6/90 - y**5/30 + y**4/3 - 4*y**3/3 - 3*y. Let m(b) be the second derivative of k(b). Find d, given that m(d) = 0.
-2, 1
Let v(w) = w - 2. Let i be v(7). Let g(k) be the third derivative of 0 + 2/21*k**3 + 0*k + 8/105*k**i - k**2 + 1/60*k**6 + 11/84*k**4. Factor g(a).
2*(a + 1)**2*(7*a + 2)/7
Factor -12*j**2 - 36 + 4/3*j**3 + 36*j.
4*(j - 3)**3/3
Let -4/3 + 10/3*b**2 - 8/3*b**3 + 14/3*b = 0. Calculate b.
-1, 1/4, 2
Let q(s) be the first derivative of s**5/25 - s**4/20 - s**3/5 + s**2/10 + 2*s/5 + 19. Factor q(v).
(v - 2)*(v - 1)*(v + 1)**2/5
Let j(o) be the third derivative of -o**5/60 + o**4/8 + o**3/2 + o**2. Let u be j(3). Solve d**2 - 5*d**3 + 4*d**u + d**2 = 0.
0, 2
Let i be 4 - (-3 - 4/(-2)). Factor -a**2 - 2*a + a - 6 + i + 3*a.
-(a - 1)**2
Suppose 3*j + 0 + 231/4*j**3 - 147/4*j**4 - 24*j**2 = 0. What is j?
0, 2/7, 1
Let j(n) = n**5 + n**3 + n. Let f(s) = -s**5 + s**4 + 2*s**3 + s. Let y(a) = -f(a) + j(a). Factor y(z).
z**3*(z - 1)*(2*z + 1)
Let g(f) be the second derivative of -4*f**5/25 - 6*f**4/5 - 11*f**3/10 - 2*f**2/5 - 5*f. Factor g(a).
-(a + 4)*(4*a + 1)**2/5
Suppose -9*x - x = -20. Find a such that 0*a + 3/2*a**4 - 7/2*a**2 + x - 1/2*a**5 + 1/2*a**3 = 0.
-1, 1, 2
Let z(t) be the third derivative of -1/27*t**3 + 1/18*t**4 - 1/378*t**8 - 1/270*t**6 - 4/135*t**5 - 2*t**2 + 0*t + 1/105*t**7 + 0. Solve z(w) = 0.
-1, 1/4, 1
Let k(y) be the third derivative of 4*y**2 - 1/300*y**6 + 0*y**3 + 1/1680*y**8 + 0*y**7 + 0*y + 1/120*y**4 + 0 + 0*y**5. Factor k(s).
s*(s - 1)**2*(s + 1)**2/5
Suppose 16 = 3*g - 2. Suppose 0*k - g = -2*k. Factor 8*t - 4*t**3 + 2 + t**2 - 4*t - k + 0*t.
-(t - 1)*(t + 1)*(4*t - 1)
Let q(o) be the first derivative of 5*o**6/2 + 63*o**5/5 + 51*o**4/2 + 26*o**3 + 27*o**2/2 + 3*o - 7. Suppose q(b) = 0. What is b?
-1, -1/5
Suppose -3*m - 3 = -h + 4*h, 0 = 4*m + h + 1. Find a, given that m*a**5 - 3*a**2 - 9*a**3 - 5*a**5 + 2*a**5 - 9*a**4 = 0.
-1, 0
Let d(c) be the third derivative of -c**9/13608 - c**8/3780 + c**6/810 + c**5/540 - 2*c**3/3 + 2*c**2. Let v(j) be the first derivative of d(j). Factor v(p).
-2*p*(p - 1)*(p + 1)**3/9
Solve 0*r + 0 + 1/2*r**2 + 1/2*r**3 - 1/2*r**5 - 1/2*r**4 = 0 for r.
-1, 0, 1
Let z(p) be the first derivative of p**6/3 + 2*p**5/5 - p**4 + 17. Factor z(s).
2*s**3*(s - 1)*(s + 2)
Let b(j) be the third derivative of j**6/96 - j**5/30 - 19*j**4/96 - j**3/4 + 32*j**2. Suppose b(u) = 0. Calculate u.
-1, -2/5, 3
Let o(q) be the second derivative of q**4/6 + 2*q**3/3 + q**2 - 15*q. Solve o(m) = 0.
-1
Let m = -2224/3 - -744. What is a in 4/3*a - 8/3*a**2 - 4/3*a**3 + m = 0?
-2, -1, 1
Let l = -29/4 - -211/28. Let -2/7*x + l*x**3 + 2/7 - 2/7*x**2 = 0. Calculate x.
-1, 1
Let v(p) be the second derivative of p**8/5040 - p**7/2520 + p**3 + p. Let i(d) be the second derivative of v(d). Suppose i(o) = 0. What is o?
