 - b**7/210 - b**6/180 + b**5/30 - 2*b**3/3 + 1. Let v(r) be the third derivative of m(r). What is f in v(f) = 0?
-1, 0, 1, 2
Suppose -2*a = -5 - 1. Suppose 0*n**a - 2 + n**3 - 3*n + 0*n**3 = 0. What is n?
-1, 2
Let l(t) = -3*t**3 - t**2 - t. Let a = -1 + 0. Let w be l(a). What is h in -6/5*h**2 + 4/5*h**w + 0*h + 2/5 = 0?
-1/2, 1
Let s(l) be the second derivative of -l**7/15120 - l**6/4320 + l**5/360 - l**4/2 + 2*l. Let y(f) be the third derivative of s(f). Factor y(m).
-(m - 1)*(m + 2)/6
Let a(y) = 6*y**3 + 14*y**2 + 42*y + 2. Let l(k) = -2*k**3 - 5*k**2 - 14*k - 1. Let c(o) = 5*a(o) + 16*l(o). Factor c(n).
-2*(n + 1)**2*(n + 3)
Suppose 10 - 30 = -5*w. Suppose -c = w*c. Solve -3*n**2 + c*n**2 + 12*n**3 - 5*n**2 - 6*n**5 + 4 + 4*n**4 - 6*n = 0.
-1, 2/3, 1
Let d(x) be the first derivative of -13/12*x**3 + 5/16*x**4 + 4 + 1/2*x**2 + x. Factor d(k).
(k - 2)*(k - 1)*(5*k + 2)/4
What is s in -2*s + 2/9*s**2 + 0 = 0?
0, 9
Let h(q) = -q**3 - 5*q**2 + 15*q + 10. Let a be h(-7). Let 1/6*z**a - 1/6*z + 0*z**2 + 0 = 0. Calculate z.
-1, 0, 1
Let z(d) be the second derivative of 1/168*d**7 - d + 0 + 1/24*d**4 - 1/60*d**6 + 0*d**2 - 1/24*d**3 + 0*d**5. What is h in z(h) = 0?
-1, 0, 1
Factor -36*t**2 + 76*t**2 - 35*t**2 - 5*t**3.
-5*t**2*(t - 1)
Let z(p) be the first derivative of -7*p**3 + 12*p + 9/2*p**6 + 9/5*p**5 + 12*p**2 - 51/4*p**4 - 4. Solve z(w) = 0 for w.
-1, -2/3, 1
Let c be (4 - 3)/((-21)/(-6)). Factor 2/7*v**3 - 2/7*v**4 - 2/7*v + c*v**2 + 0.
-2*v*(v - 1)**2*(v + 1)/7
Let f(l) be the first derivative of -l**4/26 + 14*l**3/13 - 99*l**2/13 - 242*l/13 - 3. Let f(r) = 0. What is r?
-1, 11
Solve -32/5*r - 2*r**2 + 10*r**3 - 8/5 = 0.
-2/5, 1
Let p be (38/95)/(1372/(-690) + 2). Factor -24 - 24*r - 96*r**3 - 9/2*r**5 + p*r**4 + 108*r**2.
-3*(r - 2)**4*(3*r + 1)/2
Let c be (-5)/(-10) + (-1)/2. Suppose 0 = 2*w - 8, c*u = 3*u + 5*w - 35. Find y such that -3*y**2 + 7*y**3 + y - 3*y - 7*y**4 + u*y**3 = 0.
-2/7, 0, 1
Let q(i) = -i. Let s(a) = 3 + 3 + 3*a - 2*a**3 + 2*a**2 - 6. Let u(z) = -3*q(z) - s(z). Find l such that u(l) = 0.
0, 1
Suppose -4*d + 4 = -48. Factor 10*z**2 - 26*z - 5 + d - 6*z - 12*z**3 + 26*z**3.
2*(z - 1)*(z + 2)*(7*z - 2)
Factor 3/4*l**3 + 9/4*l**2 + 3/2 - 3/4*l**4 - 15/4*l.
-3*(l - 1)**3*(l + 2)/4
Let u(n) be the first derivative of 2*n**5/45 - n**4/6 + 2*n**3/9 - n**2/9 - 7. Find i such that u(i) = 0.
0, 1
Suppose 3*f - 3*b - 6 = f, -4*b - 3 = -f. Factor 27*y**2 + 43*y**f - 4 + 2*y + 2*y - 17*y**3 + 7*y**4.
(y + 1)**2*(y + 2)*(7*y - 2)
Let t(j) be the second derivative of -2/27*j**3 - 4/45*j**5 + 5*j + 1/45*j**6 + 0*j**2 + 7/54*j**4 + 0. Suppose t(l) = 0. What is l?
