4*f + 323 - 769 = 0.
2, 3
Let s(r) be the second derivative of 625*r**4/3 - 100*r**3 + 18*r**2 - r - 199. Determine f, given that s(f) = 0.
3/25
Let m be (-10*(-4)/50)/((-2)/(-180)). Let o = m + -70. Solve 1 + 3/2*r + 1/2*r**o = 0.
-2, -1
Let a(g) be the second derivative of g**7/2520 + g**6/60 + 3*g**5/10 + 3*g**4 + 5*g**3/2 + 4*g. Let k(i) be the second derivative of a(i). Factor k(w).
(w + 6)**3/3
Let w(r) = 4 - 5 + 2. Let n(h) = 2*h**2 - 40*h + 193. Let z(m) = -2*n(m) - 14*w(m). Factor z(f).
-4*(f - 10)**2
Let u = 0 + 3. Let t be u*16/(-12) - -6. Factor 2*i**t - 32 - i + 34 + 5*i.
2*(i + 1)**2
What is d in -30/13*d**4 + 84/13*d + 0 + 134/13*d**2 + 2/13*d**5 + 18/13*d**3 = 0?
-1, 0, 3, 14
Let -1/5*z**3 - 44/5*z - 28/5 - 17/5*z**2 = 0. What is z?
-14, -2, -1
Let o be -1 + 78/21 + 6/21. Suppose -o*c + 3 = -3*z - 0*z, -z - 2*c + 8 = 0. Determine h so that -1 + 1/2*h + 1/2*h**z = 0.
-2, 1
Let v(f) be the third derivative of f**10/403200 - f**8/53760 + f**5/15 + 7*f**2. Let d(l) be the third derivative of v(l). Find t, given that d(t) = 0.
-1, 0, 1
Factor -60/7*x + 3/7*x**2 + 57/7.
3*(x - 19)*(x - 1)/7
Let z(g) be the second derivative of -g**6/30 - 3*g**5/20 + 3*g**4/4 - 5*g**3/6 + 8*g - 2. Factor z(c).
-c*(c - 1)**2*(c + 5)
Let x(u) be the third derivative of 2*u**7/7 + 35*u**6/24 + 11*u**5/4 + 15*u**4/8 - 5*u**3/6 - 148*u**2. What is d in x(d) = 0?
-1, 1/12
Suppose 5*w**4 - 1/2*w - 10*w**2 + 5 + w**3 - 1/2*w**5 = 0. Calculate w.
-1, 1, 10
Suppose 0 = 2*g + 2*k - 440, -5*g + 10*g - 1130 = k. Let v = g - 225. What is a in -2/9*a**2 - 2/9*a**5 + 2/9*a**4 + 0*a + v + 2/9*a**3 = 0?
-1, 0, 1
Let a be 2*(-6)/(-3) + -2. Factor -2*c + 1 + 7*c**2 - 2 - 8*c**a.
-(c + 1)**2
Factor -1/6*t**2 + 2/3*t - 1/2.
-(t - 3)*(t - 1)/6
Suppose 4*x - 4*t = 28, 3*t - 2 + 17 = 0. Suppose -x*s = -4*s + 4. Solve -2*j + 5*j**s + 2*j**4 - 6*j**3 + j**2 - 17 + 17 = 0 for j.
0, 1
Suppose -4*f - 5*c = -11, -3*f + 15 = f + c. Factor -h**2 - 5*h**2 + 3*h**4 - 3*h**3 + 0*h**3 + 3*h**5 + 3*h**f.
3*h**2*(h - 1)*(h + 1)*(h + 2)
Let p(n) be the third derivative of 0 + 0*n + 0*n**4 - 1/80*n**6 + 0*n**3 + 1/60*n**5 - 4*n**2 - 1/210*n**7. Solve p(a) = 0 for a.
-2, 0, 1/2
Let t be 8*3/42*(-455)/(-250). Let o(i) be the first derivative of -4/5*i**2 + 34/15*i**3 - 7 - t*i**5 + 1/3*i**6 - 8/5*i - 1/10*i**4. Solve o(g) = 0 for g.
-1, -2/5, 1, 2
Let z(g) = -4*g + 8. Let u be z(-1). Determine r so that -12*r**4 - 16*r**2 + u*r**3 + 8*r**4 - 28*r**3 = 0.
-2, 0
Let i(k) be the third derivative of k**8/1008 + k**7/105 + 11*k**6/360 + k**5/30 - k**2 + 6*k. Factor i(c).
c**2*(c + 1)*(c + 2)*(c + 3)/3
What is o in -2/17*o**2 + 166/17 - 164/17*o = 0?
