.
-y*(y - 1)**2*(y + 1)**2/4
Let z = -46 - -51. Suppose -z*m = -m. Factor 1/4*p**2 + p**3 + p**4 + 0 + m*p.
p**2*(2*p + 1)**2/4
Let h be (54*(-32)/(-1200))/(1/30). Factor -h*b**2 + 96/5*b**3 - 16/5*b**4 - 81/5 + 216/5*b.
-(2*b - 3)**4/5
Suppose 64 - 55 = 3*p. Let y(n) be the second derivative of 0*n**p - 1/30*n**5 + 0 + 6*n + 1/9*n**4 + 0*n**2. Factor y(v).
-2*v**2*(v - 2)/3
Let f(n) = 10*n**2 + 78*n + 16. Let y(u) = -2*u**2 - 15*u - 3. Let s(b) = 3*f(b) + 16*y(b). Let s(g) = 0. Calculate g.
-3, 0
Let z(i) be the first derivative of -30 + 8/7*i**2 + 12/35*i**5 + 0*i + 32/21*i**3 - 11/7*i**4. Let z(v) = 0. Calculate v.
-1/3, 0, 2
Let w be (18 - (7 + -4))/(1/1*4). Factor 3/2*d - 9/4*d**2 + 0 - w*d**3.
-3*d*(d + 1)*(5*d - 2)/4
Suppose 7*c - 3*c = 4*z - 28, -3*z - 5*c = 3. Let r(y) be the first derivative of -3/4*y**z - y**3 + 3/2*y**2 + 3*y - 1. Factor r(d).
-3*(d - 1)*(d + 1)**2
Factor 144/7 - 1200/7*k + 2500/7*k**2.
4*(25*k - 6)**2/7
Let j = -42614/15 + 2842. Let k(g) be the third derivative of 0*g - j*g**5 - 5/6*g**4 + 4/3*g**3 + 0 + g**2 - 3/10*g**6. Factor k(p).
-4*(p + 1)**2*(9*p - 2)
Let c be (-11)/1 - 36751/(-1542). Find y such that -2/3 + 121/6*y**3 - c*y**2 - 20/3*y = 0.
-2/11, 1
Let m = -447 - -1346/3. Factor -5/6*v**2 - 5/2*v - m.
-5*(v + 1)*(v + 2)/6
Let d(m) be the second derivative of -m**4/54 + 5*m**3/27 - 4*m**2/9 - 11*m - 5. Determine z so that d(z) = 0.
1, 4
Let n(t) be the second derivative of 1/15*t**6 - 12*t + 0*t**4 - t**2 + 2/3*t**3 - 1/5*t**5 + 0. Determine z so that n(z) = 0.
-1, 1
Let t(p) = 1. Let r(g) = -4*g**4 + 20*g**3 - 16*g**2 - 5. Let i(q) = r(q) + 5*t(q). Factor i(l).
-4*l**2*(l - 4)*(l - 1)
Let v(g) be the second derivative of g**8/26880 + g**7/5040 + g**6/2880 + 11*g**4/12 + 9*g. Let p(x) be the third derivative of v(x). Factor p(o).
o*(o + 1)**2/4
Let j be (-1682)/12 + (-1 - 4). Let g = -145 - j. Factor -g*u**3 + 0 + 4/3*u**2 - 8/3*u.
-u*(u - 4)**2/6
Let b = -593/6 - -99. Let d(y) be the second derivative of 0*y**2 - 1/15*y**6 - 3*y + 1/10*y**5 + 0*y**3 + 0 + b*y**4 - 1/21*y**7. Solve d(q) = 0.
-1, 0, 1
Let v(q) be the first derivative of 31 - 375*q - 225/2*q**2 - 3/4*q**4 - 15*q**3. Factor v(c).
-3*(c + 5)**3
Factor -20/3*s + 2/3*s**2 + 50/3.
2*(s - 5)**2/3
Factor -21/2*f + 3/2*f**2 + 9.
3*(f - 6)*(f - 1)/2
Suppose -5*f = -f - 2*g - 4, 0 = 5*f + 2*g - 23. Let s = -12 - -28. Factor -4*b**f - 3*b**2 + 4 + 0*b**3 - s*b**4 + 15*b**4 + 4*b.
-(b - 1)*(b + 1)*(b + 2)**2
Let m = -3166/45 + 354/5. Let k be -1*(0/(-1))/2. Factor k*y + m*y**3 + 0*y**2 + 0 - 2/3*y**4 + 2/9*y**5.
2*y**3*(y - 2)*(y - 1)/9
Factor 11 + 1/7*b**2 + 18/7*b.
(b + 7)*(b + 11)/7
Let q(s) be the first derivative of 7*s**3 - 321*s**2/2 + 90*s - 5. Factor q(v).
