 + 2/3*n**3 = 0.
2
Suppose 10 = -4*n + 22. Factor 1 + 2*b + 2*b**n - 4*b**3 + b**2 + b**2 - 3.
-2*(b - 1)**2*(b + 1)
Let s(j) be the first derivative of 2*j + j**4 - 2/3*j**3 + 3 - 2*j**2. Find k such that s(k) = 0.
-1, 1/2, 1
Factor -5*k + 85*k + 4*k**2 - 58 + 294 + 164.
4*(k + 10)**2
Let f(g) be the second derivative of g**4/21 + g**3/7 - 2*g**2/7 + 36*g. Factor f(y).
2*(y + 2)*(2*y - 1)/7
Let v be 2 - 3/(-2)*-2. Let c be (-7)/(-1) - (-3)/v. Factor -c*o**4 + 2*o**3 + 4*o**4 - 3*o**4 + 4*o**4.
o**3*(o + 2)
Let x(w) be the third derivative of -w**8/2016 + 7*w**6/720 + w**5/180 - w**4/12 - 2*w**3/9 - 5*w**2. Let x(m) = 0. What is m?
-2, -1, 2
Let n = 130/7 - 128/7. Factor n*p - 1/7 - 1/7*p**2.
-(p - 1)**2/7
Suppose 0 = -6*w + 3*w. Let d(q) be the third derivative of -q**2 - 4/3*q**3 + 1/60*q**6 + 0 + w*q**4 + 1/10*q**5 + 0*q. What is j in d(j) = 0?
-2, 1
Let z(b) = 11*b**5 - 17*b**3 + b - 5. Let r(v) = -v**3 - 6*v**5 + 0 + 3 + 0 + 10*v**3. Let f(y) = -5*r(y) - 3*z(y). Find j such that f(j) = 0.
-1, 0, 1
Let u(o) be the third derivative of -o**5/80 - 11*o**4/32 + 3*o**3/2 - 41*o**2. Factor u(j).
-3*(j - 1)*(j + 12)/4
Suppose -3*p + 0 = -9. Let f be 2 + -3*p/(-9). Solve x - 4 + 3*x + 0*x + f*x**2 = 0 for x.
-2, 2/3
Let x(p) be the second derivative of 2*p**5 + 23*p**4/6 + p**3/3 - 2*p**2 - 8*p. Find c such that x(c) = 0.
-1, -2/5, 1/4
Let t(o) be the first derivative of o**6/18 - o**4/3 - 2*o**3/9 + o**2/2 + 2*o/3 + 29. Factor t(w).
(w - 2)*(w - 1)*(w + 1)**3/3
Let b(l) = 27*l**3 + 27*l**2 + 15*l. Let c be 0 - (-60)/(5 + -1). Let y(t) = -7*t**3 - 7*t**2 - 4*t. Let i(j) = c*y(j) + 4*b(j). Factor i(w).
3*w**2*(w + 1)
Suppose 0 = 3*u + 2*u - 20. Let h(l) be the third derivative of 1/20*l**5 - 1/12*l**u + 0*l - 4*l**2 + 0 - 1/120*l**6 + 0*l**3. Find n such that h(n) = 0.
0, 1, 2
Let c = -182/3 + 61. Suppose -5*h + 5*r + 13 = -22, -22 = -h + 4*r. Solve -2/3 + 1/3*n**h - c*n = 0 for n.
-1, 2
Let h(j) be the second derivative of -2*j**6/15 + 2*j**5/5 - 4*j**3/3 + 2*j**2 + j. Factor h(f).
-4*(f - 1)**3*(f + 1)
Let a be (-1086)/504*1/(-9). Let t = 2/189 + a. Let 0 - 1/4*v**2 - t*v**3 + 0*v = 0. Calculate v.
-1, 0
Let n(k) be the second derivative of -k**5/5 - 17*k. Let n(x) = 0. What is x?
0
Let f(p) = 11*p**2 - 2*p - 2. Let l(t) = -5*t**2 + t + 1. Let v(y) = 3*f(y) + 7*l(y). Suppose v(u) = 0. What is u?
-1/2, 1
Suppose 4*g - 4 = 12. Determine s, given that -8*s + 44*s**2 + 14*s**4 + g*s**2 - 42*s**3 - 112*s**4 = 0.
-1, 0, 2/7
Suppose c - 5*l + 7 = 0, -3 = -5*l + 7. Suppose -w - 2*t + 0*t + 2 = 0, -5*t = -5. Determine q, given that -2/7 - 4/7*q**c + 2/7*q**4 + 4/7*q + w*q**2 = 0.
-1, 1
Let g(s) be the third derivative of s**7/2520 + s**6/288 + s**5/90 + s**4/72 + 40*s**2. Determine m, given that g(m) = 0.
