1
Let s(v) be the first derivative of 4*v - 1/11*v**3 - 1 - 2/11*v**2 + 1/110*v**5 + 0*v**4. Let c(y) be the first derivative of s(y). Factor c(m).
2*(m - 2)*(m + 1)**2/11
Suppose 3*u = -3*w - 6, -5*u - 2 = 3*w - 3*u. Factor -l**2 - 3*l**w + 39 + 56*l - 54 - 181.
-4*(l - 7)**2
Let h(q) = 5*q**3 + 19*q**2 - 32*q - 48. Let j(w) = -w**3 - 5*w**2 + 8*w + 12. Let n(c) = 2*h(c) + 9*j(c). Let d be n(5). Factor 2/3*b**3 + 0*b + 0 + 4/3*b**d.
2*b**2*(b + 2)/3
Factor -12/5*d**4 + 0 - 12/5*d**2 - 18/5*d**3 - 3/5*d - 3/5*d**5.
-3*d*(d + 1)**4/5
Let i(h) be the first derivative of -2*h**3/27 - 16*h**2/9 + 34*h/9 + 243. Factor i(b).
-2*(b - 1)*(b + 17)/9
Find b such that -34*b - 33*b**2 - 34*b**3 + b**4 + 98*b**2 - 2*b + 4*b = 0.
0, 1, 32
Let j(z) = z**3 + 2*z**2. Let g(h) = -14*h**3 - 32*h**2 + 52*h + 60. Let i(q) = g(q) + 10*j(q). Let i(x) = 0. What is x?
-5, -1, 3
Let p(v) be the third derivative of -v**5/180 - v**4/36 + v**3/6 + 146*v**2. Let p(c) = 0. Calculate c.
-3, 1
Suppose -5*m = -2*z - 31, -5*z + 24*m - 18 = 20*m. Factor -2/3 + 1/3*g**z + 1/3*g.
(g - 1)*(g + 2)/3
Let f(k) be the third derivative of -2*k**2 + 0*k + 21/40*k**6 + 1/3*k**3 + 17/20*k**5 + 17/24*k**4 + 9/70*k**7 + 0. Factor f(d).
(d + 1)*(3*d + 1)**2*(3*d + 2)
Let g(y) = -2*y**2 - 44*y + 644. Let v be g(-32). Factor 0 - 1/2*w**v - 1/2*w**5 + 5/2*w**3 - 3/2*w**2 + 0*w.
-w**2*(w - 1)**2*(w + 3)/2
Let n be -7 - 0 - (523/(-65) - 32/208). Let o = 0 - 0. Find x such that -n*x + o + 2/5*x**2 = 0.
0, 3
Factor 10/3*m**2 - 2/3*m**3 - 16/3 - 4/3*m.
-2*(m - 4)*(m - 2)*(m + 1)/3
Let i(j) be the third derivative of j**6/60 + 26*j**5/15 + 5*j**2 - 13. Factor i(g).
2*g**2*(g + 52)
Let j(f) be the third derivative of -1/72*f**4 - 1/180*f**5 + 0*f - 43*f**2 + 0*f**3 + 0 - 1/210*f**7 + 1/72*f**6. Solve j(q) = 0.
-1/3, 0, 1
Let h be 11/(-4) + (-7 - (-11 + 1)). Let a(b) be the first derivative of -1/6*b**3 + 5 + b + h*b**2. Let a(z) = 0. What is z?
-1, 2
Let v(p) = -2*p**4 + 11*p**3 - p**2 - 8*p - 6. Let b(z) = -z**4 + z**3 + z**2 - z - 1. Let y(h) = 6*b(h) - v(h). Factor y(d).
-d*(d - 1)*(d + 2)*(4*d + 1)
Let t = 4106 - 20526/5. Factor 0*v - 1/5*v**4 + 0*v**3 + 0 + t*v**2.
-v**2*(v - 2)*(v + 2)/5
Let t(r) = r**2 + r - 6. Let h be t(6). Let y = h + -24. Factor -5*s**3 + 6*s**2 + y*s + 2*s**3 - 15*s.
-3*s*(s - 1)**2
Let f(m) = -m**2 + 5*m + 3. Let r be f(6). Let a = r - -6. Find q, given that -24*q**2 - 3 + 3*q**5 - 3 + a*q**4 - 21*q + 3*q**4 - 6*q**3 = 0.
-1, 2
Suppose -b - 3*l = 24, 5*l + 19 = -b + 3. Let t be (-4)/(-18) - 100/b. Find o such that 3*o**5 + 3*o**t + 0*o**3 + 6*o**3 + 3*o**2 + 9*o**4 = 0.
-1, 0
Let c be (3 - 4 - -2)*4. Suppose 2*y = -y + 39. Determine a so that -c + 9*a - 4 - a**2 + y*a**2 + 5 = 0.