3*(v - 15)*(7*v - 2)
Let x be (-20)/(-9) + 4/(-18). Let w = 300 - 300. Factor 0*b - 2/9*b**x + w.
-2*b**2/9
Find u such that -1/11*u**3 - 8/11*u**2 + 1/11*u + 8/11 = 0.
-8, -1, 1
Factor 4*q**4 - 2*q**5 + 9163*q - 9161*q - 4*q**2 + 0*q**5.
-2*q*(q - 1)**3*(q + 1)
Let l(q) be the first derivative of -3*q**4/8 - 5*q**3/2 - 6*q**2 - 6*q + 85. Factor l(u).
-3*(u + 1)*(u + 2)**2/2
Let u be 70/210 - ((-20)/3)/5. Factor -u*g**3 + 1/2*g**5 - 1/6*g + 1/3*g**4 - 2*g**2 + 1/3.
(g - 2)*(g + 1)**3*(3*g - 1)/6
Let w = 50 + -47. Suppose -w*x + 12 = p - 6, p = x - 2. Factor 0*i**2 - 3/2*i**4 + 3/2 - 3*i + 3*i**p.
-3*(i - 1)**3*(i + 1)/2
Let -108/5*y - 208/5 - 2/5*y**2 = 0. Calculate y.
-52, -2
Let f(v) be the first derivative of v**6/27 - 34*v**5/15 + 403*v**4/9 - 200*v**3 - 2376*v**2 + 5184*v + 150. Let f(r) = 0. What is r?
-4, 1, 18
Let d(m) be the second derivative of 16*m - 1/2*m**2 - 1/6*m**3 + 0 - 1/48*m**4. Suppose d(z) = 0. What is z?
-2
Let j(t) = -t**4 - t**3 + t**2 + t + 1. Let b(i) = i**5 - i**4 + i**2 - i - 1. Let a(z) = -b(z) - j(z). Factor a(d).
-d**2*(d - 2)*(d - 1)*(d + 1)
Let n(x) be the first derivative of -2*x**3/15 - 98*x**2/5 - 4802*x/5 - 36. Solve n(h) = 0.
-49
Factor 1/9*q**2 + 28/9 + 11/9*q.
(q + 4)*(q + 7)/9
Let x be (5 - 3)/((-2)/(-305)). Find s, given that 4*s**5 + 3*s**3 + 12*s**4 - 8*s + s**3 - 317*s**2 + x*s**2 = 0.
-2, -1, 0, 1
Suppose -33 + 49 = 4*n. Find q such that 5*q**n - 104*q**2 + 3*q**3 + 94*q**2 - 4*q**4 = 0.
-5, 0, 2
Let p be ((-15)/6)/(8/(-16)). Suppose 57*b**4 - 3*b**2 - 24*b**5 - 29*b**4 - p*b**2 + 4*b**3 = 0. What is b?
-1/2, 0, 2/3, 1
Let d be -6 + (-1 - -3)*(-390)/(-60). Let y(a) be the first derivative of -d - 12/5*a**4 + 6/5*a**3 + 0*a + 32/25*a**5 - 1/5*a**2. Find c such that y(c) = 0.
0, 1/4, 1
Let o be (-60)/15 - (3 - (-42)/(-6)). Factor -4/5*r**3 - 2/5*r**4 + o*r**2 + 4/5*r + 2/5.
-2*(r - 1)*(r + 1)**3/5
Suppose -7*y - 9 = -10*y. Determine f, given that -298*f**2 + 68*f**4 + 19*f**3 + 73*f**y + 160*f - 24 + 2*f**4 = 0.
-3, 2/7, 2/5, 1
Let a(r) be the second derivative of -25*r + 9/98*r**7 + 4/7*r**3 + 3/14*r**6 - 3/10*r**5 + 0*r**2 + 0 - 3/7*r**4. Let a(b) = 0. What is b?
-2, -1, 0, 2/3
Let t = -192 - -192. Let p(i) be the third derivative of 1/3*i**3 + 0 - 1/8*i**4 + 1/60*i**5 + t*i - 7*i**2. Solve p(h) = 0 for h.
1, 2
Let n(x) be the first derivative of -x**3/6 - 3*x**2/4 - x - 16. Solve n(y) = 0.
-2, -1
Let f(r) be the second derivative of r**4/12 + 17*r**3/6 + 16*r**2 - 16*r. Let x be f(-15). Factor -2/5*l**3 + 0*l**x + 2/5*l + 0.
-2*l*(l - 1)*(l + 1)/5
Let t(h) = -h**2 - 2*h + 3. Suppose -3*j - 2 = 2*g - 12, -3*j + 5 = g. Let l be t(j). Determine v so that -3/4*v**4 + 15/4*v**2 + 0 + 9/4*v + 3/4*v**l = 0.