-2, -1, 0
Let q be 2/(-7) - 12/(-42). What is i in i - 1/2*i**2 + q = 0?
0, 2
Suppose 4*s + 22*s = 130. Solve -4/3 + 12*o**2 + 10*o**s - 32/3*o**4 + 2/3*o - 32/3*o**3 = 0 for o.
-1, -1/3, 2/5, 1
Let h(k) be the first derivative of -k**6/12 - k**5/5 - k**4/8 + 29. Factor h(c).
-c**3*(c + 1)**2/2
Let o be 31/45 - (-10)/(-15). Let g(a) be the second derivative of o*a**6 + 0 + 0*a**2 + 2/45*a**5 + 1/54*a**4 + 0*a**3 + a. Let g(j) = 0. What is j?
-1, -1/3, 0
Let q(n) be the second derivative of -n**7/7 - 13*n**6/15 - 11*n**5/5 - 3*n**4 - 7*n**3/3 - n**2 - 9*n. Find p, given that q(p) = 0.
-1, -1/3
Let b(w) be the second derivative of w**4/90 - 28*w**3/45 + 196*w**2/15 - 2*w + 2. Factor b(y).
2*(y - 14)**2/15
Let s(h) = -5*h - 5*h - h**2 + 4*h + 0*h**2 - 1. Let t be s(-4). Find m such that -2 - 5*m**3 + t*m**3 - 2*m**4 + 2 + 2*m**2 - 2*m = 0.
-1, 0, 1
Let q(v) be the second derivative of 11*v**5/10 - 23*v**4/6 + 13*v**3/3 - v**2 - 8*v - 3. Find i, given that q(i) = 0.
1/11, 1
Let v(j) be the third derivative of 1/270*j**5 + 0*j + 0 + 4*j**2 + 1/1512*j**8 + 0*j**3 + 0*j**4 + 1/315*j**7 + 1/180*j**6. Find d, given that v(d) = 0.
-1, 0
Let m(o) = -10*o**2 + 7*o**2 + o**3 + 3 + 11*o**2 + 7*o. Let b be m(-7). Factor 2/5*h - 8/5*h**b + 0 - 6/5*h**2.
-2*h*(h + 1)*(4*h - 1)/5
Let h(s) = s**3 - 7*s**2 + 6*s + 4. Let z be h(6). Let x(l) be the second derivative of -1/60*l**5 + 2*l + 0*l**2 - 1/36*l**z + 0 + 0*l**3. Factor x(d).
-d**2*(d + 1)/3
Let l(i) = i**3 + 13*i**2 + 31*i - 40. Let a be l(-9). Factor h**2 - 1/2*h**a + 0*h + 3/2*h**3 + 0*h**4 + 0.
-h**2*(h - 2)*(h + 1)**2/2
Let a(y) = 2*y**2 - 4*y + 2. Let p be 1/((-1)/(-6)*3). Let t(f) = 2*f**2 - 4*f + 2. Let c(r) = p*a(r) - 3*t(r). Factor c(m).
-2*(m - 1)**2
Let l be (0/3)/2 - (5 - 5). Let x(w) be the first derivative of 2/3*w - 4 + l*w**2 - 2/9*w**3. Factor x(a).
-2*(a - 1)*(a + 1)/3
Let d = -823 - -825. Factor -3/2 + t - 1/6*t**d.
-(t - 3)**2/6
Let a = 18 - 9. Let r(b) = -b**2 + 10*b - 7. Let j be r(a). Factor 3/5*u**j + 0 + 0*u.
3*u**2/5
Let i be 2 - (-3 - (-12)/4). Suppose -i*c = -2 - 2. Factor 0*q + 2/9*q**c - 2/9.
2*(q - 1)*(q + 1)/9
Suppose 0*u + 5/3*u**2 + 0 + 5/3*u**5 - 5/3*u**4 - 5/3*u**3 = 0. Calculate u.
-1, 0, 1
Let p(h) be the third derivative of -h**6/540 - h**5/60 - h**4/18 + h**3 + 3*h**2. Let b(g) be the first derivative of p(g). Factor b(s).
-2*(s + 1)*(s + 2)/3
Suppose -7 + 15 = z. Let l(c) = -53*c**3 - 63*c**2 + 69*c - 19. Let g(y) = 158*y**3 + 188*y**2 - 208*y + 56. Let v(m) = z*l(m) + 3*g(m). Factor v(d).
2*(d + 2)*(5*d - 2)**2
Suppose -2*g - 3*i + 20 = 0, -i - 4 = -5*g + 3*i. Factor -2/9 - 2/9*w**g + 4/9*w**2 + 0*w + 0*w**3.
