)/3
Let w be ((-160)/(-10))/8 - 52/30. Let d(o) be the first derivative of 1/12*o**4 + 0*o**3 + 1 + 0*o + 0*o**2 - w*o**5. Factor d(v).
-v**3*(4*v - 1)/3
Let b be 15/35 - 217/735. Let a(g) be the third derivative of 0 - b*g**5 + 0*g + 0*g**4 - 2*g**2 + 0*g**3 - 1/30*g**6. Factor a(v).
-4*v**2*(v + 2)
Let h(n) be the second derivative of 3*n**5/20 + 4*n**4/3 + n**3/2 - 5*n**2 - 2*n + 57. Factor h(y).
(y + 1)*(y + 5)*(3*y - 2)
Let v be 4 + 28605/40*(-2)/366. Let h = v + 2/61. Suppose -1/8*m**2 + h*m + 0 = 0. Calculate m.
0, 1
Factor 126*w**2 - 46*w + 34*w**3 - 61*w + 2*w**4 - 43*w - 12*w.
2*w*(w - 1)*(w + 9)**2
Suppose 4*g - 2*g - 113 = -5*h, 4*g = -2*h + 58. Determine f, given that 11*f**2 + 9 + 2*f**3 + 6*f**2 + h*f + f**3 - 2*f**2 = 0.
-3, -1
Let k(c) = -c**3 - 32*c**2 - 2*c - 61. Let v be k(-32). Let r(o) be the second derivative of -1/6*o**4 - 2*o**v - 5*o - 9*o**2 + 0. Let r(f) = 0. Calculate f.
-3
Let d = -11291/2 + 5647. Determine f so that -3/2*f + d*f**2 - 1/2*f**3 + 1/2 = 0.
1
Let j(z) be the third derivative of 4/39*z**3 + 0 + 1/390*z**5 + 0*z + 7*z**2 - 1/39*z**4. Solve j(m) = 0 for m.
2
Factor 66/5 - 3/5*j**2 + 27/5*j.
-3*(j - 11)*(j + 2)/5
Let x(r) = 3*r - 17. Let f be x(7). Factor -2*z**2 + 228 - 228 - z**f + 3*z**3.
-z**2*(z - 2)*(z - 1)
Factor -16/13*t**3 + 0 + 0*t - 2/13*t**4 + 18/13*t**2.
-2*t**2*(t - 1)*(t + 9)/13
Let 56*q - 14*q**2 - 75 + 3*q**3 - 30*q**2 + 11*q**2 + 49*q = 0. Calculate q.
1, 5
Let o(u) = -3*u**2 + 28*u + 26. Let q be o(10). Let y(j) be the first derivative of -q + 1/4*j**4 + 0*j + 0*j**5 - 1/12*j**6 - 1/4*j**2 + 0*j**3. Factor y(d).
-d*(d - 1)**2*(d + 1)**2/2
Let u be 6/(-16) + 406/16. Let n = u - 13. Factor 0*w**3 + n*w**2 + 0*w**3 - 2 - w + 7*w**3 + 4*w.
(w + 1)**2*(7*w - 2)
Let -1/3 - 1/6*x**3 - 1/3*x**4 - 1/6*x + x**2 = 0. Calculate x.
-2, -1/2, 1
Suppose 15 = 3*u, -5*n + 5*u - 37 = 8. Let w(l) = -l**2 - 7*l - 10. Let t be w(n). Factor -t*d**2 - 6*d**2 + 5*d**2 + 9*d - 6.
-3*(d - 2)*(d - 1)
Determine k so that -11*k - 246*k**3 + 244*k**2 + 411*k**2 + 586*k - 500 - 180*k**4 - 354*k**3 = 0.
-4, -1, 5/6
Let m be (-4)/90*414/(-36) - 1/9. Solve -8/5*x**3 + 0*x + 0 + 0*x**2 - m*x**4 = 0.
-4, 0
Let r(l) be the first derivative of l**7/490 + l**6/280 - l**5/70 + 11*l**2/2 - 14. Let x(v) be the second derivative of r(v). Factor x(b).
3*b**2*(b - 1)*(b + 2)/7
Let i be (3*(-1 + 0))/((-180)/80). Let j(h) be the first derivative of 0*h**2 + 0*h + 32/5*h**5 - 7/3*h**6 - 11/2*h**4 + i*h**3 - 1. Factor j(y).
