t i(j) be the second derivative of -j**6/900 - j**5/300 + j**3/3 + j. Let k(q) be the second derivative of i(q). Factor k(p).
-2*p*(p + 1)/5
Suppose 0 = 5*s - 7 + 37. Let n(x) = -7*x**3 + 3*x - 8. Let q(k) = 6*k**3 - 3*k + 7. Let v(p) = s*q(p) - 5*n(p). Find t such that v(t) = 0.
-2, 1
Suppose -k + 15 = 4. Let o = -11 + k. Factor 1/4*u**2 + o - 1/4*u - 1/4*u**4 + 1/4*u**3.
-u*(u - 1)**2*(u + 1)/4
Factor -2/3*a + 0 + 2/3*a**2 + 2/3*a**3 - 2/3*a**4.
-2*a*(a - 1)**2*(a + 1)/3
Let p(u) be the second derivative of -1/3*u**3 + u - 1/1440*u**6 + 0*u**2 + 1/480*u**5 + 0 + 1/48*u**4. Let j(r) be the second derivative of p(r). Factor j(t).
-(t - 2)*(t + 1)/4
Let r(x) be the third derivative of x**7/350 - 3*x**6/200 + x**5/50 + 4*x**2. Find s such that r(s) = 0.
0, 1, 2
Let y(x) be the second derivative of x**6/30 - x**5/20 - 7*x. What is n in y(n) = 0?
0, 1
Factor -1/5*d**4 - 2/5 - 9/5*d**2 + d**3 + 7/5*d.
-(d - 2)*(d - 1)**3/5
Let d = 2/55 - -4/11. Factor d*z**2 + 0 + 1/5*z + 1/5*z**3.
z*(z + 1)**2/5
Determine g so that 0 + 0*g + 0*g**2 - 4/7*g**3 - 4/7*g**4 = 0.
-1, 0
Let r(c) be the third derivative of 0*c + 1/735*c**7 - 1/210*c**6 + 0*c**3 + 1/210*c**5 + 0*c**4 + 0 - 3*c**2. Factor r(f).
2*f**2*(f - 1)**2/7
Let u(o) be the third derivative of o**7/735 - o**6/84 + o**5/35 + o**4/21 - 8*o**3/21 + 32*o**2. Find v, given that u(v) = 0.
-1, 2
Let q = -994 - -999. Suppose -3/2*k**3 + 2*k - k**4 + 1/2*k**q + 2*k**2 + 0 = 0. What is k?
-1, 0, 2
Let b(w) be the second derivative of w**6/15 - 3*w**5/40 - 5*w**4/24 + w**3/4 + w**2/4 - 9*w. Factor b(n).
(n - 1)**2*(n + 1)*(4*n + 1)/2
Let p = 1052/7 - 150. Let s(n) be the first derivative of p*n - 2/21*n**3 + 0*n**2 - 1. Factor s(l).
-2*(l - 1)*(l + 1)/7
Factor 3*t**2 + 3*t**4 + 3*t**5 - 3*t**2 + t**3 + t**4.
t**3*(t + 1)*(3*t + 1)
Let x = 13/81 + 5/81. Factor 4/9 - 2/9*a - x*a**2.
-2*(a - 1)*(a + 2)/9
Let s(g) be the second derivative of 0*g**4 - 2*g**2 + 0 + 4*g + 0*g**3 - 1/420*g**6 - 1/210*g**5. Let m(n) be the first derivative of s(n). Factor m(v).
-2*v**2*(v + 1)/7
Let k be 3/(36/(-6)) + 8/16. Factor 3/2*c**3 + 0*c**2 + k - 3/4*c**4 - 3/4*c**5 + 0*c.
-3*c**3*(c - 1)*(c + 2)/4
Factor -3*x**2 + 0*x + 0 - 3*x**3 - 3/4*x**4.
-3*x**2*(x + 2)**2/4
Solve 0 - 2/5*l - 2/5*l**4 + 2/5*l**3 + 2/5*l**2 = 0 for l.
-1, 0, 1
Let b(p) be the second derivative of 1/72*p**4 - 1/18*p**3 + 0 + 0*p**2 + 1/120*p**5 - 3*p. Determine h so that b(h) = 0.
-2, 0, 1
Let z(i) be the first derivative of -i**4/10 + 4*i**3/3 - 17*i**2/5 + 16*i/5 - 31. What is q in z(q) = 0?
1, 8
Let t = 1 - -1. Factor -y - 4*y**2 + 5*y**t + 3*y.
y*(y + 2)
Solve 0*b + 2/9*b**4 + 0 - 2/9*b**2 + 0*b**3 = 0 for b.
-1, 0, 1
Let p(d) be the second derivative of d**6/50 + 3*d**5/25 + 3*d**4/20 - 2*d**3/5 - 6*d**2/5 - 16*d. Let p(v) = 0. What is v?