-83, 1
Let k(d) be the third derivative of 0*d + 1/600*d**6 + 18*d**2 + 0 - 7/100*d**5 - 343/30*d**3 + 49/40*d**4. Let k(b) = 0. Calculate b.
7
Let h(q) be the first derivative of 0*q + 14 - 1/3*q**3 - 5/2*q**2. Factor h(o).
-o*(o + 5)
Let j(r) be the third derivative of -r**6/60 + 4*r**5/15 + r**4/12 - 8*r**3/3 + 110*r**2. Factor j(k).
-2*(k - 8)*(k - 1)*(k + 1)
Suppose -99*q + 39 = -69 - 90. Find p, given that -3/2 + 9/2*p - 3*p**3 - 3/2*p**5 + 9/2*p**4 - 3*p**q = 0.
-1, 1
Let q(d) be the second derivative of -9*d**5/140 + d**4/42 + 6*d**3/7 - 4*d**2/7 - 2*d - 438. Factor q(n).
-(n - 2)*(n + 2)*(9*n - 2)/7
Let n(c) be the second derivative of 0*c**5 + 13*c + 1/2*c**4 + 0*c**2 + 0 - 1/15*c**6 - 2/3*c**3. Factor n(f).
-2*f*(f - 1)**2*(f + 2)
Let f(b) be the third derivative of b**6/30 + 2*b**5/5 + 5*b**4/6 + 22*b**2. Factor f(o).
4*o*(o + 1)*(o + 5)
Let j(h) be the first derivative of h**4 + 47*h**3/3 - 32*h**2 + 13*h - 61. Factor j(x).
(x - 1)*(x + 13)*(4*x - 1)
Let z(b) be the second derivative of 5*b**7/42 + b**6/2 - b**5/4 - 5*b**4/4 - 659*b. Find m, given that z(m) = 0.
-3, -1, 0, 1
Let i be (-9)/(-2)*(11 - (-279)/(-27)). Solve 0 + 0*v**2 - 4/7*v + 3/7*v**i - 1/7*v**4 = 0 for v.
-1, 0, 2
Let o = 1983 + -13880/7. Let u(q) be the first derivative of -2/21*q**3 + 4/7*q + o*q**2 + 9. Factor u(w).
-2*(w - 2)*(w + 1)/7
Let f(z) be the second derivative of 13*z**4/36 + 7*z**3/18 - z**2 + 26*z. Solve f(i) = 0 for i.
-1, 6/13
Let n(p) = -248*p**2 + 192*p - 28. Let z(j) be the first derivative of -j**3/3 - j - 25. Let t(m) = -n(m) - 8*z(m). Factor t(g).
4*(8*g - 3)**2
Let z = 40 - 38. Solve -60 - 70*q**z - 64*q**2 + 120*q + 34*q**2 + 24 = 0.
3/5
Factor 7*w**2 + w**3 - 11*w**2 - 5*w + w**4 + w.
w*(w - 2)*(w + 1)*(w + 2)
Factor -3*i**4 - 6 + i**3 - 30*i + 17*i + 16*i - 4*i**3 + 9*i**2.
-3*(i - 1)**2*(i + 1)*(i + 2)
Let f(a) = -3*a. Let i be f(-6). Suppose -l + 4*v - 1 = 0, -5*l - 4*v + i = -1. Suppose 0*c**2 + 2/9 + 4/9*c - 2/9*c**4 - 4/9*c**l = 0. What is c?
-1, 1
Let h(n) be the second derivative of n**5/4 - 25*n**4/24 - 5*n**3/3 - 6*n**2 + 8*n. Let m(y) be the first derivative of h(y). Factor m(t).
5*(t - 2)*(3*t + 1)
Let y be ((-3 - -4) + -1)*(-6)/12. Let j(r) be the third derivative of y - 3/7*r**3 - 1/14*r**4 + 2*r**2 + 0*r - 1/210*r**5. Find s, given that j(s) = 0.
-3
Let i(o) be the third derivative of 5*o**8/336 + o**7/14 + 3*o**6/32 + 8*o**2 + 4*o. Solve i(h) = 0 for h.
-3/2, 0
Suppose -14*f + 10*f = -320. Suppose -f = -6*y + 4*y. Let 20*m**4 - 70*m**2 + 5*m**3 - 2 - 100*m + 2 - 2*m**5 - y + 7*m**5 = 0. What is m?
-2, -1, 2
Let p(r) be the second derivative of r**5/20 - r**4/32 - 11*r**2/2 + 20*r. Let t(w) be the first derivative of p(w). Factor t(n).
3*n*(4*n - 1)/4
Let p be (-141)/(-162) + 3/6 + -1. Let o = -43/189 + p. Suppose o*t**2 - 4/7*t + 4/7 = 0. What is t?
