n be b/(-1 - 4)*-2. Factor 3/2*q**3 - 3/2*q**n + 1/2*q + 0 - 1/2*q**4.
-q*(q - 1)**3/2
Let o(c) be the second derivative of c**4/48 + c**3 + 18*c**2 - 18*c. Factor o(t).
(t + 12)**2/4
Let h(k) = k**2 - 3*k. Let l(p) = 2*p**2 - 7*p. Suppose -7*o + 5*o - 2 = -5*w, -4*o + 2*w = -12. Let b(r) = o*l(r) - 10*h(r). Let b(s) = 0. What is s?
0, 1
Factor -15/7*v**2 + 27/7 + 3/7*v**3 + 9/7*v.
3*(v - 3)**2*(v + 1)/7
What is q in 3/4*q**4 + 0 - 1/4*q**3 + 1/2*q**5 - 1/4*q - 3/4*q**2 = 0?
-1, -1/2, 0, 1
Let j(o) be the second derivative of o**6/5 - o**5/10 - 5*o**4/6 + o**3/3 + 2*o**2 - 26*o. Factor j(r).
2*(r - 1)**2*(r + 1)*(3*r + 2)
Factor 97*u**3 + 192*u - 96*u**3 + 28*u**2 - 4*u**2 + 512.
(u + 8)**3
Find k such that -8/5*k**2 + 16/5*k + 32/5 - 4/5*k**3 = 0.
-2, 2
Find b, given that -1/4*b**4 - 1/4*b**2 + 3/4*b**3 + 1/2 - 3/4*b = 0.
-1, 1, 2
Let j(l) be the first derivative of l**4/4 - l**2/2 - 5. Factor j(n).
n*(n - 1)*(n + 1)
Let m be 1 + 6 + 133/(-19). Factor 0*h + 0 + 4/3*h**3 + 14/3*h**4 + m*h**2.
2*h**3*(7*h + 2)/3
Suppose 2*v - 3*v = -3. Let b be v/(-2)*(-12)/9. Factor 1/2*t + 1/4*t**b + 0.
t*(t + 2)/4
Let f = 749/285 + -36/19. Let m = f + -2/5. Factor 1/3*l**2 - 1/3*l**3 - 1/3 + m*l.
-(l - 1)**2*(l + 1)/3
Let c be 1 - 2 - 3/3 - -2. Let n(x) be the third derivative of -1/6*x**3 + c*x - 1/12*x**5 + 1/60*x**6 + 3*x**2 + 0 + 1/6*x**4. Factor n(g).
(g - 1)**2*(2*g - 1)
Let m(y) be the third derivative of y**8/1344 - y**6/480 - 9*y**2. Factor m(z).
z**3*(z - 1)*(z + 1)/4
Let n(h) be the third derivative of -h**7/70 - h**6/20 + h**5/20 + h**4/4 - 10*h**2. Factor n(f).
-3*f*(f - 1)*(f + 1)*(f + 2)
Let i(g) be the first derivative of g**7/252 + g**6/90 + g**5/120 - 3*g - 1. Let n(y) be the first derivative of i(y). Factor n(s).
s**3*(s + 1)**2/6
Let t(d) be the first derivative of d - 4 - 7/8*d**4 + 3/20*d**5 + 23/12*d**3 - 2*d**2. Factor t(i).
(i - 2)*(i - 1)**2*(3*i - 2)/4
Let c(x) be the third derivative of 2*x**2 + 13/90*x**5 + 0 + 0*x + 23/315*x**7 - 3/20*x**6 + 0*x**3 - 1/18*x**4 - 1/72*x**8. Find y, given that c(y) = 0.
0, 2/7, 1
Suppose 2*r - 5*r - 5*x + 25 = 0, 5*r + 5*x = 35. Let a(y) = y**2 - 5*y + 4. Let d be a(r). Factor 0 - d*s**3 - 2/3*s - 10/3*s**2.
-2*s*(2*s + 1)*(3*s + 1)/3
Let q(s) be the third derivative of -1/480*s**6 - s**2 + 0*s + 0 + 1/96*s**4 - 1/24*s**3 + 1/240*s**5. What is r in q(r) = 0?
-1, 1
Suppose -x + 5*d = 3*d - 4, 36 = -5*x - 4*d. Let t be (x/6)/((-14)/525). Factor -t*h + 1 + 23*h - h**2 - 2.
-(h + 1)**2
Let x = 23/9 - 11/9. Suppose x - 2/3*v**5 + 0*v**4 + 8/3*v**3 - 4/3*v**2 - 2*v = 0. Calculate v.
-2, -1, 1
Let v(g) = -4*g**5 - 8*g**4 + 8*g**2 - 4*g. Let k(y) = 12*y**5 + 23*y**4 - y**3 - 23*y**2 + 11*y. Let i(t) = -4*k(t) - 11*v(t). Determine q so that i(q) = 0.