-2, -1, 1
Let h(a) = a**2 - 9*a - 88. Let m be h(-6). Factor -15/2*j**m - 8*j - 2.
-(3*j + 2)*(5*j + 2)/2
Let k(h) = -12*h**3 + 25*h**2 - 14*h - 3. Let x(a) = 23*a**3 - 49*a**2 + 29*a + 7. Let c(d) = 5*k(d) + 2*x(d). Factor c(q).
-(q - 1)**2*(14*q + 1)
Suppose -13 = -5*d + 3*y, y = -0*y - 1. Suppose 4*r + 0*b + 5*b - 25 = 0, -5*r = 2*b - 10. Factor r - 2/5*c**3 + 4/5*c - 2/5*c**d.
-2*c*(c - 1)*(c + 2)/5
Suppose -2 + 14 = -2*h. Let t(u) = -10*u**2 - 5*u + 5. Let q(y) = -y**2 + 1. Suppose 1 = -z + 2*z. Let g(k) = h*q(k) + z*t(k). Factor g(j).
-(j + 1)*(4*j + 1)
Let q(m) be the third derivative of -m**5/60 - 5*m**4/24 - 2*m**3/3 - 5*m**2. Let l be q(-4). Factor l - 18/7*z**3 - 4/7*z + 18/7*z**2.
-2*z*(3*z - 2)*(3*z - 1)/7
Let h(m) be the third derivative of -m**8/560 + m**7/350 - 3*m**2. Factor h(s).
-3*s**4*(s - 1)/5
Let t(m) = -m**2 + 1. Let c(r) = 4*r**2 - 2*r - 2. Let i(s) = 2*c(s) + 6*t(s). Factor i(g).
2*(g - 1)**2
Let t(i) be the first derivative of i**3/9 - i**2/3 + i/3 - 7. Solve t(x) = 0 for x.
1
Let a(b) be the second derivative of 3*b - 1/60*b**5 + b**2 - 1/24*b**4 - 1/360*b**6 + 0 - 1/18*b**3. Let r(j) be the first derivative of a(j). Factor r(g).
-(g + 1)**3/3
Suppose -151 - 40 - 104 - 60*w - 5 - 3*w**2 = 0. Calculate w.
-10
Let o(d) be the first derivative of d**3/12 - 3*d**2/8 - d - 11. Suppose o(b) = 0. Calculate b.
-1, 4
Let g(i) = i**3 - 10*i**2 + 9*i + 4. Let c be g(9). Suppose 8 = c*f - 0*p + 2*p, -p = 2. Suppose 3*y - 7*y + y**f + 2*y + y = 0. What is y?
-1, 0, 1
Suppose 1 = -0*f - 2*f - w, -3*f + 4*w + 26 = 0. Factor 2/9*k**4 + 0*k**f + 0*k - 2/9*k**3 + 0.
2*k**3*(k - 1)/9
Let k be (1 - 7)/(2 - 4). Find o, given that 92*o**k - 2*o + 7*o - o + 8*o**3 - 40*o**2 = 0.
0, 1/5
Let v be (10/(-35))/((-30)/196). Let s(d) be the second derivative of 2*d - 4/5*d**2 + v*d**3 - 28/25*d**5 - 11/10*d**4 - 16/75*d**6 + 0. What is n in s(n) = 0?
-2, 1/4
Let l(p) be the first derivative of -13*p**3 + 9/5*p**5 - 6*p - 5 + p**6 - 15/4*p**4 - 27/2*p**2. Find v such that l(v) = 0.
-1, -1/2, 2
Factor 0 + 0*n + 44/5*n**3 + 4/5*n**5 - 28/5*n**4 - 4*n**2.
4*n**2*(n - 5)*(n - 1)**2/5
Let s(m) be the third derivative of 4*m**2 + 0*m**3 + 3/50*m**5 + 0*m - 1/40*m**4 - 1/40*m**6 + 0. Factor s(i).
-3*i*(i - 1)*(5*i - 1)/5
Let j(u) = -u**2 + 8*u + 12. Let a be j(9). Find t such that 2*t**3 - a + 2*t**4 + 3 - 4*t**4 = 0.
0, 1
Let w(s) be the third derivative of 0*s**3 + 0 + 0*s - 1/60*s**5 + 8*s**2 + 0*s**4. Solve w(n) = 0 for n.
0
Let h = 0 - 1. Let s be 0/1 - (h + 1). Find u, given that -u + 10*u**2 - 3*u + s*u**3 - 6*u**3 = 0.
0, 2/3, 1
Let a(n) = n**2 - 2*n - 1. Let c be a(-1). Let 6*v**3 - 8*v**4 + 2*v - 2*v**3 - 8*v**4 + 10*v**c = 0. Calculate v.