2
Let i be (-1 + -5)/(8/16*-4). Let x(d) be the first derivative of 9/8*d**2 + 3 + 0*d - 1/4*d**i. Factor x(w).
-3*w*(w - 3)/4
Suppose -5*a + 29*h = 32*h + 12, -3*h = a + 12. Let n = -8/45 + 178/495. Factor 0 + a*r - n*r**4 + 0*r**3 + 2/11*r**2.
-2*r**2*(r - 1)*(r + 1)/11
Let m be ((-18)/9 + 0)/(36/(-8) + 1). Factor 2/7*z**3 - 2/7*z + m - 4/7*z**2.
2*(z - 2)*(z - 1)*(z + 1)/7
Let k = -21/5 + 29/5. Let q(d) be the first derivative of 2/3*d**3 + 0*d + k*d**5 + 5/2*d**4 - 2 + 0*d**2. Let q(o) = 0. What is o?
-1, -1/4, 0
Let n(q) = -q**3 - 2*q**2 - 3*q - 1. Let l be n(-2). Factor 15*i**2 + 544*i + 105*i**2 - 1504*i - l*i**3 + 2560.
-5*(i - 8)**3
Let z = 168 - 177. Let f be (-321)/(-535)*(1 + (-1)/z). Factor f*m + 4/3 - 2/3*m**2.
-2*(m - 2)*(m + 1)/3
Suppose 36 = 34*q - 32. Factor 3/2 - 5/4*t + 1/4*t**q.
(t - 3)*(t - 2)/4
Let f(y) be the second derivative of y**8/1680 + y**7/840 - y**6/180 + 17*y**3/3 + 8*y. Let s(p) be the second derivative of f(p). Factor s(b).
b**2*(b - 1)*(b + 2)
Let s(x) = 4*x**2 - 40. Let o(t) = t - 1. Let r(z) = -24*o(z) - s(z). Let r(a) = 0. What is a?
-8, 2
Let h(j) be the first derivative of 0*j**2 + 16/5*j**5 + 30 - 3*j**4 + 0*j - 4/3*j**3. Factor h(w).
4*w**2*(w - 1)*(4*w + 1)
Let k(c) be the third derivative of c**5/180 + c**4/18 - 5*c**3/18 + 8*c**2 - 4. Factor k(l).
(l - 1)*(l + 5)/3
Let p be 500/160 - 1/8. Factor 1/3*w + 0 - 5/6*w**4 - 7/3*w**p - 7/6*w**2.
-w*(w + 1)*(w + 2)*(5*w - 1)/6
Let a be ((-10)/(-3))/(16/24). Let -a*l**3 - 2*l**4 - 357*l**5 - 2 + 4*l + 4*l**2 + l**3 + 359*l**5 - 2*l = 0. What is l?
-1, 1
Let x(j) = j**3 + 4*j**2 - 2*j + 1. Let b be x(-4). Let q be 0 + (b - 5) - (-2)/(-2). Solve 1/5*o**4 - 2*o**q - 54/5*o + 27/5 + 36/5*o**2 = 0.
1, 3
Let h(s) be the third derivative of 2*s**7/105 - 11*s**6/15 - 4*s**2 - 6. Determine a so that h(a) = 0.
0, 22
Let f(y) be the first derivative of -2*y**3/21 - 6*y**2/7 + 2*y - 1026. Factor f(v).
-2*(v - 1)*(v + 7)/7
Let o(c) be the second derivative of -c**4/3 + 40*c**3/3 + 42*c**2 - 187*c. Suppose o(u) = 0. Calculate u.
-1, 21
Let a(v) = -5*v**2 - 10*v - 13. Let r(d) = 9*d**2 + 15 + 22*d + 10 + 2*d - 5*d. Let b(y) = 7*a(y) + 4*r(y). Factor b(g).
(g + 3)**2
Let h be ((-450)/1575)/((-20)/574). Suppose 5 + h*a**2 + 22*a + 4/5*a**3 = 0. Calculate a.
-5, -1/4
Let b(o) be the second derivative of o**5/24 + o**4/8 - 2*o**3/9 - o**2 - 446*o. Factor b(p).
(p + 1)*(p + 2)*(5*p - 6)/6
Let f(h) be the second derivative of h**7/315 - h**6/90 - 5*h**2/2 - 6*h. Let m(j) be the first derivative of f(j). Factor m(s).
2*s**3*(s - 2)/3
Let l(m) be the third derivative of -5*m**6/24 + 23*m**5/6 + 505*m**4/24 - 55*m**3/3 - 100*m**2. Determine d, given that l(d) = 0.
-2, 1/5, 11
Let s(b) = -b**2 - 6*b - 7. Let h be s(-5). L