q + j + 2. Suppose 2*o**3 - 1 - 5*o**3 + q + 6*o**2 = 0. Calculate o.
0, 2
Let v(b) be the third derivative of -b**5/180 - 71*b**4/18 - 10082*b**3/9 - b**2 + 236. Find t, given that v(t) = 0.
-142
Suppose -11*m - 2*m + 78 = 0. Let h be 3 + ((-4)/(-16))/(m/(-40)). Factor -4/3*v**3 + h*v + 4/3*v**2 - 4/3.
-4*(v - 1)**2*(v + 1)/3
Let w(k) be the third derivative of 3*k**7/70 - 2*k**6/5 - 3*k**5/20 + 9*k**4/2 + 10*k**3 + 286*k**2. Solve w(p) = 0.
-1, -2/3, 2, 5
Let j(d) be the second derivative of -2*d**7/21 + 2*d**6/5 - 3*d**5/5 + d**4/3 + 55*d + 2. Suppose j(f) = 0. Calculate f.
0, 1
Let u(j) be the first derivative of 8/15*j**3 - 5 - 12/25*j**5 + 6/5*j**2 - 2/15*j**6 + 4/5*j - 2/5*j**4. Factor u(f).
-4*(f - 1)*(f + 1)**4/5
Let v be ((-52)/65)/((-87)/15 - -4). Factor 2/9 + 2/9*j**2 - v*j.
2*(j - 1)**2/9
Let m(i) be the second derivative of 0 - 6*i - 8*i**3 - 67/10*i**5 - 19/2*i**4 - 13/5*i**6 - 3/7*i**7 - 4*i**2. Suppose m(u) = 0. Calculate u.
-1, -2/3
Factor 0 - t**2 + 3/2*t - 1/2*t**3.
-t*(t - 1)*(t + 3)/2
Let d = -39 + 44. Let 2 - 7 + d + s**2 - s**4 + s**3 - s = 0. What is s?
-1, 0, 1
Let k(x) = 9*x**3 + 30*x**2 + 45*x + 20. Let w(j) = 19*j**3 + 60*j**2 + 90*j + 40. Let u(y) = -9*k(y) + 4*w(y). Factor u(g).
-5*(g + 1)**2*(g + 4)
Let n(q) be the first derivative of q**6/9 - q**5/15 - 2*q**4/3 + q**3/9 + q**2 + 208. Solve n(w) = 0.
-3/2, -1, 0, 1, 2
Suppose 125 = 2*f + 11. Find i, given that -178*i**2 - 17 + 144*i - 10 + 43*i**2 - f*i**2 = 0.
3/8
Solve -1/4*j**5 - 19239*j + 18*j**4 - 1857/4*j**3 + 9977/2*j**2 + 23958 = 0.
3, 22
Factor -81/2 - 5*v**2 + 1/4*v**3 + 117/4*v.
(v - 9)**2*(v - 2)/4
Let b(r) = -3*r**2 + 43*r + 32. Let j(u) = 2*u**2 - 22*u - 16. Suppose 0 = -3*q - 0*q + 18. Let a(l) = q*b(l) + 11*j(l). Factor a(i).
4*(i + 2)**2
Let s(g) be the second derivative of 0*g**5 + 0 + 0*g**2 - 5*g + 1/10*g**6 - 3/4*g**4 + g**3. Solve s(d) = 0.
-2, 0, 1
Let v = -21 + 40. Let a = v - 17. Factor a*k**2 + k**2 + 3*k**2 - 2*k - 4*k**2.
2*k*(k - 1)
Suppose -25*m + 6 + 194 = 0. Suppose 3*a - m*a - 20 = -2*h, -4*h - 12 = 3*a. Find i, given that 1/2*i**5 + 0 + 0*i**2 - i**3 + 1/2*i + h*i**4 = 0.
-1, 0, 1
Let n(j) = 4*j**2 + 10*j - 2. Let s(u) = -u**3 + u**2 - u + 1. Let p(f) = n(f) + 2*s(f). Factor p(v).
-2*v*(v - 4)*(v + 1)
Let 475*g**4 - 17*g**5 + 305*g**3 + 142*g**5 - 475*g**2 + 180 - 240*g - 10*g**3 = 0. Calculate g.
-2, -1, 3/5
Factor 7*s**2 + 5*s**2 - 10*s + 6*s**2 - 6 - 12*s**2 + 10*s**3.
2*(s - 1)*(s + 1)*(5*s + 3)
Factor 0 + 56/3*x**3 + 0*x - 8/3*x**2 - 98/3*x**4.
-2*x**2*(7*x - 2)**2/3
Let f(p) be the first derivative of -2*p**5/15 - 7*p**4/3 - 40*p**3/3 - 50*p**2/3 + 250*p/3 - 56. Factor f(g).