0, 1
Let a be (-8)/10 - (-264)/55. Let o(t) be the second derivative of 0*t**3 - 4*t + 1/24*t**a - 1/4*t**2 + 0. Factor o(n).
(n - 1)*(n + 1)/2
Let p(j) be the third derivative of 0*j**3 + 0*j - 1/105*j**7 + 0 + 1/30*j**6 - 1/30*j**5 + 0*j**4 + 4*j**2. Solve p(b) = 0 for b.
0, 1
Let h(p) be the second derivative of -p**4/12 - p**3/6 - 7*p. What is f in h(f) = 0?
-1, 0
Let n(l) be the third derivative of -l**7/560 + l**6/160 - l**4/32 + l**3/16 - 4*l**2. Factor n(g).
-3*(g - 1)**3*(g + 1)/8
Solve j**2 + 4/5 - 1/5*j**3 - 8/5*j = 0.
1, 2
Let x be 2 - ((-2)/525 + 2). Let k(g) be the third derivative of 0*g**3 + x*g**7 + 0*g**4 + 0 + 0*g**5 + 1/840*g**8 + 1/300*g**6 + 0*g - 2*g**2. Factor k(w).
2*w**3*(w + 1)**2/5
Let q = -214534/7 + 30758. Let r = q + -110. Factor -2/7*o**3 - 6/7*o + 6/7*o**2 + r.
-2*(o - 1)**3/7
Let v(b) be the first derivative of 1/2*b**4 - 2/3*b**3 + 0*b + 2/5*b**5 - b**2 - 4. Suppose v(j) = 0. What is j?
-1, 0, 1
Let z(y) = y - 1. Let o(c) = -7*c**3 + 2*c**2 - 6. Let i(j) = -j**3 - j. Let k(n) = -6*i(n) + o(n). Let h(u) = -k(u) + 6*z(u). Factor h(g).
g**2*(g - 2)
Let x(q) be the first derivative of -1/5*q**5 - 1 + 0*q + 1/4*q**2 - 2/3*q**3 + 5/8*q**4. Factor x(d).
-d*(d - 1)**2*(2*d - 1)/2
Factor 1/2*k - 1/2 - 1/2*k**3 + 1/2*k**2.
-(k - 1)**2*(k + 1)/2
Let c(p) be the third derivative of p**5/210 + p**4/42 + 13*p**2. Factor c(f).
2*f*(f + 2)/7
Let s(f) = -26*f**5 + 46*f**3 - 36*f**2 + 16*f + 16. Let x(o) = 5*o**5 - 9*o**3 + 7*o**2 - 3*o - 3. Let l(u) = 3*s(u) + 16*x(u). Solve l(c) = 0 for c.
-2, 0, 1
Let d = 8 - 5. Suppose d*u = -u + 8. Solve 1 - 1 - 4*a**2 + 2*a + 3*a**u = 0 for a.
0, 2
Suppose -4*x + 5*c = c - 8, 2*x - 4*c = 2. Solve 2/3*g**4 + 0*g**2 + 4/3*g - 4/3*g**x - 2/3 = 0.
-1, 1
Let v(s) = 5*s**3 + 12*s**2 + 9*s. Let d(l) = -l**3 - l. Let t(x) = d(x) + v(x). Factor t(o).
4*o*(o + 1)*(o + 2)
Suppose 6/7*t**2 - 8/7*t**4 - t + 2/7 + 3/7*t**5 + 4/7*t**3 = 0. What is t?
-1, 2/3, 1
Let x = -26 + 10. Let f = -78/5 - x. Solve -2/5*o**5 + 2/5*o**3 + 0*o + f*o**2 - 2/5*o**4 + 0 = 0 for o.
-1, 0, 1
Let i(k) = -8*k**4 + 11*k**3 + 12*k**2 - 29*k - 5. Let o(z) = -39*z**4 + 54*z**3 + 60*z**2 - 144*z - 24. Let a(r) = -24*i(r) + 5*o(r). Factor a(b).
-3*b*(b - 2)**2*(b + 2)
Let m(j) = j**3 - 3*j**2 + 5*j - 6. Let c be m(2). Determine k, given that 1/5*k**2 + c - 1/5*k + 1/5*k**3 - 1/5*k**4 = 0.
-1, 0, 1
Let -8/5*q - 16/5*q**4 + 16/5*q**2 + 2/5*q**3 + 0 + 6/5*q**5 = 0. What is q?
-1, 0, 2/3, 1, 2
Let v = -35 - -37. Let j(c) be the third derivative of 0*c**4 + 0*c + 0*c**3 + c**v + 0 + 1/30*c**5. Suppose j(y) = 0. What is y?
0
Factor 2/3*z - 2/3*z**2 + 0.