-2*y**2*(y - 1)**2*(7*y - 2)
Let a be ((-3)/((-81)/(-186)))/((-6)/3) + -3. Factor -a*v**2 - 2/9*v**3 - 2/9*v + 0.
-2*v*(v + 1)**2/9
Let n(v) be the second derivative of -8*v + 3/8*v**3 + 5/32*v**4 + 0 + 3/16*v**2. Find l such that n(l) = 0.
-1, -1/5
Let i(u) be the second derivative of u**8/1344 - u**7/84 + 5*u**6/144 - 5*u**4/3 - 15*u. Let o(q) be the third derivative of i(q). Solve o(c) = 0.
0, 1, 5
Let t(c) be the first derivative of -15/4*c**4 + c**5 - 5/2*c**2 + 5*c**3 + 0*c - 5. Find z, given that t(z) = 0.
0, 1
Let g(p) be the third derivative of -1/48*p**4 - 1/960*p**6 + 0*p**3 + 9*p**2 - 1/120*p**5 + 0*p + 0. Find i, given that g(i) = 0.
-2, 0
Let b(i) be the third derivative of 512*i**7/35 - 112*i**6/15 - 52*i**5/5 - 15*i**4/4 - 2*i**3/3 - 107*i**2 - 1. What is t in b(t) = 0?
-1/8, 2/3
Let d = 9358 - 18713/2. Factor -1 + 1/2*f**3 + 0*f**2 - d*f.
(f - 2)*(f + 1)**2/2
Let b = -1/898 - -451/1796. Factor 0 - 3/4*x - b*x**3 + x**2.
-x*(x - 3)*(x - 1)/4
Let m be (3/21)/(6/42). Let n = m + 36. Factor n*v - 13*v + 12*v**2 - 15*v + 3*v**3.
3*v*(v + 1)*(v + 3)
Let b = 38 - 33. Suppose -8*h**2 + h**4 - b*h**4 + 73*h**3 - 85*h**3 = 0. Calculate h.
-2, -1, 0
Let f(r) be the third derivative of 0 + 1/6*r**4 + 7*r**2 + 1/35*r**7 + 1/5*r**5 + 1/336*r**8 + 13/120*r**6 + 0*r + 0*r**3. Find u such that f(u) = 0.
-2, -1, 0
Let p be 1468/4404 - 2/(-12). Determine x so that -2*x + p*x**3 + x**2 - 4 = 0.
-2, 2
Factor -3760*r - 21*r**3 + 476*r**2 + 566 - 25*r**3 + 10*r**3 + 234 + 252*r**2.
-4*(r - 10)**2*(9*r - 2)
Let x(z) be the first derivative of 3*z**4/10 - 148*z**3/15 - 27*z**2/5 + 20*z - 17. Factor x(d).
2*(d - 25)*(d + 1)*(3*d - 2)/5
Let i(w) be the third derivative of -w**7/420 + w**6/20 - 11*w**5/60 - 7*w**4/4 - 49*w**3/12 + 3*w**2 - 6*w. Factor i(y).
-(y - 7)**2*(y + 1)**2/2
Let p be ((-5)/(-6))/(18/24*5). Determine c so that -2/9*c - 2/9*c**4 - p*c**5 + 4/9*c**3 - 2/9 + 4/9*c**2 = 0.
-1, 1
Suppose 10*z = 11*z - 4. Determine j so that -j**2 + 5*j**2 - z*j - 6*j**2 = 0.
-2, 0
Suppose -29*y = 446 - 533. Suppose -1/6*k**y + 0*k**2 + 0 + 0*k = 0. Calculate k.
0
Let z be (-4)/(-10) - (-288)/80. Factor -z*v**2 - 4*v**4 + 5*v**3 + 3*v**4 + 9*v + 4*v**4 - 13*v.
v*(v - 1)*(v + 2)*(3*v + 2)
Suppose 4*j = 5*n + 225, -2*n + j - 90 = -0*j. Let r be (-15)/n - 52/(-6). Let -r*y**3 - 40*y + 16 + 36*y**2 + 2*y**4 - 5*y**3 + 0*y**3 = 0. Calculate y.
1, 2
Let n be 11/(-9)*96/(-704). Suppose -1/6*a - n + 1/6*a**2 + 1/6*a**3 = 0. What is a?
-1, 1
Let b be