-2*(g - 1)*(g + 5)**3/3
Let r(o) be the first derivative of -3*o**4/16 - o**3/4 + 15*o**2/4 - 6*o + 75. Find n, given that r(n) = 0.
-4, 1, 2
Let -51/4 - 1/4*f**2 - 13*f = 0. Calculate f.
-51, -1
Let m(f) = -f**2 + 11*f + 39. Let s be m(-6). Let k = s - -127/2. Factor 1/2*g**4 - 1/2*g**2 + 0 + 1/2*g**3 - k*g.
g*(g - 1)*(g + 1)**2/2
Let y(o) be the first derivative of -o**4/10 + 26*o**3/15 - 48*o**2/5 + 72*o/5 - 54. Factor y(u).
-2*(u - 6)**2*(u - 1)/5
Let x(p) be the second derivative of -p**6/60 + 4*p**5/75 - p**4/60 - 2*p**3/15 - 7*p**2/2 - 10*p. Let t(v) be the first derivative of x(v). Factor t(h).
-2*(h - 1)**2*(5*h + 2)/5
Let l(j) be the third derivative of j**5/210 - 17*j**4/84 + 16*j**3/21 + 168*j**2. Factor l(i).
2*(i - 16)*(i - 1)/7
Let f be 12/5 - (-10380)/(-4325). What is o in 4/3*o**3 + 0 - 2/3*o**4 + f*o - 2/3*o**2 = 0?
0, 1
Factor 0 + 0*o - 1/8*o**4 - 1/4*o**3 - 1/8*o**2.
-o**2*(o + 1)**2/8
Let v(x) = -6*x**2 - 4*x + 2. Suppose 6*b - 4*b - 8 = 0. Let f(w) = -w**2 - w. Let l(k) = b*f(k) - v(k). What is h in l(h) = 0?
-1, 1
Suppose 155 - 131 = 8*q. What is g in 4/3*g**q + 2/3*g**2 - 2/3*g**4 + 0 - 4/3*g = 0?
-1, 0, 1, 2
Let j(a) = 7*a**4 + 7*a**3 - 9*a**2 - 7*a + 7. Let d(z) = 8*z**4 + 8*z**3 - 8*z**2 - 8*z + 6. Let l(i) = -5*d(i) + 6*j(i). Determine k so that l(k) = 0.
-3, -1, 1, 2
Let t(r) be the third derivative of 0 - 1/42*r**7 + 0*r**3 - 3*r**5 + 0*r + 1/2*r**6 + 23*r**2 + 0*r**4. Factor t(o).
-5*o**2*(o - 6)**2
Let c(u) = -u**2 + 23*u - 49. Let k be (-2)/(-1) + (-11 - -13). Let n(p) = -p. Let z(t) = k*c(t) + 36*n(t). Find i such that z(i) = 0.
7
Let z be ((-44)/1 + -1)*(-18)/(116 + -8). Solve -25/6 - 5/2*v**2 + 5/6*v**3 - z*v = 0 for v.
-1, 5
Let s(d) be the third derivative of -d**7/420 + 7*d**6/120 - 2*d**5/5 - 7*d**4/24 + 49*d**3/12 - 15*d**2 - 4. Factor s(v).
-(v - 7)**2*(v - 1)*(v + 1)/2
Let q(p) be the third derivative of -1/420*p**7 + 1/16*p**4 - 1/120*p**5 + 0*p + 0 + 1/6*p**3 - 24*p**2 - 1/80*p**6. Let q(z) = 0. Calculate z.
-2, -1, 1
Let s be -13*(-2 - 18/(-11)). Let v = 1179/53 + -12121/583. Factor s*m + 14/11*m**2 - v.
2*(m + 4)*(7*m - 2)/11
Suppose -3*x**2 + 20*x - 34*x + 4*x**2 = 0. Calculate x.
0, 14
Suppose -4*g = 4*u - 8, 0*u + g + 13 = 4*u. Suppose -x = -u - 1. Factor -4*y**3 - x*y**3 + y**2 + y**2 + 2*y**4 + 2 - 8*y + 10*y**2.
2*(y - 1)**4
Let o(h) be the first derivative of -h**8/672 + h**6/240 + 3*h**2 + 20. Let s(k) be the second derivative of o(k). Factor s(b).
-b**3*(b - 1)*(b + 1)/2
Factor 8 + 52/5*c + 4/5*c**4 - 12/5*c**2 - 4*c**3.
4*(c - 5)*(c - 2)*(c + 1)**2/5
Let i(z) be the first derivative of 3*z**4/28 - 12*z**3/7 - 81*z**2/14 - 6*z - 17. Determine a, given that i(a) = 0.
-1, 14
Suppose -3632*m**3 - 161 + 8360*m**4 + 1420*m - 265*m**2 + 400*m**5 - 6063*m**3 + 48 - 112 + 5 = 0. Calculate m.
