ate p.
-1, 1, 3
Let b(j) be the second derivative of 0*j**2 + 0*j**4 + 1/50*j**5 + 5*j + 0 - 1/15*j**3. Factor b(r).
2*r*(r - 1)*(r + 1)/5
Let b(n) be the second derivative of -3*n**5/20 - 3*n**4/4 + 6*n**2 - 2*n. Factor b(s).
-3*(s - 1)*(s + 2)**2
Suppose -3*w = -2 - 4. Let b = 29/6 + -191/42. Find a such that 4/7*a - 2/7 - b*a**w = 0.
1
Let b be ((-5)/70)/((-18)/8 + 2). Suppose 0*f**2 - 4/7*f**5 + 0*f**3 + 0*f + 0 - b*f**4 = 0. Calculate f.
-1/2, 0
Let x(j) be the first derivative of j**5/240 - j**4/32 - 7*j**2/2 + 2. Let b(t) be the second derivative of x(t). Solve b(w) = 0.
0, 3
Let g be 3*4/30 + (-24)/210. Suppose 0 - 8/7*k**3 - 10/7*k**2 - g*k = 0. What is k?
-1, -1/4, 0
Let i(t) be the third derivative of t**7/70 + t**6/24 + t**5/60 - t**4/24 - 9*t**2. What is m in i(m) = 0?
-1, 0, 1/3
Suppose -3*q = -3*x - 2*q + 17, 0 = 4*x - 3*q - 31. Factor 4*z**2 + 3*z**2 - x*z**2 - 6*z + 3.
3*(z - 1)**2
Let f(u) be the first derivative of -1/288*u**6 + 0*u + 1 + 0*u**4 - 1/240*u**5 + 0*u**2 - 1/3*u**3. Let w(p) be the third derivative of f(p). Factor w(r).
-r*(5*r + 2)/4
Factor 28/3*x - 8/3*x**3 - 2*x**2 - 16/3 + 2/3*x**4.
2*(x - 4)*(x - 1)**2*(x + 2)/3
Let t(j) be the first derivative of -j**7/105 + j**5/25 - j**3/15 + 4*j + 3. Let o(z) be the first derivative of t(z). Factor o(s).
-2*s*(s - 1)**2*(s + 1)**2/5
Factor 52/3*b**2 + 92/3*b**4 + 36*b**3 + 8/3*b + 28/3*b**5 + 0.
4*b*(b + 1)**3*(7*b + 2)/3
Let z(k) be the second derivative of k**7/840 + k**6/80 - k**5/10 - 5*k**4/6 - 2*k. Let t(j) be the third derivative of z(j). Factor t(x).
3*(x - 1)*(x + 4)
Let a(o) be the third derivative of -2*o**7/175 + o**6/40 - o**5/100 + 54*o**2. Let a(x) = 0. Calculate x.
0, 1/4, 1
Let d(v) be the third derivative of v**8/12 + 8*v**7/35 - 11*v**6/30 - 4*v**5/5 + 2*v**4/3 - 13*v**2. What is n in d(n) = 0?
-2, -1, 0, 2/7, 1
Let z(l) = -19*l**2 - 11*l + 11. Let t(g) = -10*g**2 - 6*g + 6. Let j(c) = 11*t(c) - 6*z(c). Factor j(x).
4*x**2
Suppose 4/3*m**4 - 8/3*m - 4/3*m**2 + 4*m**3 - 4/3*m**5 + 0 = 0. What is m?
-1, 0, 1, 2
Let r(o) be the first derivative of 3*o**4/4 - 2*o**3/3 + 7*o**2/2 - 4*o - 4. Let y(l) = 6*l**3 - 3*l**2 + 15*l - 9. Let z(x) = -9*r(x) + 4*y(x). Factor z(m).
-3*m*(m - 1)**2
Let o(c) = -2*c**2 + 2*c - 4. Let b(l) = -4*l**2 + 2*l - 13. Let y(j) = 2*j**2 - j + 7. Let n(u) = 4*b(u) + 7*y(u). Let t(k) = -4*n(k) + 3*o(k). Factor t(f).
2*f*(f + 1)
Let f(r) be the first derivative of -r**6/30 + 8*r**5/25 - 5*r**4/4 + 38*r**3/15 - 14*r**2/5 + 8*r/5 + 7. Suppose f(i) = 0. What is i?
1, 2
Let z(c) = c**3 + 5*c**2 + 2. Let y be z(-5). Suppose -18/5*w**2 + 14/5*w - 2/5*w**4 + y*w**3 - 4/5 = 0. What is w?
1, 2
Factor 4/11*y**2 - 2/11*y**3 + 0*y + 0.
-2*y**2*(y - 2)/11
Suppose 24*i**4 - 9*i**4 - 10*i**4 - 5*i**2 = 0. Calculate i.
