12 - 12. Let q be d + (2/(-3))/(-2). Determine u, given that 0 + q*u + 1/3*u**3 - 2/3*u**2 = 0.
0, 1
Let y = -125/21 - -44/7. Suppose 0 - 1/6*q**2 + y*q = 0. What is q?
0, 2
Let m = 1 + 1. Factor -8*v - v**2 + 12*v - 3*v**m.
-4*v*(v - 1)
Suppose -36 = -2*x + 5*m, -2*m = -4*x + x + 32. Let s be x/(-24) - 20/(-6). Suppose 2/3*c**5 + 0 + 0*c**2 - 4/3*c**s + 2/3*c + 0*c**4 = 0. Calculate c.
-1, 0, 1
Let j(k) be the first derivative of -1/18*k**4 - 2 + 0*k**2 + 0*k + 2/27*k**3. What is d in j(d) = 0?
0, 1
Let t(z) be the second derivative of -1/40*z**5 + 0*z**2 - 1/36*z**3 + 1/180*z**6 + 1/24*z**4 - 5*z + 0. Determine d so that t(d) = 0.
0, 1
What is s in -4/3 + 10/9*s + 2/9*s**2 = 0?
-6, 1
Let c be (-6)/4*20/(-45). Suppose 0*z + c*z**4 + 0 + 10/9*z**3 + 4/9*z**2 = 0. What is z?
-1, -2/3, 0
Factor -46*m**2 + 4*m**3 - 38*m**3 - 56*m - 4 - 2*m**4 - 20 + 18*m**3.
-2*(m + 1)*(m + 2)**2*(m + 3)
Let f be 3/(-1) + 6 - -6. Factor -3*i**4 + 3*i - f*i**2 + 6*i**3 + 0*i**4 + 3*i**3.
-3*i*(i - 1)**3
Suppose 0 = -g + 5*v - 12, 2*g + 3*v = -2*v + 21. Let 10*d - 10*d**3 + 12*d**2 + 2*d**g - 14*d = 0. Calculate d.
0, 1/2, 1
Let u = -27 - -28. Let q(a) be the first derivative of 0*a**2 + u + 1/5*a - 1/15*a**3. Suppose q(s) = 0. What is s?
-1, 1
Let x(w) = w**2 + 8*w + 9. Suppose 4*s - 5*n = 6*s + 34, 1 = s - 2*n. Let p be x(s). Find v, given that 4*v**p + v**2 - 6*v**2 - 1 + 2*v = 0.
1
Let r(d) be the third derivative of d**6/140 - d**5/105 - d**4/28 + 2*d**3/21 - 23*d**2. Find k, given that r(k) = 0.
-1, 2/3, 1
Let l = -19 - -31. Let u be 4/(-4) + 68/l. Let -14/3*d**2 - 4/3 - 4/3*d**3 - u*d = 0. Calculate d.
-2, -1, -1/2
Let q(p) be the second derivative of -p**7/14 + 2*p**6/5 - 3*p**5/4 + p**4/2 + 2*p. Find h, given that q(h) = 0.
0, 1, 2
Let b(p) be the third derivative of -p**8/756 + p**7/189 - p**6/135 + p**5/270 + 10*p**2. Suppose b(r) = 0. What is r?
0, 1/2, 1
Let b(z) be the third derivative of z**7/105 - 11*z**6/150 + 14*z**5/75 - 2*z**4/15 + 7*z**2. Determine o, given that b(o) = 0.
0, 2/5, 2
Let s be (-115)/(-105) + (-24)/36. Factor 0 + 0*p + s*p**2 - 3/7*p**3.
-3*p**2*(p - 1)/7
Let v(s) = -2*s**2 - 6*s + 4. Let z = -3 + 10. Suppose 20 = -z*q + 2*q. Let c(j) = -j**2 - j + 1. Let b(y) = q*c(y) + v(y). Factor b(t).
2*t*(t - 1)
Let j be 9 + (-1 - -2) + -4. Let x(p) be the third derivative of 0 + 1/84*p**4 - 1/210*p**5 - p**2 - 1/420*p**j + 0*p + 1/21*p**3. Find m such that x(m) = 0.
-1, 1
Let y(c) be the first derivative of 1 + 0*c + 2*c**2 - 4/5*c**5 + 4/3*c**3 - c**4. Find t, given that y(t) = 0.
-1, 0, 1
Factor -4/9*r + 2/9*r**2 + 0.
2*r*(r - 2)/9
Let c(h) be the third derivative of -243*h**6/200 - 81*h**5/50 - 9*h**4/10 - 4*h**3/15 - 21*h**2. Find x such that c(x) = 0.
