- 26*m**3/7 + 314*m**2. Find s, given that a(s) = 0.
-13, -3, -2, -1
Let y(h) = 7*h**4 - 13*h**3 + 5*h**2 - 4*h - 5. Let w(t) = 98 - 47 - 4*t**4 + 7*t**3 + 2*t - 2*t**2 - 48. Let x(v) = -5*w(v) - 3*y(v). Factor x(k).
-k*(k - 2)*(k - 1)**2
Let s(v) = -1 + 1 + 5 - 2*v - 2. Let c be s(-3). Suppose -r - 6*r + r + r**2 + c = 0. Calculate r.
3
Suppose 0 = -2*d + 5*t + 9, -2*t + 0 - 6 = -2*d. Suppose -y = d*y - 6. Factor 0 + 0*p + 1/4*p**3 + 1/2*p**y.
p**2*(p + 2)/4
Let u(g) be the second derivative of 3*g**5/20 - 15*g**4/4 + 25*g - 3. Solve u(a) = 0.
0, 15
Let o(y) be the second derivative of y**7/280 + y**6/40 + 3*y**5/40 + y**4/8 - 13*y**3/6 - 4*y. Let i(w) be the second derivative of o(w). Factor i(z).
3*(z + 1)**3
Suppose -9*z - 89 = 19. Let l be (-52)/z + (-5)/1 + 2. Solve -22/3*o**3 - 10/3*o**2 + 0 + l*o - 8/3*o**4 = 0.
-2, -1, 0, 1/4
Let j(y) be the first derivative of -y**3/18 + y**2/6 + y/2 - 12. Factor j(a).
-(a - 3)*(a + 1)/6
Let f = -13 - -35. Let q = -78 - -81. Let 5*g**3 + 22 - f - q*g**3 = 0. What is g?
0
Let s(d) be the first derivative of -9/8*d**2 + 3 - 4/3*d**3 - 3/10*d**5 - 1/24*d**6 - 1/2*d - 7/8*d**4. Factor s(o).
-(o + 1)**4*(o + 2)/4
Suppose 4*f = 5*y - 12, y + 4 = 3*y - 2*f. Let w be 52/13*21/4. Factor -4 + 0*u**4 - 5*u - y*u**4 + 16*u**3 - 24*u**2 + w*u.
-4*(u - 1)**4
Find c, given that 0 + 9*c**2 - 2*c**4 - 1/2*c**5 + 3/2*c**3 + 0*c = 0.
-3, 0, 2
Let t(k) be the first derivative of 46 + 0*k - 8/33*k**3 - 4/11*k**2 + 3/22*k**4. Let t(p) = 0. Calculate p.
-2/3, 0, 2
Factor 135/4*x**2 - 3/8*x**3 - 1587 - 1449/2*x.
-3*(x - 46)**2*(x + 2)/8
Let l(k) be the second derivative of -3*k**5/20 - 7*k**4/4 + 69*k**3/2 - 351*k**2/2 + 48*k + 2. Let l(y) = 0. Calculate y.
-13, 3
Factor 47/7*z**2 + 13/7*z**4 + 45/7*z**3 - 1/7*z**5 + 16/7*z + 0.
-z*(z - 16)*(z + 1)**3/7
Let k(x) be the third derivative of 0*x - 2*x**3 + 11/12*x**4 + 0 - 26*x**2 - 1/10*x**5. Factor k(q).
-2*(q - 3)*(3*q - 2)
Let f(g) be the second derivative of 18*g - 4/21*g**3 + 0*g**2 + 0 - 1/5*g**6 - 4/147*g**7 - 4/7*g**4 - 37/70*g**5. What is x in f(x) = 0?
-2, -1, -1/4, 0
Suppose 4*n + 2 - 7 = 5*g, -4*g - 20 = 0. Let w be (-2 - 0) + n/(210/(-144)). Find m, given that -2/7*m**3 - 8/7*m**2 - w*m - 4/7 = 0.
-2, -1
Let f(v) = -5*v**4 + 3*v**3 + 42*v**2 + 20*v + 21. Let o(l) = 5*l**4 - 4*l**3 - 41*l**2 - 20*l - 18. Let a(x) = -6*f(x) - 7*o(x). Let a(j) = 0. What is j?
-1, 0, 4
Determine p, given that -114/11 + 32/11*p + 2/11*p**2 = 0.
-19, 3
Let q = -10581 - -63487/6. Factor 0 - q*o**4 - 1/2*o**3 - 1/6*o - 1/2*o**2.
-o*(o + 1)**3/6
Let g be (25*-2)/5 - 4. Let u be 20/g*1 + (-49 - -51). Solve 0 - 6/7*p**2 - u*p - 2/7*p**3 = 0 for p.
-2, -1, 0
Let x(t) be the first derivative of -2*t**6/15 - 2*t**5/5 - t**4/3 + 31*t - 33. Let r(o) be the first derivative of x(o). Factor r(w).