-1, 0, 3
Let b be 4895/(-178)*(-8)/22. Let d(q) be the first derivative of -q**5 - 25/4*q**4 - b*q**3 + 10*q**2 + 40*q - 5. What is n in d(n) = 0?
-2, 1
Find i, given that 18*i**2 + 4*i + 9374*i**3 - 2*i**2 - 9378*i**3 - 16 = 0.
-1, 1, 4
Suppose 5*s = 2*h - 6, 35*s - 9 = 37*s - 3*h. Factor s*k - 1/8*k**3 + 1/8*k**4 + 0*k**2 + 0.
k**3*(k - 1)/8
Let s(i) be the third derivative of -17*i**2 + 1/12*i**5 + 0*i + 0 + 25/24*i**4 + 0*i**3. Let s(q) = 0. Calculate q.
-5, 0
Suppose -4*y = 2*a + 170, -5*y + 0*a = a + 208. Let n = 46 + y. Suppose 5/7*j**3 - 9/7*j**2 + 2/7*j + 9/7*j**4 - j**n + 0 = 0. Calculate j.
-1, 0, 2/7, 1
Let y be 5/((-35)/(-28)) - -1. Let c(u) be the third derivative of 0*u**3 + 0*u**y - 1/420*u**6 + 0*u**4 + 0 + 5*u**2 + 1/735*u**7 + 0*u. Factor c(p).
2*p**3*(p - 1)/7
Let b(z) = 10*z - 2*z**2 - 14*z**2 + z**2 + 60. Let p(j) = 5*j**2 - 3*j - 20. Let k(y) = -3*b(y) - 10*p(y). Let k(a) = 0. What is a?
-2, 2
Let l(o) = -8*o - 1. Let q be l(-1). Let m be q/(1 + -4 + 4). Solve 6*b**2 - b**2 - m*b**2 = 0 for b.
0
Let x(t) = t - 2. Let p be x(-1). Let l = p + 7. Factor l*q + 4 - q**2 - 8 + 0*q**2.
-(q - 2)**2
Let q(t) be the second derivative of t + 21/2*t**4 - 98/3*t**3 + 11 - t**5 + 1/30*t**6 - 343/2*t**2. Factor q(w).
(w - 7)**3*(w + 1)
Let f(s) be the third derivative of -s**7/840 - s**6/90 - s**5/24 - s**4/12 - s**3 - 3*s**2. Let d(x) be the first derivative of f(x). Factor d(g).
-(g + 1)**2*(g + 2)
Solve 0 + 1/6*y**2 - 1/3*y = 0.
0, 2
Let u(r) be the third derivative of 0*r - 1/120*r**5 - 16*r**2 + 1/12*r**4 - 1/4*r**3 + 0. Let u(y) = 0. Calculate y.
1, 3
Let a(o) be the third derivative of o**7/42 + o**6/24 - o**5/6 - 2*o**2 - 13*o. Factor a(r).
5*r**2*(r - 1)*(r + 2)
Factor 1410/11*u**2 - 3158/11*u**3 - 192/11*u + 8/11 - 882/11*u**5 + 2814/11*u**4.
-2*(u - 1)**3*(21*u - 2)**2/11
Let n = 44982 + -404830/9. Let d = 97/558 + 3/62. Suppose d*t**3 + n - 8/9*t - 2/9*t**2 = 0. Calculate t.
-2, 1, 2
Let j(t) be the second derivative of -t**5/20 + t**4/12 + t**3 + 17*t. Factor j(v).
-v*(v - 3)*(v + 2)
Let y(x) be the third derivative of -x**7/42 + 29*x**6/24 - 27*x**5/2 - 440*x**4/3 - 1280*x**3/3 - 4*x**2 - 26. Determine a, given that y(a) = 0.
-2, -1, 16
Let n = -52 - -45. Let l(y) = -9*y**2 + 6*y. Let b(k) = -k - 6. Let o be b(0). Let c(q) = 8*q**2 - 6*q. Let a(f) = n*c(f) + o*l(f). Let a(z) = 0. Calculate z.
0, 3
Let z(d) = -d**3 + 3*d**2 + 6*d - 4. Let t be z(4). Suppose -13*g + 4*g**3 - 4*g + g - 12 - t*g**2 - 4*g = 0. What is g?
-1, 3
Let z(j) = -j**3 - 7*j**2 + 4*j - 30. Let o be z(-8). Let c = 12 - 34/3. Solve c*x + 1/3 + 1/3*x**o = 0.
-1
Determine a, given that 1/3*a**4 - 2/3*a**3 + 0*a + 1/6*a**5 + 0 - 4/3*a**2 = 0.
-2, 0, 2
Let g be (10 - 9) + (-35)/(-1). Let h be 12/g - 238/(-6). Factor 4*c**2 + 4*c**5 - 9*c**3 + 12*c**4 + h*c**3 