-1, 0, 1
Let n(i) be the third derivative of -i**10/2016 + i**9/1260 + i**8/2240 + i**4/8 + i**2. Let l(t) be the second derivative of n(t). Solve l(q) = 0 for q.
-1/5, 0, 1
Let y(v) be the second derivative of v**7/3360 - v**6/1440 - v**3/2 + 2*v. Let p(o) be the second derivative of y(o). Factor p(z).
z**2*(z - 1)/4
Let n be ((-2)/(-3))/(2/3). Let f = 44 - 42. Factor 1 + 5 + f*l + l**2 - n - 4.
(l + 1)**2
Let t(x) be the second derivative of 2*x**6/15 - 7*x**5/10 + x**4 + x**3/3 - 2*x**2 + 3*x. Let t(d) = 0. What is d?
-1/2, 1, 2
Let -1/2*b**3 + 1/2*b + 1/4*b**4 - 1/4*b**2 + 0 = 0. What is b?
-1, 0, 1, 2
Suppose 4*m = 3*u + 28, m + 12 = 3*m - 2*u. Suppose -p - 3*p = 5*b - m, -5*p + 8 = 4*b. Factor 6/7*r**3 + 4/7*r**2 + 2/7*r**4 + p*r + 0.
2*r**2*(r + 1)*(r + 2)/7
Let h be (2 - (3 + 0))*9. Let r = -6 - h. Suppose -3 - a + 4*a**2 - 4*a**2 - r*a**2 + 7*a = 0. Calculate a.
1
Let n(b) = b**2 + b - 1. Let o be n(2). Let s = -2 + o. Find c such that c - 2*c + c**s + 8*c**2 - 7*c**2 - 1 = 0.
-1, 1
Suppose -8 = -5*u + 7. Suppose u = 3*g - 12. Factor -4/7*k**3 + 0*k + 0*k**2 + 2/7*k**4 + 0 + 6/7*k**g.
2*k**3*(k + 1)*(3*k - 2)/7
Let a = 7/38 + 117/190. Let o(t) be the first derivative of 8/5*t + 2/15*t**3 + 2 - a*t**2. Determine g so that o(g) = 0.
2
Suppose -5*r = -4 - 6. Let i be (2 - 2) + (1 - -1). Factor -2*b - b**i + b**2 - r*b**2.
-2*b*(b + 1)
Let a be (-12)/2*(-2)/4. Let g be ((-48)/54)/(2/(-3)). What is n in -2/3*n**4 - 2/3 + 0*n + g*n**2 + 0*n**a = 0?
-1, 1
Let f(n) be the first derivative of 6/5*n**5 + 0*n**2 + 0*n - 1/2*n**6 - 3/4*n**4 - 6 + 0*n**3. Factor f(o).
-3*o**3*(o - 1)**2
Let v(t) be the second derivative of -t**4/84 + 2*t. What is p in v(p) = 0?
0
Let o(j) be the third derivative of -j**7/5460 - j**6/1170 + j**5/780 + j**4/78 - j**3/3 + 9*j**2. Let p(a) be the first derivative of o(a). Factor p(r).
-2*(r - 1)*(r + 1)*(r + 2)/13
Let q(z) be the first derivative of -3*z**5/25 - 9*z**4/20 - 2*z**3/5 - 15. Factor q(c).
-3*c**2*(c + 1)*(c + 2)/5
Suppose 3*p - 5 - 13 = 0. Let u(v) be the third derivative of 0 - 1/300*v**p + 1/75*v**5 + 0*v**3 - 2*v**2 + 0*v - 1/60*v**4. Find z, given that u(z) = 0.
0, 1
Let u be (-11)/(-5) - 1*(2 - 0). Find b, given that 0*b - u*b**3 - 2/5*b**2 + 0 = 0.
-2, 0
Let x(o) = -o**2 + 72*o + 55. Let u(c) = 36*c + 28. Let h(i) = -9*u(i) + 4*x(i). Factor h(q).
-4*(q + 1)*(q + 8)
Let k(r) be the third derivative of -r**8/252 - 2*r**7/105 - r**6/45 + 3*r**2. Factor k(c).
-4*c**3*(c + 1)*(c + 2)/3
Suppose 14*t**3 + 25*t**4 - 60*t + 40 - 3*t**3 + 4*t**3 - 110*t**2 = 0. What is t?
-2, -1, 2/5, 2
What is n in 2/5*n**2 - 1/5*n - 2/5 + 1/5*n**3 = 0?
-2, -1, 1
Find l, given that 50/3*l**4 - 8/3 - 40/3*l - 14*l**2 + 40/3*l**3 = 0.
-1, -2/5, 1
Determine p so that 1/3*p**3 + 1/3*p**2 + 0*p + 0 = 0.