0, 2/3, 1
Let f(x) be the second derivative of x**7/252 - x**6/90 - x**5/40 + x**4/18 + x**3/9 + 5*x. Find s such that f(s) = 0.
-1, 0, 2
Let l be (29 - 25) + (-1 + 0 - -1). Let u(d) be the second derivative of -d + 1/60*d**5 - 1/36*d**l - 1/18*d**3 + 1/6*d**2 + 0. What is o in u(o) = 0?
-1, 1
Let u(g) be the first derivative of 3/20*g**5 + 0*g - 3/16*g**4 - 2 - 1/24*g**6 + 0*g**2 + 1/12*g**3. Factor u(w).
-w**2*(w - 1)**3/4
Suppose 0*d - 193 = -d. Let g = d - 1349/7. Find f such that -g*f + 0 + 2/7*f**2 = 0.
0, 1
Let k(c) be the third derivative of 5*c**8/896 + c**7/70 + c**6/320 - c**5/80 + 11*c**2. Let k(o) = 0. Calculate o.
-1, 0, 2/5
Let p(s) be the first derivative of 1/300*s**5 + 1/60*s**4 + 0*s + 1/30*s**3 - 3 - 1/2*s**2. Let l(v) be the second derivative of p(v). What is n in l(n) = 0?
-1
Let d(y) be the third derivative of -y**6/480 + y**4/32 + y**3/12 + 5*y**2. Let d(g) = 0. Calculate g.
-1, 2
Let u(m) be the second derivative of -5*m**4/6 - 8*m**3/3 + 4*m**2 + 7*m. Factor u(i).
-2*(i + 2)*(5*i - 2)
Let o(b) = 5*b**4 - 10*b**3 - 13*b**2 + 18*b + 20. Let k(l) = -20*l**4 + 40*l**3 + 51*l**2 - 71*l - 80. Let n(p) = 2*k(p) + 9*o(p). Factor n(s).
5*(s - 2)**2*(s + 1)**2
Let r = 418/13 + -578/39. Let g = r - 16. Factor 4/3*q**4 - 2*q**3 + 0 + g*q**2 - 1/3*q**5 - 1/3*q.
-q*(q - 1)**4/3
Suppose 4*j - 20 = -2*x, 5*x - 3*x = 5*j - 16. Suppose 6 - 8*h**2 + 0*h**2 - 5*h**x + 8*h - h**2 = 0. What is h?
-3/7, 1
Suppose -4*g + 7*g + 9 = 0. Let v = g + 5. Factor o**v + 2*o - 3*o**2 - 6*o.
-2*o*(o + 2)
Let z(k) = -k - 3 - 1 + 3. Let w be 18/(-6) - -1*7. Let y(x) = -2*x**2 + 6*x + 4. Let v(g) = w*z(g) + y(g). Suppose v(q) = 0. What is q?
0, 1
Let k(w) be the second derivative of w**7/840 - w**6/90 + w**5/24 - w**4/12 - w**3/2 + 2*w. Let o(t) be the second derivative of k(t). Factor o(n).
(n - 2)*(n - 1)**2
Let b(d) be the second derivative of -d**6/180 + d**5/15 - d**4/3 + 2*d**3/3 - 3*d. Let c(w) be the second derivative of b(w). Solve c(x) = 0 for x.
2
Find j, given that -2*j - 18/5*j**5 - 16/5*j**2 + 28/5*j**3 + 12/5*j**4 + 4/5 = 0.
-1, -2/3, 1/3, 1
Find v such that 2*v**3 - 5*v**2 - 4*v**3 + 5*v**4 - 3*v**3 + 5*v = 0.
-1, 0, 1
Suppose 20 = 2*l - 7*w + 11*w, -5*l - 3*w + 15 = 0. Find o such that l - 2/3*o - 1/3*o**2 = 0.
-2, 0
Let a(g) be the first derivative of -3/5*g**5 - 3 + 1/6*g**6 + 2/3*g**3 - 3/2*g**2 + 1/2*g**4 + g. Factor a(q).
(q - 1)**4*(q + 1)
Let q be -1*3 + (-2 - 847/(-168)). Let w(u) be the second derivative of q*u**4 - 1/60*u**6 + 0*u**2 + 0 - u + 1/120*u**5 - 1/36*u**3. Find l such that w(l) = 0.
-1, 0, 1/3, 1
Suppose -3 = p - 2*l, -p + 6 + 11 = 3*l. Factor 4/5*d**3 + 2/5*d**4 + 0 - 6/5*d**p + 0*d**2 + 0*d.
-2*d**3*(d - 1)*(3*d + 2)/5
Let c(p) be the second derivative of -p**7/6300 + p**6/1800 + p**4/4 + 2*p. Let x(d) be the third derivative of c(d). Factor x(b).
