- m**5/35 + 2*m**3/21 - m**2/7 + 2*m. Find b such that h(b) = 0.
-1, 1
Let d(b) be the second derivative of -2*b**7/21 + b**5/5 - 5*b. Solve d(f) = 0 for f.
-1, 0, 1
Let p(z) be the third derivative of -z**7/210 - z**6/60 - z**5/60 - 10*z**2. Factor p(t).
-t**2*(t + 1)**2
What is g in 1/10*g - 2/5*g**4 + 0 - 2/5*g**2 + 3/5*g**3 + 1/10*g**5 = 0?
0, 1
Let v(o) be the first derivative of -o**5/15 + o**3/9 - 10. What is r in v(r) = 0?
-1, 0, 1
Let z(a) be the second derivative of -a**5/20 + a**4/2 - 3*a**3/2 + 9*a. Factor z(f).
-f*(f - 3)**2
Suppose -u - 1 = -2*l, 3*l + l = -u + 17. What is n in 6/11*n**l + 2/11*n**4 + 0 + 0*n**2 - 8/11*n = 0?
-2, 0, 1
Let q(x) be the second derivative of x**6/12 - 17*x**5/30 + 4*x**4/3 - 4*x**3/3 + 3*x**2/2 - 3*x. Let g(d) be the first derivative of q(d). Factor g(s).
2*(s - 2)*(s - 1)*(5*s - 2)
Let w(k) be the third derivative of -k**7/945 - k**6/540 + k**5/90 + k**4/108 - 2*k**3/27 + 7*k**2. Suppose w(n) = 0. What is n?
-2, -1, 1
Let b(f) be the third derivative of -f**8/1680 + f**6/180 - f**4/24 - f**3/2 - 3*f**2. Let r(g) be the first derivative of b(g). Solve r(k) = 0.
-1, 1
Let r(q) be the third derivative of -q**7/1260 - q**6/180 - q**5/90 - q**3/6 + 2*q**2. Let l(i) be the first derivative of r(i). Factor l(g).
-2*g*(g + 1)*(g + 2)/3
Let q(p) be the third derivative of -2*p**5/45 - p**4/9 - p**3/9 - 3*p**2. Factor q(a).
-2*(2*a + 1)**2/3
Let c = -1 - 0. Let b(r) = -3*r**4 - 3*r**3 + r**2 + r. Let w(m) = -m**2 - m. Let g(f) = c*b(f) + 2*w(f). Let g(y) = 0. What is y?
-1, 0, 1
Let c(m) = -2*m**2 - 6*m - 16. Let d be 3/3 + (-1 - 12). Let v(s) = -s - 1. Let b(w) = d*v(w) + c(w). What is k in b(k) = 0?
1, 2
Let m(r) = 10*r**3 + 4*r + 7. Let z(x) = -3*x**3 - x - 2. Let c(n) = 2*m(n) + 7*z(n). Factor c(v).
-v*(v - 1)*(v + 1)
Let x be ((-86)/(-903))/(1 - 4/7). Factor 2/9*j - x*j**3 + 4/9*j**2 - 4/9.
-2*(j - 2)*(j - 1)*(j + 1)/9
Let z(g) = g + 2. Let o be z(0). Suppose 4*k - u - 11 = 1, 4*u = o*k - 20. Factor 0*v + 2/3*v**3 + 2/3*v**4 + 0 - 4/3*v**k.
2*v**2*(v - 1)*(v + 2)/3
Let w(r) = -r**2 + 14*r - 7. Let f(v) = -15*v**2 + 225*v - 111. Let n(b) = -2*f(b) + 33*w(b). Suppose n(c) = 0. What is c?
1, 3
Suppose 3*y - 5 = 271. Suppose c = i - 0 - 2, -5*c + 4*i = 5. Solve y*s**4 + 50*s**5 - 48*s - 82*s**2 - 2*s**4 - 3*s**3 + s**c - 6 - 2 = 0.
-1, -2/5, 1
Let v(l) = 2*l**2 - 19*l - 8. Let i be v(10). Determine a, given that -i*a**2 + 10/3*a**3 - 8*a - 8/3 = 0.
-1, -2/5, 2
Suppose 3/2*w**3 + 12*w + 6 + 15/2*w**2 = 0. What is w?
-2, -1
Determine n so that -9/2*n - 3/2*n**2 + 6 = 0.
-4, 1
Let w(c) be the third derivative of c**7/42 + 5*c**6/24 + 3*c**5/4 + 35*c**4/24 + 5*c**3/3 - 25*c**2. Factor w(j).