-1, 1/4
Factor -1 + 13*w**2 + 24*w + 8*w**2 - 3*w**4 + 10 - 3*w**2.
-3*(w - 3)*(w + 1)**3
Let v(p) = -5*p**4 - 2*p**3 + 27*p**2 - 56*p + 28. Let q(w) = 11*w**4 + 4*w**3 - 54*w**2 + 113*w - 56. Let u(k) = -4*q(k) - 9*v(k). Suppose u(h) = 0. What is h?
-7, 1, 2
Determine u, given that -4*u**2 + 8 - 22*u**2 - u**3 - 12*u**3 + 5*u**3 + 26*u = 0.
-4, -1/4, 1
Suppose 158 - 14 = 72*g. Let 0 + 0*h - 1/4*h**4 + h**g - 3/4*h**3 = 0. What is h?
-4, 0, 1
Let t(u) be the first derivative of u**4/2 - 6*u**3/7 - 12*u**2/7 + 8*u/7 + 400. Factor t(o).
2*(o - 2)*(o + 1)*(7*o - 2)/7
Factor 12 + 5*t**2 - 19*t + 32*t - 2*t**2.
(t + 3)*(3*t + 4)
Let l(g) be the second derivative of -g**8/11760 - g**7/735 - g**6/140 + g**4/4 + 6*g. Let p(t) be the third derivative of l(t). Factor p(n).
-4*n*(n + 3)**2/7
Factor 32/5*q**3 + 32 + 256/5*q + 144/5*q**2 + 2/5*q**4.
2*(q + 2)**3*(q + 10)/5
Let g(j) = -16*j**3 + 125*j**2 - 381*j + 90. Let q(n) = -18*n**3 + 126*n**2 - 380*n + 96. Let s(m) = -4*g(m) + 3*q(m). Let s(a) = 0. Calculate a.
1/5, 6
Let y(r) be the first derivative of 5*r**6/6 + 2*r**5 - 25*r**4/2 - 100*r**3/3 + 45*r**2/2 + 90*r + 959. What is z in y(z) = 0?
-3, -2, -1, 1, 3
Let r(i) be the second derivative of -i**6/6 + 2*i**5 - 35*i**4/4 + 55*i**3/3 - 20*i**2 - 3*i + 18. Find o such that r(o) = 0.
1, 2, 4
Let s be (-4)/(-12)*-4*198/(-4). Solve -3*f**2 - s*f**4 + 70*f**4 - 6*f**5 + 2*f + 4*f**5 - f**2 = 0 for f.
-1, 0, 1
Let x(i) be the first derivative of -2/3*i**3 + 10 - 2/3*i**2 - 2/9*i - 2/9*i**4. Suppose x(d) = 0. Calculate d.
-1, -1/4
Let v(x) be the second derivative of x**4/12 + x**3 + 9*x**2/2 + 5*x. Let l be v(-5). Determine z, given that -8/3 - l*z - 4/3*z**2 = 0.
-2, -1
Let r(d) be the third derivative of d**7/1680 + d**6/80 + 3*d**5/40 + 3*d**2 + 1. Factor r(l).
l**2*(l + 6)**2/8
Let r be -1 - -8 - (-2 + 8)/3. Suppose -b**2 + r - 9 + 2*b + 4 = 0. What is b?
0, 2
Let k(o) be the third derivative of 0*o - 10/3*o**3 - o**4 + 0 - 4*o**2 - 1/15*o**5. What is v in k(v) = 0?
-5, -1
Let u(l) be the first derivative of 2*l**5/5 - l**4 - 2*l**3 + 8*l**2 - 8*l - 99. Let u(q) = 0. Calculate q.
-2, 1, 2
Suppose 5*k - j = 6, 0 = 5*k - 0*j + 4*j - 26. Factor 4*l - 2*l**k - l**2 + 5*l - 3*l.
-3*l*(l - 2)
Let r be 0 - -1*(0 + 1) - (-2)/2. Factor -2/5 + 4/5*i - 2/5*i**r.
-2*(i - 1)**2/5
Let n(c) be the second derivative of -c**5/40 + c**3/4 + 5*c**2 - 6*c. Let x(p) be the first derivative of n(p). Find k such that x(k) = 0.
-1, 1
Let x(b) be the second derivative of -b**7/210 + b**6/45 - b**5/30 - b**3/2 - 10*b. Let s(z) be the second derivative of x(z). Determine d, given that s(d) = 0.
0, 1
Let x(k) be the first derivative of -2*k**6/27 - 4*k**5/15 - k**4/3 - 4*k**3/27 - 54. Factor x(h).