-2*z*(z - 1)/3
Factor -4/13 - 18/13*q - 14/13*q**2.
-2*(q + 1)*(7*q + 2)/13
Determine s so that 4/7*s + 0 + 8/7*s**3 + 10/7*s**2 + 2/7*s**4 = 0.
-2, -1, 0
Let k = 4482/7 - 638. Let b = -2091/7 + 299. Suppose k*m**2 + 38/7*m**3 + b*m + 0 + 24/7*m**4 = 0. What is m?
-1, -1/3, -1/4, 0
Factor -13 + 13 + 2*i**4 + 0 - 12*i**3.
2*i**3*(i - 6)
Let z(u) be the third derivative of -u**6/40 + u**4/8 + 5*u**2. Suppose z(m) = 0. What is m?
-1, 0, 1
Let s(u) = u**3 + 6*u**2 - 8*u - 9. Let p be s(-7). Let n be -4*3/(-6) - p. Determine h so that -4*h - 5 + n + h**2 + 4*h**3 - h**2 + h**2 = 0.
-1, -1/4, 1
Let l(k) be the third derivative of k**5/40 - 3*k**4/8 - 7*k**3/4 - 13*k**2. What is o in l(o) = 0?
-1, 7
Let o(l) = -l. Let k be o(0). Let d be (-8)/(-20) + (-36)/(-10). Let -m**3 + 1/2*m**5 + 1/2*m + 0*m**2 + 0 + k*m**d = 0. What is m?
-1, 0, 1
Suppose -3*n - 6 = n - 3*a, -2*a + 4 = -n. Let t(x) be the second derivative of n - 1/6*x**2 + 0*x**3 + 1/36*x**4 + x. Let t(p) = 0. What is p?
-1, 1
Factor 2 + 3 - 6*y + 7 - 2*y**2 - 4.
-2*(y - 1)*(y + 4)
Let v be 464/504 + (-22)/(-99). Factor 0 + 2/7*z**3 + 8/7*z + v*z**2.
2*z*(z + 2)**2/7
Let h(b) be the third derivative of 2*b**7/15 + 13*b**6/10 + 76*b**5/15 + 10*b**4 + 32*b**3/3 + 7*b**2 - 6*b. Factor h(x).
4*(x + 1)*(x + 2)**2*(7*x + 4)
Let c(k) be the third derivative of -k**6/120 + k**5/240 - 3*k**2. Factor c(b).
-b**2*(4*b - 1)/4
Let t(r) be the second derivative of 0 + 0*r**2 - 1/3*r**3 - 1/14*r**7 - 1/30*r**6 + 1/12*r**4 + 1/4*r**5 - 2*r. Let t(d) = 0. What is d?
-1, 0, 2/3, 1
Let u(m) be the second derivative of -m**8/3360 + m**7/420 - m**6/180 + 2*m**4/3 - 3*m. Let h(s) be the third derivative of u(s). Factor h(o).
-2*o*(o - 2)*(o - 1)
Let a be ((-14)/(-6) + -2)/(2/6). Let c(k) be the first derivative of 3*k**2 + 4*k + a + 2/3*k**3. Factor c(o).
2*(o + 1)*(o + 2)
Let b(o) be the second derivative of 0 + 0*o**2 + o + 0*o**5 + 0*o**3 + 0*o**4 + 1/105*o**6. Factor b(m).
2*m**4/7
What is t in -9*t + 3*t**2 + 2*t**2 - 2*t**2 = 0?
0, 3
Let b be (3/10)/((-78)/(-156)). Solve 12/5*o**2 + 0 - b*o = 0 for o.
0, 1/4
Factor 0 + 13/9*z + 1/9*z**2.
z*(z + 13)/9
Solve -62*j + 16*j**3 - 34*j**2 + 47*j - 65*j - 50 - 2*j**4 + 22*j**2 = 0 for j.
-1, 5
Let c = 161 - 3863/24. Let w(z) be the third derivative of -c*z**4 - 3*z**2 + 0 - 1/30*z**5 + 0*z + 1/120*z**6 + 1/3*z**3. Determine v, given that w(v) = 0.
-1, 1, 2
Let b(c) be the third derivative of -c**5/15 - c**4/6 + 4*c**3 - 20*c**2. Suppose b(w) = 0. What is w?
-3, 2
Let j(r) be the first derivative of 2*r**3/15 - 4*r**2/5 + 6*r/5 + 6. Factor j(v).
2*(v - 3)*(v - 1)/5
Suppose -3*l - 92 = 4*y - 5*l, -y + 2*l = 29. Let g be 0*(y/(-6) - 3). Factor 0*z**2 - 1/3*z**3 - 1/3*z**5 + g*z + 0 + 2/3*z**4.
-z**3*(z - 1)**2/3
Let a(x) = -2*x - 5. Let c be a(-4). Suppose 5*u 