-2/9
Let r(n) = -n**3 + 4*n**2 + 3*n - 3. Let o(w) = w**2 + w - 1. Let g be (-78)/24 + 1/4. Let b(y) = g*o(y) + r(y). Factor b(q).
-q**2*(q - 1)
Let x be (-5)/75*(-5)/2. Let z(l) be the second derivative of -x*l**4 + 1/15*l**6 + 1/21*l**7 + l - 1/10*l**5 + 0*l**2 + 0 + 0*l**3. Factor z(a).
2*a**2*(a - 1)*(a + 1)**2
Let p(n) = -2*n**5 + 4*n**3 - 4*n**2 - 4*n + 2. Let i(b) = 2*b**5 + b**4 - 4*b**3 + 4*b**2 + 5*b - 2. Let g(h) = 2*i(h) + 3*p(h). Solve g(o) = 0 for o.
-1, 1
Let a(q) be the third derivative of -q**8/168 - q**7/35 + q**6/60 + 7*q**5/30 - 4*q**3/3 - 23*q**2. Let a(x) = 0. What is x?
-2, -1, 1
Let m(a) be the first derivative of -a**5/50 - a**4/15 + 4*a**3/15 - 2*a**2 - 5. Let q(p) be the second derivative of m(p). Determine x so that q(x) = 0.
-2, 2/3
Suppose -48 = r + 51. Let o be 11/r + 2/6. Factor 0*m**3 - 4/9*m**2 + o + 0*m + 2/9*m**4.
2*(m - 1)**2*(m + 1)**2/9
Let i(x) = x**2 - 1. Let a(v) = -30*v + 30. Let h(b) = -a(b) - 3*i(b). Solve h(r) = 0.
1, 9
Let h(g) be the first derivative of -5*g**3/3 + 5*g**2 + 4. Find p such that h(p) = 0.
0, 2
Let l(c) be the third derivative of c**8/672 + c**7/140 - c**6/120 - c**5/20 + c**4/48 + c**3/4 + 2*c**2. What is r in l(r) = 0?
-3, -1, 1
Let q(t) be the third derivative of t**7/280 - t**6/60 + t**5/30 + t**4/6 - 3*t**2. Let g(h) be the second derivative of q(h). Factor g(d).
(3*d - 2)**2
Let v be 20/(-6)*60/(-50). Suppose 5*l**2 - 3*l**2 + l - 9*l + v + 4 = 0. What is l?
2
Let i(k) be the first derivative of -k**6/3 + 2*k**5 - 9*k**4/2 + 14*k**3/3 - 2*k**2 - 6. Find c, given that i(c) = 0.
0, 1, 2
Let l(m) = -m**2 + 2*m - 1. Let d(t) = 3 - 4 + 2. Let k(u) = 4*d(u) + l(u). Determine j, given that k(j) = 0.
-1, 3
Let l = -27/2 + 363/26. Factor -2/13*y**3 + 0*y + 0 + 4/13*y**2 - l*y**4.
-2*y**2*(y + 1)*(3*y - 2)/13
Factor -2 - 1 + 64*h**2 + 4 - 32*h + 3.
4*(4*h - 1)**2
Let d = 22 + -17. Factor 4*k**4 + 2*k**d - 3*k**5 - k**4 + 4*k**2 - 2 + 2*k**3 - k - 5*k**4.
-(k - 1)**2*(k + 1)**2*(k + 2)
Solve -2/7*y + 2/7*y**2 - 4/7 = 0.
-1, 2
Let z(l) be the second derivative of -l**5/20 - 5*l**4/8 - 19*l**3/12 - 3*l**2/2 - 35*l. Factor z(v).
-(v + 1)*(v + 6)*(2*v + 1)/2
Let u be 12/3*(-1 - -2). Determine k, given that k**2 - 4*k + u*k + 2*k - k = 0.
-1, 0
Let p(t) be the first derivative of -t**4/18 - 2*t**3/27 - 3. Factor p(m).
-2*m**2*(m + 1)/9
Let g = -1 + 4. Let s = 77/340 + 2/85. Solve -2*y**g - 1/2*y**2 + y**5 + y + 1/4*y**4 + s = 0.
-1, -1/4, 1
Determine p, given that 0*p**3 + 2*p - 3/2*p**2 + 1/4*p**4 - 3/4 = 0.
-3, 1
Let k(b) be the third derivative of b**7/315 + b**6/180 - b**5/45 - 3*b**2. Determine y so that k(y) = 0.
-2, 0, 1
Let r(g) be the third derivative of -g**2 + 0*g**3 + 0*g + 1/720*g**6 + 0 + 1/144*g**4 + 1/180*g**5. Factor r(n).
n*(n + 1)**2/6
Let g be 24/(-63)*33/(-44). Factor g*p**2 + 0*p - 2/7.