-4*w**2*(w + 1)**2
Solve 125/3*b**2 + 1/3*b**3 - 1323 + 1281*b = 0 for b.
-63, 1
Let r(f) be the first derivative of 44 - 15/4*f**4 - 2*f**3 + 0*f**2 + 0*f - 12/5*f**5 - 1/2*f**6. Factor r(m).
-3*m**2*(m + 1)**2*(m + 2)
Let p = -135 + 138. Suppose 0 = -3*v + 6. Find y, given that -4*y**p - 16*y - y**3 + 16*y**v + y**3 = 0.
0, 2
Let d = -898 - -17961/20. Let b(u) be the third derivative of 0 + d*u**5 + u**3 + 0*u - 4*u**2 + 3/8*u**4. Factor b(j).
3*(j + 1)*(j + 2)
Let p(r) be the second derivative of -3*r**5/20 + 7*r**3/2 + 9*r**2 - 567*r. Factor p(x).
-3*(x - 3)*(x + 1)*(x + 2)
Factor 2/3*l - 2/3*l**5 + 0 + 4/3*l**4 + 0*l**3 - 4/3*l**2.
-2*l*(l - 1)**3*(l + 1)/3
Let n(r) be the second derivative of -r**6/80 + 27*r**5/160 - 11*r**4/32 - 21*r**3/16 + r - 220. Suppose n(u) = 0. What is u?
-1, 0, 3, 7
Let i(v) be the third derivative of v**7/1365 - v**5/130 - v**4/78 - 2*v**2 - 30*v. Factor i(c).
2*c*(c - 2)*(c + 1)**2/13
Let s = 44 + -33. Factor -8*h - 72 - s*h - 5*h - 2*h**2.
-2*(h + 6)**2
Suppose 0 + 3*c**2 + 0*c + 1/10*c**4 + 13/10*c**3 = 0. Calculate c.
-10, -3, 0
Suppose -x + 2*d = -4, 11 = -5*x - 5*d + 1. Let c(j) be the first derivative of -1/9*j**2 + x*j + 2/27*j**3 + 4. What is k in c(k) = 0?
0, 1
Let a = -97 + 97. Let r(x) be the third derivative of 0 + a*x + 1/5*x**5 + 0*x**3 - 5*x**2 + 1/8*x**4. Factor r(h).
3*h*(4*h + 1)
Let z(q) = -7*q**4 + q**3 + 33*q**2 - 30*q + 3. Let p(a) = -20*a**4 + 4*a**3 + 100*a**2 - 92*a + 8. Let k(o) = 3*p(o) - 8*z(o). Suppose k(v) = 0. What is v?
-3, 0, 1, 3
Let q(r) be the first derivative of -r**7/1400 - r**6/75 + 9*r**5/200 + 17*r**3 - 52. Let p(i) be the third derivative of q(i). Factor p(h).
-3*h*(h - 1)*(h + 9)/5
Let g = -28121/120 - 1473/40. Let b = -270 - g. Factor -2*i - 2/3 + b*i**2.
(i - 2)*(7*i + 2)/6
Suppose -20*f - 2*i + 24 = -17*f, 18 = 3*i. Find n such that -2*n**3 - 1/5*n**5 + 2*n**2 + n**f - n + 1/5 = 0.
1
Let r be 40/6*(-18)/(-15). Suppose r = 4*h - 0*h. Let -h*t**2 - t**2 + 13*t**4 - 6*t**4 + 16*t**3 + 7*t**2 = 0. What is t?
-2, -2/7, 0
Factor 42/13 + 254/13*o + 18/13*o**3 + 30*o**2.
2*(o + 21)*(3*o + 1)**2/13
Let r(a) = a**3 + a**2 + 1. Let p(c) = -6*c**3 - 2*c**2 - 3*c. Let f(d) = p(d) + 5*r(d). Let u(w) be the first derivative of f(w). Factor u(n).
-3*(n - 1)**2
Let j be ((-9)/(-6))/((-15)/12 - -2). Suppose -j*x - 1 = -9. Let 0 + 12/7*t**x + 8/7*t + 2/7*t**5 + 24/7*t**2 + 26/7*t**3 = 0. What is t?
-2, -1, 0
Factor 36/7 + 4/7*l**5 - 24/7*l**3 - 12/7*l**4 + 12*l + 40/7*l**2.
4*(l - 3)**2*(l + 1)**3/7
Let r(l) be the first derivative of 3/5*l + 1 + 1/5*l**3 + 3/5*l**2. Find u such that r(u) = 0.
-1
Let v(w) be the third derivative of -w**8/504 - 4*w**7/63 + w**6/90 + 4*w**5/9 - w**4/36 - 20*w**3/9 - 6*w**2 - 5. Solve v(g) = 0 for g.