5*(j + 1)**3*(j + 2)
Let x(n) = -n**2 + 9*n - 17. Let a be x(5). Factor 0*h + 1/3*h**4 + 0 + 0*h**a + 0*h**2.
h**4/3
Let p be 2/(1 + 0) - 0. Factor -4*r**2 + 2*r**p + 0*r**2 + r + 3*r**2.
r*(r + 1)
Let h(o) be the third derivative of o**7/2520 - o**6/360 + o**5/120 + o**4/12 + o**2. Let n(m) be the second derivative of h(m). Let n(j) = 0. What is j?
1
Factor -8/3*o**2 - 16/3*o**3 + 0 - 2*o**4 + 0*o.
-2*o**2*(o + 2)*(3*o + 2)/3
Let w(n) be the second derivative of n**6/45 + n**5/30 - n**4/6 - n**3/9 + 2*n**2/3 + 10*n. Suppose w(k) = 0. Calculate k.
-2, -1, 1
Let a(d) be the first derivative of -d**6/15 - 2*d**5/25 + 3*d**4/10 + 2*d**3/3 + 2*d**2/5 + 2. Factor a(i).
-2*i*(i - 2)*(i + 1)**3/5
Factor -1/2*y**3 + 3/2*y**2 + 0*y - 2.
-(y - 2)**2*(y + 1)/2
Suppose 5*k = -4*j + 9*j + 5, 4*k - 2*j - 10 = 0. Factor -4/3*i + 0 - 8/3*i**3 - 2/3*i**k - 10/3*i**2.
-2*i*(i + 1)**2*(i + 2)/3
Let l(c) be the first derivative of c**4/10 - 2*c**3/15 - c**2/5 + 2*c/5 + 2. Factor l(d).
2*(d - 1)**2*(d + 1)/5
Let b(u) be the first derivative of -4*u**5/5 - 5*u**4 - 32*u**3/3 - 8*u**2 - 19. Factor b(s).
-4*s*(s + 1)*(s + 2)**2
Let s(w) be the first derivative of -w**3 + 24*w**2 - 192*w + 35. Let s(c) = 0. What is c?
8
Factor -2*c**2 + 0*c**2 + 24*c**3 + 16*c**3 - 42*c**3.
-2*c**2*(c + 1)
Let g be (1 + -3)/8 - (-9)/20. Let d(w) be the second derivative of 0 + 3/10*w**2 + 1/20*w**4 + g*w**3 + 2*w. Let d(f) = 0. What is f?
-1
Let j be (48/(-3))/(-1*2). Let a(q) be the first derivative of 0*q - 25/3*q**6 - 2*q**4 + j*q**5 + 0*q**2 + 0*q**3 + 1. Factor a(c).
-2*c**3*(5*c - 2)**2
Let a = -27 - -30. Determine r so that 0*r + 1/3*r**4 + 0 + 1/3*r**a + 0*r**2 = 0.
-1, 0
Factor 2*c + 8/5 + 2/5*c**2.
2*(c + 1)*(c + 4)/5
Let q(z) = 5*z**3 + 14*z**2 + 11*z - 6. Let o(j) = -2*j**3 - 5*j**2 - 4*j + 2. Let r(m) = 8*o(m) + 3*q(m). Determine w so that r(w) = 0.
-1, 1, 2
Let w = 36 + -32. Let g(s) be the second derivative of 0*s**2 - 2/3*s**w + 0 - 2*s - 4/5*s**5 - 1/6*s**3. Determine y, given that g(y) = 0.
-1/4, 0
Factor -2/7*v**2 + 0 - 2/7*v.
-2*v*(v + 1)/7
Suppose 0*k + 9/5*k**5 - 2/5*k**4 - 9/5*k**3 + 2/5*k**2 + 0 = 0. Calculate k.
-1, 0, 2/9, 1
Let y be -1 - -3 - -2 - (-2)/(-1). Factor 65/6*q**y - 8/3*q - 2/3.
(5*q - 2)*(13*q + 2)/6
Let v(h) = -h**3 + 24*h**2 - 65*h + 44. Let c be v(21). Factor -3/7*t**3 + 0*t**c + 3/7*t + 0.
-3*t*(t - 1)*(t + 1)/7
Let h(q) = 6*q + 2. Let j be h(-3). Let o = 16 + j. Determine b so that 3/4*b**2 + 1/4*b + o = 0.
-1/3, 0
Let x(j) = -3*j**2 + 4*j + 2. Let s be x(3). Let c = s - -16. Factor 1/4*d**c + 0*d + 0*d**2 + 0.
d**3/4
Let u(t) = -t**2 + 12*t - 2. Let i be u(10). Suppose 2 = -4*m + i. Factor -105/2*a**3 + 441/2*a**m + 0 - 24*a**2 + 6*a.
3*a*(3*a + 1)*(7*a - 2)**2/2
Factor -2*b + 14*b**2 - 3 - 1 - 12*b**2.