-1, 0, 1
Let b = -2579/7866 + 13/342. Let c = 1/23 - b. Factor -c*v - 1/6*v**2 + 0 + 1/6*v**3.
v*(v - 2)*(v + 1)/6
Let z = -17 + 7. Let k be 8 + -8 - 4/z. Solve k + 2/5*c**2 + 4/5*c = 0.
-1
Let z(w) be the third derivative of -w**6/240 + 10*w**2. Factor z(d).
-d**3/2
Let x(c) be the second derivative of c**8/840 - c**6/180 + c**3/2 + 2*c. Let u(l) be the second derivative of x(l). Factor u(p).
2*p**2*(p - 1)*(p + 1)
Let o(a) = 9*a**2 + 10*a - 4. Let m(n) = -36*n**2 - 42*n + 12. Let y(k) = k + 1. Let j(d) = -m(d) - 3*y(d). Let s(i) = -4*j(i) + 15*o(i). Factor s(r).
-3*r*(3*r + 2)
Suppose -2/7*y**2 + 8/7*y**4 - 3/7*y**5 - 3/7*y**3 + 0*y + 0 = 0. What is y?
-1/3, 0, 1, 2
Find d, given that 2/11*d**3 + 2/11 + 6/11*d + 6/11*d**2 = 0.
-1
Let r(y) be the first derivative of -y**6/15 - 8*y**5/25 - 2*y**4/5 + 4*y**3/15 + y**2 + 4*y/5 - 5. Suppose r(z) = 0. Calculate z.
-2, -1, 1
Let y be 0 - 2 - (-12 + 2). Let p = -16 - -24. What is h in h + p*h - h + y + 2*h**2 = 0?
-2
Factor 0*b**2 + 0 + 0*b - 2/9*b**3 + 2/3*b**4.
2*b**3*(3*b - 1)/9
Let s = 16924/14095 - 2/2819. Factor 2/5*t**3 + 4/5*t**2 + 0 - s*t**4 + 0*t.
-2*t**2*(t - 1)*(3*t + 2)/5
Let i = -26 - -26. Let r(p) be the second derivative of 0*p**5 + 1/165*p**6 + i + 0*p**3 + 3*p + 0*p**2 - 1/66*p**4. Let r(g) = 0. What is g?
-1, 0, 1
Let i(z) be the third derivative of z**8/1512 - 8*z**7/945 + 4*z**6/135 - 13*z**2. Factor i(c).
2*c**3*(c - 4)**2/9
Let d be (-12)/60 - 12/(-10). Let k be 2 + d - 9/3. Factor -2*c**5 + 0 - 6/5*c**4 + 4/5*c**3 + 0*c**2 + k*c.
-2*c**3*(c + 1)*(5*c - 2)/5
Let -45*q**3 - 2*q**4 - 3*q**4 + 5*q**5 - 1335*q + 1415*q + 25*q**2 - 60 = 0. What is q?
-2, 1, 3
Let w = 234 - 231. Factor -2/9*a + 0 + 2/9*a**5 + 4/9*a**4 + 0*a**w - 4/9*a**2.
2*a*(a - 1)*(a + 1)**3/9
Let d(g) be the second derivative of g**6/120 - 3*g**5/80 + g**3/6 - 2*g. Factor d(q).
q*(q - 2)**2*(q + 1)/4
Factor 0*v - 1/4*v**2 + 0.
-v**2/4
Let y = 65 + -53. Factor 1/3 + y*d**2 - 4*d.
(6*d - 1)**2/3
Factor 0*x + 0 + 0*x**2 - 1/2*x**3 + 1/4*x**4.
x**3*(x - 2)/4
Suppose -3*n = 4*r - 22, 0 = -3*n - n - 4*r + 24. Let b(i) be the second derivative of 0 + 1/6*i**4 - 4*i + 1/15*i**6 + 0*i**n - 1/5*i**5 + 0*i**3. Factor b(p).
2*p**2*(p - 1)**2
Let q(u) be the second derivative of -4/21*u**3 + 2/21*u**4 + 1/7*u**2 + u + 0. What is s in q(s) = 0?
1/2
Let w(d) be the second derivative of -d**6/20 + 9*d**5/40 - 3*d**4/8 + d**3/4 + 6*d. Find k, given that w(k) = 0.
0, 1
Suppose -4*z = 2 - 26. Let y be (4/18)/(z/9). Factor y*q + 0 - 1/3*q**2.
-q*(q - 1)/3
Let a = 1 + 2. Factor 7 - 6 - s - s**2 + 2*s**a - s**3.
(s - 1)**2*(s + 1)
Let z = 1/153 + 301/765. Let v(q) be the first derivative of -1 + 2/15*q**3 + z*q - 2/5*q**2. Solve v(d) = 0.