-2*(w - 1)**2*(w + 1)**2/9
Factor -2/5*v**3 - 1/5*v**2 + 2/5*v + 1/5*v**4 + 0.
v*(v - 2)*(v - 1)*(v + 1)/5
Let i = -19 + 20. Let c(k) be the first derivative of -2/3*k - 2/3*k**2 - i - 2/9*k**3. Factor c(m).
-2*(m + 1)**2/3
Let n = 42 + -81/2. Let s(u) be the second derivative of -1/5*u**5 + u**2 + 1/4*u**4 + 0 + n*u**3 - u. Factor s(l).
-(l - 2)*(l + 1)*(4*l + 1)
Let m = -439/3050 + 10/61. Let t(g) be the second derivative of 0 + 1/15*g**3 - 2*g - m*g**5 - 1/5*g**2 + 1/30*g**4. Factor t(i).
-2*(i - 1)**2*(i + 1)/5
Let m(u) be the third derivative of u**8/84 - 2*u**7/105 - u**6/30 + u**5/15 - 35*u**2. Factor m(z).
4*z**2*(z - 1)**2*(z + 1)
Let d(i) be the first derivative of -7 - 3/5*i**5 - 9/4*i**4 - i**3 + 9/2*i**2 + 6*i. Solve d(j) = 0 for j.
-2, -1, 1
Let -17/6*a - 1/3 - 5/2*a**2 = 0. Calculate a.
-1, -2/15
Let n(y) be the third derivative of 0*y**4 + 1/35*y**7 + 0*y**3 + 1/15*y**5 - y**2 - 1/12*y**6 + 0*y + 0. Factor n(s).
2*s**2*(s - 1)*(3*s - 2)
Suppose 0 = -2*o + 5 - 1. Factor -p**2 - 3*p + 12*p + 5*p**2 - p**o.
3*p*(p + 3)
Let r(u) be the third derivative of 0*u**5 + 5*u**2 + 0*u**6 + 0 - 1/672*u**8 + 0*u + 0*u**3 - 1/420*u**7 + 0*u**4. Factor r(c).
-c**4*(c + 1)/2
Let l(g) be the second derivative of g**4/20 - 2*g**3/5 + 9*g**2/10 - 8*g. Suppose l(x) = 0. What is x?
1, 3
Suppose 0 = -3*g + 2*g - 4*h + 16, -5*h + 20 = -3*g. Let k(u) be the third derivative of u**2 + g + 0*u - 1/240*u**6 + 0*u**5 + 1/48*u**4 + 0*u**3. Factor k(v).
-v*(v - 1)*(v + 1)/2
Let a(i) be the third derivative of -1/240*i**6 - i**2 + 0*i + 0*i**4 + 0*i**3 + 0 - 1/280*i**7 + 1/240*i**5. Factor a(z).
-z**2*(z + 1)*(3*z - 1)/4
Let x be 5/(-4)*100/(-25). Solve 0*y + 0 + 2/3*y**4 - 2/3*y**2 - 8/3*y**x + 8/3*y**3 = 0 for y.
-1, 0, 1/4, 1
Suppose -1/2*g + 1/4*g**2 + 1/4 = 0. Calculate g.
1
Let p(q) be the third derivative of q**7/315 + q**6/180 - q**5/180 + q**3/6 - 2*q**2. Let j(u) be the first derivative of p(u). What is h in j(h) = 0?
-1, 0, 1/4
Let -20*c**4 + c**2 + 14*c**2 + 36*c**3 + 13*c**2 - 12*c - 24*c**5 - 8 = 0. What is c?
-1, -1/2, 2/3, 1
Let k(u) be the third derivative of -u**5/12 + 5*u**4/4 - 25*u**3/6 + 18*u**2. Factor k(r).
-5*(r - 5)*(r - 1)
Let m(l) be the third derivative of l**9/151200 - l**8/50400 - l**5/12 + 3*l**2. Let o(t) be the third derivative of m(t). Suppose o(s) = 0. What is s?
0, 1
Let v = 14 - 10. Let y(f) be the first derivative of -2 - 3/5*f**5 + 1/2*f**v + 0*f**3 + 0*f**2 + 0*f. Determine r so that y(r) = 0.
0, 2/3
Let s = -16 - -16. Let i(k) be the third derivative of 0 - 1/1050*k**7 + s*k + 0*k**4 + 1/80*k**8 + 0*k**3 + k**2 - 1/300*k**6 + 0*k**5. Factor i(f).
f**3*(3*f - 1)*(7*f + 2)/5
Solve 3*v**3 - 14 - 12*v**2 + 7 + 9*v + 7 = 0.
0, 1, 3
Suppose -x = -4*n, -2*x = -3*x - 2*n + 6. Factor -2*w**3 - 2*w**4 + 2*w + 3*w**4 - 2*w**2 + w**x.
2*w*(w - 1)**2*(w