-4*h**2*(h + 1)**3/9
Let m be 2*((-378)/24 - -2). Let l = m + 28. Determine j so that 0 + 1/2*j**2 + l*j = 0.
-1, 0
Let g(p) be the third derivative of p**6/180 - 11*p**5/225 + 7*p**4/45 - 8*p**3/45 + 20*p**2. Factor g(l).
2*(l - 2)**2*(5*l - 2)/15
Let c(r) = r**3 + 5*r**2 - 7*r - 4. Suppose 0 = -4*f + b - 25 - 3, -5*b + 44 = -4*f. Let k be c(f). Determine y, given that -4/5*y - 2/5*y**k + 0 = 0.
-2, 0
Let a(m) be the second derivative of m**7/42 + m**6/15 - m**5/5 - m**4/6 + m**3/2 + m - 554. Suppose a(z) = 0. What is z?
-3, -1, 0, 1
Factor 189/2 + 24*b + 3/2*b**2.
3*(b + 7)*(b + 9)/2
Let b be (-3)/12 + 28/48. Let y(f) be the first derivative of -1/9*f**3 + 0*f**2 + 3 + b*f. Factor y(q).
-(q - 1)*(q + 1)/3
Let l(m) = 38*m**2 - 344*m + 18. Let g be l(9). Factor -2/11*h**3 - 18/11*h**2 + g*h + 0.
-2*h**2*(h + 9)/11
Solve -288/17 - 14/17*l**3 + 40/17*l**2 - 2/17*l**4 + 264/17*l = 0.
-6, 1, 4
Let h(n) be the second derivative of -n**5/390 - n**4/52 + 15*n**2/2 - 15*n. Let q(d) be the first derivative of h(d). Let q(j) = 0. What is j?
-3, 0
Let y(f) be the second derivative of 0*f**2 - 1/315*f**7 + 1/90*f**4 + 1/150*f**5 - f + 0 + 0*f**3 - 1/225*f**6. Factor y(o).
-2*o**2*(o - 1)*(o + 1)**2/15
Let x be -2 - -4 - (-3284)/520. Let l = x + -77/10. Factor 10/13*k + 2/13*k**3 + l*k**2 + 4/13.
2*(k + 1)**2*(k + 2)/13
Let i be ((-948)/(-12166)*(0 - -11))/((-6)/(-112)). Determine o, given that -5/2*o**3 + 16*o - 1/2*o**4 - i + 3*o**2 = 0.
-4, 1, 2
Factor 0 - 10/11*m - 2/11*m**2.
-2*m*(m + 5)/11
Let l be 202/6 + (-16)/24. Let z(p) = -p**2 + 4*p + 3. Let f be z(4). Factor l*s**3 + 0*s**2 - 3*s**2 - 42*s**f.
-3*s**2*(3*s + 1)
Determine k, given that 1/4*k**3 + 0 - k - 3/4*k**2 = 0.
-1, 0, 4
Solve 0*h**2 + 2/5*h**4 + 0 + 0*h - 2*h**3 = 0 for h.
0, 5
Factor 17*z - 3*z + 28*z + 26 + 40*z**2 + 6*z**3 + 36*z + 10.
2*(z + 3)**2*(3*z + 2)
Let h(f) = 47*f**2 - 14*f - 1. Let j(q) = 16*q + 23*q - 2 + 6 + 3*q - 140*q**2. Let d = 17 + -24. Let g(o) = d*h(o) - 2*j(o). Factor g(u).
-(7*u - 1)**2
Let g(o) be the first derivative of -4/3*o + 5/3*o**4 + 14 + 2/3*o**2 + 43/9*o**3. Let g(a) = 0. Calculate a.
-2, -2/5, 1/4
Factor -116/7*z + 2/7*z**2 + 1682/7.
2*(z - 29)**2/7
Let a(t) = 3*t**2 + 16*t + 16. Let s be a(-4). Let v(n) be the first derivative of -1 + s*n - n**3 + 3/2*n**2. Suppose v(c) = 0. Calculate c.
0, 1
Let t = -7933 + 7937. Factor -56/3*r + 20/3*r**2 - t.
4*(r - 3)*(5*r + 1)/3
Let n(u) be the third derivative of u**5/210 + u**4/28 - 4*u**3/21 + 326*u**2. Solve n(h) = 0.
-4, 1
Solve -20*o**3 + 20 - 14*o + 11 + 18*o**3 + 0*o - 20*o**2 + 5 = 0.
-9, -2, 1
Let b be (-10)/(-14)*76/95 + 1*2. Find i, given that 24/7*i**2 - b*i**3 + 5/7*i**4 + 3/7 - 2*i = 0.
3/5, 1
Let w(i) = -67*i**3 + i**2 - i + 1. Let k be w(1). Let t = -37 - k. Let -4*c**2 - 2*c - 17*c**5 