-1/2, -1/4, 0, 1
Let m(r) be the third derivative of -r**5/60 + r**4/2 - 6*r**3 + 33*r**2 + 2*r. Let m(w) = 0. What is w?
6
Suppose -3*g - 3 = -3*i, -7*i + 1 = -4*g - 4*i. Solve -2/5*q**3 - 2/5 + 2/5*q + 2/5*q**g = 0.
-1, 1
Let f(l) be the third derivative of -l**7/210 + l**6/30 + l**5/12 + 34*l**2. Determine q, given that f(q) = 0.
-1, 0, 5
Let y(x) be the first derivative of -5/6*x**4 + 0*x - 2/3*x**2 - 14/9*x**3 + 7. Factor y(h).
-2*h*(h + 1)*(5*h + 2)/3
Let k(z) = 5*z + 2*z**2 + 3 - z**2 + 0. Let g be k(-5). Suppose 1/4*v**g + 3/4*v + 3/4*v**2 + 1/4 = 0. Calculate v.
-1
Let j(a) be the second derivative of -3*a**5/100 + 7*a**4/20 - 4*a**3/5 - 24*a**2/5 + 6*a. Factor j(b).
-3*(b - 4)**2*(b + 1)/5
Let a(l) be the third derivative of l**7/315 + l**6/60 + l**5/90 - l**4/12 - 2*l**3/9 + 7*l**2. Solve a(r) = 0.
-2, -1, 1
Let h(b) be the second derivative of 1/6*b**4 - 1/20*b**5 + 4*b + 0 - 1/6*b**3 + 0*b**2. Find z, given that h(z) = 0.
0, 1
Let z = 2 + 0. Suppose -3*q = -8 + z. Let 6*y - 2*y**5 - 2 - 4*y**q - y**3 + 6*y**4 - 3*y**3 + 0*y**3 = 0. What is y?
-1, 1
Let p(k) be the first derivative of -k**7/735 + k**6/210 + k**5/210 - k**4/42 + k**2/2 + 8. Let s(g) be the second derivative of p(g). Solve s(l) = 0.
-1, 0, 1, 2
Find m, given that -2/19*m**2 + 0*m + 8/19 = 0.
-2, 2
Let q(p) be the third derivative of -p**7/210 - p**6/60 + 2*p**5/15 - 17*p**2. Factor q(i).
-i**2*(i - 2)*(i + 4)
Factor -4/5 - 6/5*n + 2/5*n**3 + 0*n**2.
2*(n - 2)*(n + 1)**2/5
Suppose 2*z - 6*z - 4 = 0, 3*z = -f. Suppose -7*r + 4*r = -6. Let 5*m + m - 9*m**r - m**f - 5*m**3 = 0. What is m?
-2, 0, 1/2
Suppose -2*c = 2*c - 20. Let q(y) be the second derivative of y**2 + 8/3*y**3 + 0 + 11/3*y**4 + 12/5*y**c + 2*y + 3/5*y**6. What is d in q(d) = 0?
-1, -1/3
Suppose 4*s - 20 - 16 = 0. Let a = s + -26/3. Solve -1/3*f**2 + 0 + 0*f + 0*f**3 + a*f**4 = 0.
-1, 0, 1
Let i(d) be the first derivative of -5*d**3/3 - 25*d**2 - 125*d + 28. Factor i(n).
-5*(n + 5)**2
Solve 0 - 4/7*y**4 - 2*y**5 - 16/7*y**2 + 6*y**3 - 8/7*y = 0.
-2, -2/7, 0, 1
Let a(k) be the first derivative of -4*k**5/15 + 3. Suppose a(n) = 0. What is n?
0
Let v be (-2)/10 - (-2)/10. Let q(r) = r + 4. Let b be q(v). Solve -j**3 + 1/2*j**5 - 1/2*j**b + j**2 + 1/2*j - 1/2 = 0 for j.
-1, 1
Suppose 3/2*b**4 + 9/2*b + 3/2*b**2 - 3 - 9/2*b**3 = 0. Calculate b.
-1, 1, 2
Let w be 15/40 - 29/(-8). Let b(c) be the first derivative of -7*c**2 - 2 - w*c - 10/3*c**3. Let b(r) = 0. What is r?
-1, -2/5
Factor 3/5*l**5 - 9/5*l**4 + 12/5*l**2 + 0 + 0*l**3 + 0*l.
3*l**2*(l - 2)**2*(l + 1)/5
Let z be (-2)/((-4)/5) + 9/6. Suppose -2/3*n + 2/3*n**z + 2/9*n**5 - 4/9*n**2 + 4/9*n**3 - 2/9 = 0. What is n?
-1, 1
Let w(y) be the first derivative of -3*y**4/20 - 3*y**3/5 + 9*y**2/5 