-2*b*(b - 1)/5
Let s(p) = 2*p - 20. Let l be s(13). Let z(g) be the second derivative of 0*g**2 - g + 2/105*g**l + 1/21*g**3 + 1/14*g**5 + 2/21*g**4 + 0. Factor z(a).
2*a*(a + 1)**2*(2*a + 1)/7
Let w(q) = 9*q - 6. Let d(k) be the first derivative of k**3/3 - 3. Let c(p) = -3*d(p) + w(p). Factor c(r).
-3*(r - 2)*(r - 1)
Let x(t) be the first derivative of 0*t**2 + 0*t**3 - 1/12*t**6 - 1/8*t**4 - 3 - 1/5*t**5 + 0*t. Determine l, given that x(l) = 0.
-1, 0
Let r(c) = -c**3 - 12*c**2 + 27*c - 19. Let o(q) = 3*q**3 + 24*q**2 - 55*q + 39. Let z(j) = -3*o(j) - 7*r(j). Factor z(a).
-2*(a - 2)**3
Factor -2/3 - 1/3*a**2 - a.
-(a + 1)*(a + 2)/3
Let c(j) be the first derivative of -7*j**5/15 - j**4/6 + 7*j**3/9 + j**2/3 + 18. Let c(l) = 0. Calculate l.
-1, -2/7, 0, 1
Let t(k) be the first derivative of -4/15*k**2 - 2/45*k**3 - 5 - 8/15*k. Determine a so that t(a) = 0.
-2
Let b = 34 + -21. Suppose -13 + b - a - a**2 = 0. Calculate a.
-1, 0
Factor -7*c + c**2 - 10 + 0*c + 5*c + 11*c**2.
2*(c - 1)*(6*c + 5)
Let g(i) = -3*i**3 - 3*i**2 + 3*i + 3. Let s = -1 + -3. Let k(v) = -6*v**3 + 2*v**3 + v**3 + 1 + 2*v**3. Let t(q) = s*k(q) + g(q). Factor t(w).
(w - 1)**3
Let o(x) = 2*x + 5. Let g be o(0). Factor 15*r**2 - g*r**2 + 3*r**4 - 6*r**3 - 7*r**2.
3*r**2*(r - 1)**2
Let v(o) be the first derivative of -o**4/16 + o**3/4 + o**2/2 + 44. Suppose v(c) = 0. What is c?
-1, 0, 4
Let p = -932/5 + 187. Solve -24/5*x - p*x**2 - 48/5 = 0.
-4
Let t(x) be the second derivative of -x**8/168 + x**6/60 - 5*x**2 + x. Let a(u) be the first derivative of t(u). Let a(j) = 0. What is j?
-1, 0, 1
Let k = -419/2 + 2945/14. Let z(x) = -2*x + 1. Let q be z(-2). Find r such that 0 + 6/7*r**2 + 10/7*r**3 - 8/7*r**q - k*r**4 - 2/7*r = 0.
-1, 0, 1/4, 1
Let j = 317 - 597. Let b be (60/j)/((-6)/32). Factor -8/7*n**2 + 0 + b*n + 2/7*n**3.
2*n*(n - 2)**2/7
Let u be (-4)/10 + 2*(-4)/(-10). Suppose -u*g**2 + 4/5*g - 2/5*g**3 + 0 = 0. What is g?
-2, 0, 1
Determine a, given that -a - 12/5*a**2 + 2/5 = 0.
-2/3, 1/4
Let d(r) be the first derivative of -r**8/1008 + r**6/180 - r**4/72 - r**2 + 1. Let h(k) be the second derivative of d(k). Let h(n) = 0. Calculate n.
-1, 0, 1
Solve 7/3*n**4 - 1/3*n**5 + 25/3*n**2 - 19/3*n**3 + 4/3 - 16/3*n = 0.
1, 2
Let g(y) be the third derivative of -y**8/840 + y**7/630 + y**3/6 - 3*y**2. Let i(t) be the first derivative of g(t). Let i(m) = 0. What is m?
0, 2/3
Let d(a) be the third derivative of -a**5/66 + a**4/66 - 8*a**2. Suppose d(m) = 0. What is m?
0, 2/5
Let j = -5 - -5. Let s be (15/6)/(-5)*j. Factor -2*n**2 + 4 + s*n**2 - 2*n + 0.
-2*(n - 1)*(n + 2)
Let y(c) be the third derivative of -c**5/15 + 2*c**4/3 - 8*c**3/3 + 2*c**2. Factor y(o).
-4*(o - 2)**2
Let n(o) = -15*o**3 + 31*o**2 - 48*o + 45. Let d(i) = 7*i**3 - 15*