2*(b - 2)*(b + 1)
Let b(x) be the first derivative of 9*x**6/2 + 36*x**5 + 435*x**4/4 + 150*x**3 + 90*x**2 + 24*x + 15. Factor b(c).
3*(c + 2)**3*(3*c + 1)**2
Let u(g) be the first derivative of g**6 - 3*g**5 + 9*g**4/4 + g**3 - 3*g**2/2 - 3. Determine y so that u(y) = 0.
-1/2, 0, 1
Let d(u) be the third derivative of 6*u**6/5 + 89*u**5/15 + 6*u**4 + 8*u**3/3 - 26*u**2. Suppose d(o) = 0. What is o?
-2, -1/4, -2/9
Let l(n) = n + 4. Let c be l(-2). Find v, given that -2 + 4 - 6*v - c + 3*v**2 + 3 = 0.
1
Factor 4/17*f**3 + 2/17*f**5 + 2/17 + 4/17*f**2 - 6/17*f**4 - 6/17*f.
2*(f - 1)**4*(f + 1)/17
Suppose 20 = -2*c + 6*c. Suppose -10*d + 10 = -c*d. Find j such that 2/11*j**d - 2/11*j - 4/11 = 0.
-1, 2
Let p(y) be the third derivative of -y**6/120 - y**5/40 - y**3/2 + 6*y**2. Let b(d) be the first derivative of p(d). What is z in b(z) = 0?
-1, 0
Let f(a) be the first derivative of 0*a**2 + 12*a**4 + 0*a + 25/3*a**6 + 18*a**5 - 2 + 8/3*a**3. Factor f(s).
2*s**2*(s + 1)*(5*s + 2)**2
Factor -5*r - 8*r + 3*r + r**2 - 6*r**2.
-5*r*(r + 2)
Let x = 917 + -914. Factor -6/5*s**x + 0 + 0*s + 2/5*s**4 + 4/5*s**2.
2*s**2*(s - 2)*(s - 1)/5
Let x(c) be the second derivative of -c**7/280 + c**6/60 - c**5/40 + c**3/3 + 8*c. Let d(k) be the second derivative of x(k). Factor d(z).
-3*z*(z - 1)**2
Factor -1/6*r + 0 + 1/6*r**2.
r*(r - 1)/6
Let h(v) be the third derivative of v**6/30 + 2*v**5 + 50*v**4 + 2000*v**3/3 - 37*v**2. Find x such that h(x) = 0.
-10
Suppose -4*w = -9*w + 110. Let g = -20 + w. Factor g*s + 2/5 + 2/5*s**5 + 4*s**3 + 2*s**4 + 4*s**2.
2*(s + 1)**5/5
Solve 0*l**3 - 6*l**5 + 3*l**3 - 3*l**5 - 14*l**4 + 8*l**4 = 0 for l.
-1, 0, 1/3
Let d(s) be the first derivative of s**5/5 - 11*s**4/4 + 9*s**3 - 25*s**2/2 + 8*s - 4. Find q, given that d(q) = 0.
1, 8
Solve -3/2*y + 3/2*y**3 - 3/2*y**2 + 3/2 = 0.
-1, 1
Factor 3*n**2 - 7*n + 11 + 0*n**2 + 1 - 5*n.
3*(n - 2)**2
Let t(p) be the third derivative of -14*p**5/45 - 5*p**4/12 - 2*p**3/9 - 14*p**2. What is q in t(q) = 0?
-2/7, -1/4
Find n, given that -6/7 - 9/7*n + 24/7*n**2 + 15/7*n**5 + 54/7*n**4 + 66/7*n**3 = 0.
-1, 2/5
Let g be -4 + (17 + 4 - -3). Suppose 0 = 3*n + 2*n + 5*d + g, d + 4 = 0. Let n*q - 3/2*q**2 + 3/4*q**3 + 0 = 0. Calculate q.
0, 2
Let z(a) = a**2 + 5*a + 2. Let t be z(-3). Let o(s) = -s**3 + 5*s**2 + s - 1. Let u(j) = -2*j**3 + 6*j**2 - 2. Let x(r) = t*u(r) + 6*o(r). Factor x(g).
2*(g + 1)**3
Let b be 15/(7/(-2) - -2). Let w be (4/12)/(b/(-6)). Find i such that 0 - w*i**2 - 1/5*i = 0.
-1, 0
Suppose 4*v = -4*f - 8, v = -4*v + 2*f + 18. Let k = 0 + v. Factor -2*t**2 + 0*t + k*t + 2*t**4 - 6*t**3 + 4*t**3.
2*t*(t - 1)**2*(t + 1)
Let a(m) be the second derivative of m**7/231 - m**6/165 - m**5/55 - 6*m - 2. Let a(s) = 0. Calculate s.
-1, 0, 2
Let a(j) be the second deriva