1
Let g(k) be the third derivative of 49*k**5/60 + 7*k**4/12 + k**3/6 + 3*k**2. Determine j so that g(j) = 0.
-1/7
Let q(f) be the second derivative of f**9/2016 + f**8/224 + f**7/70 + f**6/60 + f**3/2 + 4*f. Let i(o) be the second derivative of q(o). Factor i(v).
3*v**2*(v + 1)*(v + 2)**2/2
Let p(t) be the second derivative of 7/12*t**7 + 5/6*t**4 + 0*t**2 - 7/6*t**6 + 1/3*t**3 - 3/40*t**5 - t + 0. Determine a so that p(a) = 0.
-2/7, 0, 1
Factor 0*a**3 - 1/5*a**5 - 1/5*a**4 + 0*a**2 + 0*a + 0.
-a**4*(a + 1)/5
Let a(t) = 4*t**3 - 5*t**2 + 9*t + 5. Let s(g) = -g**3 + g**2 - g - 1. Let p(o) = -a(o) - 5*s(o). Factor p(l).
l*(l - 2)*(l + 2)
Let u(c) be the third derivative of -1/70*c**7 + 0*c - 1/24*c**4 + 1/12*c**5 + 1/120*c**6 - 1/3*c**3 - 3*c**2 + 0. Determine t, given that u(t) = 0.
-1, -2/3, 1
Factor 72*s**4 + 83*s**4 - 15*s**3 - 6*s**2 - 164*s**4.
-3*s**2*(s + 1)*(3*s + 2)
Factor 93*v**3 + 8 + 25*v - 9*v - 42*v**2 + 14*v**4 - 89*v**3.
2*(v - 1)**2*(v + 2)*(7*v + 2)
Let o(h) = 2*h**3 - h**2 - 2*h + 3. Let w be o(1). Factor -1/2 + 1/2*v**w - 3/2*v**3 + 3/2*v.
-(v - 1)*(v + 1)*(3*v - 1)/2
Let v = -181 + 181. Factor 1/6*t**3 + 1/6*t + v + 1/3*t**2.
t*(t + 1)**2/6
Let q(d) = 4*d**2 - 10*d + 5. Let l be q(0). Determine w, given that 4/7*w**3 - 4/7 - 4/7*w**4 - 2/7*w - 2/7*w**l + 8/7*w**2 = 0.
-2, -1, 1
Let i(k) be the first derivative of -k**3/3 - 5*k**2 - 25*k - 4. Determine h, given that i(h) = 0.
-5
Let d(g) = 12*g**2 - 3*g - 2. Let v be d(-1). Let t(n) = -n**2 + 12*n + 15. Let i be t(v). Factor 2/7 - 4/7*x + 2/7*x**i.
2*(x - 1)**2/7
Let y = -15 + 17. Determine s so that -1 + 212*s - 212*s + s**y = 0.
-1, 1
Suppose 4*h = -3*p + 3*h + 9, 0 = 3*p - 3*h - 9. Let w(c) be the first derivative of -p - 1/2*c**4 + 2/5*c**5 + 0*c**2 + 2/9*c**3 - 1/9*c**6 + 0*c. Factor w(a).
-2*a**2*(a - 1)**3/3
Let t be (5 - 5)/(-1 - 1). Determine m so that t*m**5 - 4*m**4 + 2*m**3 + 2*m**5 + 0*m**5 = 0.
0, 1
Let r(j) be the first derivative of 0*j + 1/5*j**2 - 1/10*j**4 + 2 + 0*j**3. Solve r(v) = 0.
-1, 0, 1
Let m(t) be the second derivative of -2/13*t**2 + 0 + 7/39*t**3 - 2*t + 3/26*t**4. Determine g so that m(g) = 0.
-1, 2/9
Let z(a) = -3*a**2 + 14*a - 36. Let w(d) = -d**2 + d. Let h(n) = -10*w(n) + 5*z(n). Factor h(p).
-5*(p - 6)**2
Suppose -10 = -k - 4*k. Factor n**3 - 3*n**5 - k*n**5 - 2*n**4 + 2*n**5 + 4*n**4.
-n**3*(n - 1)*(3*n + 1)
Let n(p) = -p**3 - 6*p**2 - 8*p + 2. Let q be n(-2). Let i(f) be the second derivative of -1/12*f**3 + 0 + 1/6*f**q + f + 1/72*f**4. Factor i(v).
(v - 2)*(v - 1)/6
Let n(h) be the first derivative of h**9/1944 + h**8/840 + h**7/1890 + 2*h**3/3 + 3. Let l(y) be the third derivative of n(y). Factor l(r).
2*r**3*(r + 1)*(7*r + 2)/9
Let d(x) = -x**3 + 1. Let z be d(-1). Factor 3