-20, -1, 1
Let a(v) be the third derivative of -v**5/30 + v**4/3 - v**3 - 313*v**2. Solve a(j) = 0 for j.
1, 3
Suppose -2*g - 62 = 2*h, 4*g - 100 = -0*h + 4*h. Let x be (-4 + (-148)/h)/(1*3). Factor 0*t**2 + x*t + 0 - 3/7*t**3.
-3*t*(t - 1)*(t + 1)/7
Let n(x) = 12*x**2 - 5*x + 3. Let d(g) = -50*g**2 - 2*g + 11. Let a(o) = -17*o**2 - o + 4. Let b(v) = 17*a(v) - 6*d(v). Let i(m) = 5*b(m) - 4*n(m). Factor i(p).
(p - 1)*(7*p + 2)
Suppose 8*v - 1382 + 1126 = 0. Factor 64/5 - 8/5*n**3 - v*n + 68/5*n**2.
-4*(n - 4)**2*(2*n - 1)/5
Suppose -4*n - 3*g = 2*g - 20, 4*n - 5*g = -20. Suppose -4*k + 6 = y, -y = -n*y + 2*k - 6. Find w such that -y*w**2 - 3*w + 3*w**2 + 15 + 15*w = 0.
-1, 5
Factor -36*y - 195*y**4 + 18*y**3 + 392*y**4 - 15*y**2 - 200*y**4.
-3*y*(y - 4)*(y - 3)*(y + 1)
Let w(a) = 2*a - 23. Let h be w(7). Let r be 2 + 15/h + 10/18. Factor 8/9 + 2/9*f**2 + r*f.
2*(f + 2)**2/9
Let x(q) be the first derivative of 0*q + 0*q**2 + 1/40*q**5 - 22 + 0*q**4 + 0*q**3. Factor x(k).
k**4/8
Suppose -5*g + 15 = -t, 12*g + 5*t + 21 = 10*g. Factor -6/7*o**g + 0 + 2/7*o**3 + 4/7*o.
2*o*(o - 2)*(o - 1)/7
Let w = 2/13849 - -193860/180037. Factor 0 + 30/13*c**3 + 2/13*c - w*c**2 + 8/13*c**5 - 2*c**4.
2*c*(c - 1)**3*(4*c - 1)/13
Let p(f) be the third derivative of 7/60*f**6 - 60*f**2 + 2*f**3 + 0 + 0*f - 5/12*f**4 - 4/15*f**5. What is c in p(c) = 0?
-6/7, 1
Let i(j) be the second derivative of 0 + 0*j**2 - 1/12*j**4 + 1/84*j**7 - 1/40*j**5 - 9*j + 0*j**3 + 1/30*j**6. Factor i(a).
a**2*(a - 1)*(a + 1)*(a + 2)/2
Let r = 10 + -3. Suppose -5*g + 12 = 2*c, -3*c - r = -5*g - 0*c. Find v, given that -5*v + 3*v**g + 6 - 4*v - 3*v + 3*v = 0.
1, 2
Let o be (-4)/(-64) + 756/2240. Let x(y) be the first derivative of 0*y**2 - 1/2*y**4 + 0*y + o*y**5 - 13 + 0*y**3. Let x(a) = 0. Calculate a.
0, 1
Let o be (-7)/(-45)*39/273. Let n(b) be the second derivative of 0*b**2 + 1/6*b**4 - o*b**6 + 6*b + 0*b**5 + 0 + 2/9*b**3. Factor n(f).
-2*f*(f - 2)*(f + 1)**2/3
Let a be (-3 + 2)*13*-1. Suppose 3*t + a = 5*s - 7, -3*t + s - 4 = 0. Factor 0*q**2 + t + 0*q + 2/7*q**3.
2*q**3/7
Let d(c) = -16*c**4 + 20*c**3 - 16*c**2 - 8*c - 8. Let y(l) = -5*l**4 + 7*l**3 - 6*l**2 - 3*l - 3. Let t(u) = 3*d(u) - 8*y(u). Let t(g) = 0. What is g?
0, 1/2
Let c = 1537/38 + -759/19. Factor 5/8*u**2 - 1/8*u**3 - u + c.
-(u - 2)**2*(u - 1)/8
Suppose 8 - 34 = -p. Suppose -2*o + 4*x = 12, -6*x + x = 3*o - p. Factor 0 - 4/17*c**o - 2/17*c - 8/17*c**4 + 14/17*c**3.
-2*c*(c - 1)**2*(4*c + 1)/17
Suppose -3*h - 31 = -4*o - 0*o, 2*o - 2*h = 18. Factor 0*v + 2/9*v**o - 2/9*v**2 + 0 + 0*v**3.
2*v**2*(v - 1)*(v + 1)/9
Let j(m) be the first derivative of -m**5/60 + 7*m**4/24 + 4*m**3/9 - 7*m**2/1