2*(p - 1)*(p + 1)/7
Let f(n) be the third derivative of 1/360*n**6 - 1/2*n**3 + 2*n**2 + 1/60*n**5 + 0*n**4 + 0 + 0*n. Let t(r) be the first derivative of f(r). Factor t(b).
b*(b + 2)
Let l(z) be the third derivative of 0*z + z**2 + 0 - 4/25*z**5 - 2/15*z**3 - 4/75*z**6 + 1/4*z**4. Factor l(d).
-2*(d + 2)*(4*d - 1)**2/5
Let s be (-6)/(-3) + (-6 - 0)/(-3). Let k(x) be the second derivative of 0*x**2 + 3*x + 0 + 1/18*x**s + 1/90*x**6 + 0*x**3 + 1/20*x**5. Factor k(n).
n**2*(n + 1)*(n + 2)/3
Let b = -7 + 9. Factor -b + 7*d + 2*d**2 - 7*d.
2*(d - 1)*(d + 1)
Let a be (-7)/(49/(-511)) - 3. Factor a*n**2 + 8/3 + 275/3*n**3 + 125/3*n**4 + 68/3*n.
(n + 1)*(5*n + 2)**3/3
Let q(b) be the second derivative of -b - 2/9*b**3 + 0 + 0*b**2 + 1/18*b**4. Factor q(p).
2*p*(p - 2)/3
Let r = 356/1197 + -2/171. Suppose 4*g - 3 - 13 = 0. Determine d so that -2/7*d**g + 2/7*d**2 + r*d**3 - 2/7*d + 0 = 0.
-1, 0, 1
Let n(l) = -l**3 + 7*l**2 - 6*l - 1. Let g be n(6). Let p be 8 + (g - 4/2). Factor 0*o**2 - 4/3*o**p + 0 + 0*o + 2/3*o**3 - 2/3*o**4.
-2*o**3*(o + 1)*(2*o - 1)/3
Let r(o) = -o**5 - o - 2*o**2 - o**2 + 0*o**2 + 2*o**2. Let k(x) = 14*x**5 - 2*x**3 + 12*x**2 + 12*x. Let v(s) = k(s) + 12*r(s). Factor v(j).
2*j**3*(j - 1)*(j + 1)
Let l(o) be the third derivative of -o**5/75 - o**4/3 - 10*o**3/3 - 20*o**2. Factor l(d).
-4*(d + 5)**2/5
Let u(l) = 57*l**3 + 15*l**2 - 9*l + 33. Let q(t) = 7*t**3 + 2*t**2 - t + 4. Let j(y) = 33*q(y) - 4*u(y). Factor j(d).
3*d*(d + 1)**2
Let h be 2/(1088/26 - 2/(-13)). Let c(i) be the second derivative of -h*i**7 - 3/5*i**5 - 2/3*i**4 + 0*i**2 + 0 - 1/3*i**3 - 4/15*i**6 + i. Factor c(b).
-2*b*(b + 1)**4
Suppose 0 = 3*w - 3*u + 3, 4*w - 3*u + 9 + 0 = 0. Let v = -4 - w. Find p, given that -2/5*p**3 + 0*p + 0 + 4/5*p**v = 0.
0, 2
Let l = 20 - 18. Let q(o) = -o**3 + o**2 + o + 1. Let p be q(-1). Determine i, given that i - 2*i**p + i**2 + l*i**2 = 0.
-1, 0
Let r(v) = v - 6. Let t be r(10). Suppose -l - t*j = -36 + 14, l + j = 7. Factor -7*a**3 + 5*a**2 - a**l - 3*a**3 + 4*a**3 + 2*a**4.
2*a**2*(a - 2)*(a - 1)
Let s(p) be the third derivative of p**8/2520 + p**7/225 + 19*p**6/900 + p**5/18 + 4*p**4/45 + 4*p**3/45 + 9*p**2. Factor s(u).
2*(u + 1)**3*(u + 2)**2/15
Suppose 2*b = -3*b + 5. Suppose -i**5 - 5*i**4 - 10*i**3 - 10*i**2 - 4*i + 0*i**4 - i - b = 0. What is i?
-1
Let j(m) be the first derivative of -7*m**6/15 - 31*m**5/25 + 19*m**4/10 + 13*m**3/15 - 3*m**2/5 - 56. Solve j(x) = 0 for x.
-3, -1/2, 0, 2/7, 1
Determine b so that -10*b**3 - 8*b - 2228*b**4 - 16*b**2 - b**2 + 2227*b**4 = 0.
-8, -1, 0
Let i = -16 - -18. Determine r, given that -2/5*r + 2/5*r**i - 4/5 = 0.
-1, 2
Let c(a) = -39*a**2 + 66*a + 261. Let s(j) = 3*j*