-22, -2/5, 1/4, 1
Factor -3364/3 - 1/3*a**2 + 116/3*a.
-(a - 58)**2/3
Let z = -9090 - -45453/5. Let k be 2/(2*(-2)/(-4)). Factor -3/5*p**k - z - 6/5*p.
-3*(p + 1)**2/5
Let g(f) be the third derivative of -11*f**8/1008 - f**7/18 - f**6/60 + 11*f**5/45 + f**4/9 - 544*f**2. Suppose g(v) = 0. What is v?
-2, -2/11, 0, 1
Let z(l) be the first derivative of -l**6/450 + l**5/50 - 4*l**3 - 12. Let m(s) be the third derivative of z(s). Suppose m(t) = 0. Calculate t.
0, 3
Factor -2304/5 + 3/5*z**3 + 87/5*z**2 + 96*z.
3*(z - 3)*(z + 16)**2/5
Let w(r) be the third derivative of r**8/84 + 2*r**7/35 - r**6/3 + 2*r**5/15 + 3*r**4/2 - 10*r**3/3 + 5*r**2 + 43. Factor w(b).
4*(b - 1)**3*(b + 1)*(b + 5)
Let a(i) = -9*i**2 + 21*i + 18. Let v(q) = q**2 - q. Let g(k) = a(k) + 6*v(k). Factor g(c).
-3*(c - 6)*(c + 1)
Let z = 2789 - 2787. Factor -1/4*i**z + 0 + 1/2*i.
-i*(i - 2)/4
Let i = -2671/6 + 897/2. Solve -i - 1/3*n**2 - 7/3*n = 0 for n.
-5, -2
Suppose 6 = 8*s - 7*s. Factor 9*b**3 + s*b - 2*b**4 + 15*b**2 - 4*b**5 + b**5 - b**4.
-3*b*(b - 2)*(b + 1)**3
Let j(t) be the second derivative of -47*t + 0 - 7/2*t**2 - t**3 + 1/12*t**4. Suppose j(s) = 0. Calculate s.
-1, 7
Let a = 14323/5 + -2864. What is w in -3/5*w - a*w**2 + 0 = 0?
-1, 0
Let s(h) be the first derivative of -2*h**3/27 - 7*h**2/3 - 12*h - 132. What is n in s(n) = 0?
-18, -3
Let f(m) be the third derivative of 0*m**7 + 0 + 1/900*m**6 + 0*m**3 - 1/2520*m**8 + 0*m**4 + 0*m**5 + 21*m**2 + 0*m. Determine z, given that f(z) = 0.
-1, 0, 1
Let i(h) be the first derivative of h**3/15 - 19*h**2/5 - 39*h/5 + 50. Let i(y) = 0. What is y?
-1, 39
Let o(j) be the second derivative of -j**5/60 + j**4/18 + 10*j**3/9 + 4*j**2 - 2*j - 25. Determine m, given that o(m) = 0.
-2, 6
Let y(i) be the second derivative of i**7/126 - i**6/10 + 11*i**5/60 + 7*i**4/12 - 173*i. Factor y(q).
q**2*(q - 7)*(q - 3)*(q + 1)/3
Determine m so that -2 - 1 + 611*m - 5 + m**2 - 604*m = 0.
-8, 1
Suppose 2*p + 4*h = 12, -40*p = -42*p + 2*h. Let 0 + 0*f**3 - 2/9*f**p + 0*f + 2/9*f**4 = 0. Calculate f.
-1, 0, 1
Let i be 6/((105/350)/((-2)/(-10))). Let g(s) = -s**3 + 5*s**2 - 3*s. Let p be g(4). Solve -8*x - 2*x**4 - i*x + 27*x**3 - 9*x**5 - p*x**4 = 0.
-2, -2/3, 0, 1
Let a(b) be the first derivative of 2*b**3/15 + b**2/10 - 97. Solve a(n) = 0 for n.
-1/2, 0
Find q, given that 1/5*q**2 - 14/5*q - 32/5 = 0.
-2, 16
Factor 1/5*p**3 + 18/5*p + 21/5*p**2 - 8.
(p - 1)*(p + 2)*(p + 20)/5
Let q(i) = i**3 + 15*i**2 - 17*i - 14. Let o be q(-16). Let v(l) be the second derivative of -1/60*l**5 + 0*l**3 - 4*l + 0*l**o + 0 + 1/36*l**4. Factor v(m).
-m**2*(m - 1)/3
Solve 24 + 7619*c + c**2 + 2*c**2 - 7601*c = 0.
-4, -2
Let d(z) be the third derivative of -z**6/30 + z**5/3 - z**4 + 47*z**2 - 2. Suppose d(n) = 0. What is n?
0, 2, 3
F