-1, 0
Let z(c) be the first derivative of 2/9*c**3 + 4/3*c**2 + 8/3*c + 2. Find a such that z(a) = 0.
-2
Let b(u) = -54*u - 30. Let o be b(-7). Let c = 2442/7 - o. Factor -4/7 + 2/7*j**4 + 2/7*j**2 - c*j + 6/7*j**3.
2*(j - 1)*(j + 1)**2*(j + 2)/7
Let t(s) be the first derivative of 8 - 3/2*s - 1/4*s**6 - 3/4*s**2 + 3/4*s**4 - 3/10*s**5 + s**3. Determine l so that t(l) = 0.
-1, 1
Let p(n) be the third derivative of -1/180*n**5 - 1/36*n**4 + 0 + 0*n + 3*n**2 - 1/18*n**3. Let p(b) = 0. What is b?
-1
Let o = 16 + -10. Let d be (4/o)/(26 + -24). Factor 0 + 1/3*a**2 + d*a**3 - 1/3*a - 1/3*a**4.
-a*(a - 1)**2*(a + 1)/3
Suppose -3*l - 16 = -4. Let u(h) = -2*h**2 - 8*h - 5. Let z(o) = -o**2 - 7*o - 4. Let d(w) = l*u(w) + 5*z(w). Let d(q) = 0. Calculate q.
0, 1
Suppose 19 + 5*a**2 + 10 - 39 - 4*a - a = 0. What is a?
-1, 2
Suppose -4 = -7*b + 6*b. Factor 1/2*r**5 + 0*r**3 + r**b - r**2 - 1/2*r + 0.
r*(r - 1)*(r + 1)**3/2
Factor -2/9*w**3 - 4/9*w**2 + 0*w + 2/3*w**4 + 0.
2*w**2*(w - 1)*(3*w + 2)/9
Let i(b) be the first derivative of b**5 + 7*b**4/4 - b**3 - 7*b**2/2 - 2*b - 18. What is x in i(x) = 0?
-1, -2/5, 1
Solve -16*a + 4*a + 2 - 4*a**3 + 12*a**2 + 2 = 0 for a.
1
Let s(p) be the second derivative of -1/36*p**4 - 1/9*p**3 + 0 - 4*p + 1/2*p**2. Factor s(v).
-(v - 1)*(v + 3)/3
Let m be 3/(-6) + 14/4. Let z = 251/5 - 49. Factor 4/5*s + 0 + 2/5*s**m + z*s**2.
2*s*(s + 1)*(s + 2)/5
Let x(v) be the second derivative of -v**6/45 + v**4/18 - 3*v. Factor x(t).
-2*t**2*(t - 1)*(t + 1)/3
Suppose 0*l - 3 = -l. Suppose -15 = -4*w + z, -5*w - l*z + 3 = z. Factor -5*u**3 + 0*u**w + 4*u**3 - 3*u**2 - 1 - 3*u.
-(u + 1)**3
Let a(i) be the second derivative of 0*i**3 + 2*i - i**2 + 0*i**5 + 0*i**4 + 0 - 1/240*i**6. Let y(z) be the first derivative of a(z). Factor y(t).
-t**3/2
What is f in -25/2*f**2 - 20*f - 10 - 5/2*f**3 = 0?
-2, -1
Find y such that 3*y**3 - 338*y - 3*y**2 + 338*y = 0.
0, 1
Let b(r) = -20*r**3 - 60*r**2 - 28*r. Let d(h) = 8*h**3 + 24*h**2 + 11*h. Let o(j) = 5*b(j) + 12*d(j). Let o(m) = 0. What is m?
-2, -1, 0
Let l(o) = -o**3 + 30*o**2 - 303*o + 997. Let z(i) = -i**3 + 30*i**2 - 304*i + 996. Let u(a) = 4*l(a) - 3*z(a). What is p in u(p) = 0?
10
Let k(z) be the third derivative of -z**8/294 - 3*z**7/245 - z**6/70 - z**5/210 - 3*z**2. Let k(s) = 0. Calculate s.
-1, -1/4, 0
Suppose -5*a = -5*w + 25, 9 = 2*w - a - 1. Let x be (-1 + -2)*(-6 + w). Factor 0 - 1/5*g - 2/5*g**2 - 1/5*g**x.
-g*(g + 1)**2/5
Let b be 2 - (-3)/(1 + 2). Find r, given that -r + 0*r**3 + b*r**2 + r**3 + 1 - 4*r**2 = 0.
-1, 1
Determine v so that -1/2*v + 0 - 1/2*v**2 + 1/2*v**3 + 1/2*v**4 = 0.
-1, 0, 1
Let w(v) be the second derivative of v**4/42 + v**3/21 - 5*v. Determine y, given 