
Let h(x) = -x**3 + 5*x**2 - x - 8. Let g be h(4). Let w(a) be the second derivative of 0 + 0*a**2 + 0*a**3 + 2*a - 1/54*a**g. Factor w(o).
-2*o**2/9
Let o(s) = s**3 - s**2 + 2*s + 4. Let l be o(0). Find w, given that -3*w**5 + 0*w**5 - l*w**4 + 2*w**5 = 0.
-4, 0
Suppose 25*w - 28*w = -9. Let h(s) be the second derivative of 1/80*s**5 - 3*s - 1/24*s**4 + 0*s**2 + 1/60*s**6 - 1/24*s**w + 0. Factor h(y).
y*(y - 1)*(y + 1)*(2*y + 1)/4
Let o(s) = 4*s**2 - 5 + 0*s - s - 4*s. Let c(j) = j**2 - j - 1. Let i(l) = 5*c(l) - o(l). What is t in i(t) = 0?
0
Let v be -3 + -4 - (-767)/91. Factor -v*h**3 + 2/7*h + 2/7*h**2 + 0 + 6/7*h**4.
2*h*(h - 1)**2*(3*h + 1)/7
Suppose 0 = 5*a - 46 - 39. Suppose -3*r - 3*i - 3 = 0, 4*i + a = 5*r - 23. Determine n so that -9*n**2 - 5*n**3 - 4*n**3 + 4*n**4 - 5*n**4 - 2*n**r - 3*n = 0.
-1, 0
Let f(d) be the second derivative of -d**10/15120 + d**8/1680 - d**6/360 + d**4/6 - d. Let v(t) be the third derivative of f(t). Factor v(g).
-2*g*(g - 1)**2*(g + 1)**2
Let s(u) be the second derivative of -u**4/12 - u**3/6 + 5*u. Let n(w) = -4*w**2 - 5*w - 1. Let a(c) = 2*n(c) - 10*s(c). What is x in a(x) = 0?
-1, 1
Let h(q) = 3*q**2 + 2*q - 1. Let o = -2 + 0. Let x be h(o). Factor -18*a**3 + 8*a**2 - 15*a + 16*a**2 + x*a.
-2*a*(3*a - 2)**2
Let u(t) be the second derivative of 0 + 1/18*t**3 + 0*t**2 + t - 1/18*t**4 + 1/60*t**5. Solve u(y) = 0 for y.
0, 1
Solve 0*c - 4*c**4 + 4/5*c**2 - 2/5*c**3 + 0 = 0 for c.
-1/2, 0, 2/5
Let w(b) = -3*b**2 - 16*b - 13. Let j(r) = -2*r**2 - 11*r - 9. Let u(o) = 7*j(o) - 5*w(o). Find c, given that u(c) = 0.
-2, -1
Let z(g) be the first derivative of g**5/20 - 3*g**4/8 + g**3 - g**2/2 + 2. Let k(t) be the second derivative of z(t). Find x, given that k(x) = 0.
1, 2
Let q(i) be the first derivative of 27*i**4/8 - 5*i**3/2 - 8*i**2/3 - 2*i/3 - 10. Determine w, given that q(w) = 0.
-2/9, 1
Let u = 2/2937 + 26423/14685. Determine h, given that 12/5*h**2 + 39/5*h + u = 0.
-3, -1/4
Let f(d) = -d**2 - 8*d - 5. Let n be f(-7). Let h(l) be the first derivative of -n + 0*l - 1/12*l**3 - 1/8*l**2. Factor h(w).
-w*(w + 1)/4
Factor -3/7*g**2 + 0*g + 4/7 + 1/7*g**3.
(g - 2)**2*(g + 1)/7
Suppose 4/9*t + 2/9*t**3 + 0 - 2/3*t**2 = 0. What is t?
0, 1, 2
Let j be 36/(-27)*(-3)/2. Suppose -3*s = -3*k + s + 17, 2*s = 3*k - 13. Factor -k*m**j - 3*m + 2 + 2*m**2 + 2*m.
-(m - 1)*(m + 2)
Let o(z) be the third derivative of -z**5/210 + 2*z**4/21 - 16*z**3/21 + 6*z**2. Factor o(u).
-2*(u - 4)**2/7
Let g(l) be the third derivative of l**8/10080 - l**7/1260 + l**5/10 - 8*l**2. Let v(o) be the third derivative of g(o). Determine h so that v(h) = 0.
0, 2
Let a be (-4 + 6)/4*(-2)/(-5). Factor 1/5*q**2 + 0 + 2/5*q**3 + a*q**4 + 0*q.
q**2*(q + 1)**2/5
Let i(y) be the first derivative of 7/15*y**6 + 2/3*y**3 - 2/5*y**5 + 1 - 9/10*y**4 + 2/5*y**2 + 0*y. Suppose i(d) = 0. Calculate d.
-1, -2/7, 0, 1
Let k(g) be the second derivative of g**7/84 - g**5/40 + 9*g. Factor k(v).
v**3*(v - 1)*(v + 1)/2
Suppose -13*u = -8*u - 10. Suppose u = -3*a + 5. Factor 5/4*x**2 - 2*x - a.
(x - 2)*(5*x + 2)/4
Let b(s) be the second derivative of -s**5/12 - 35*s**4/18 - 245*s**3/18 - 9*s. Factor b(z).
-5*z*(z + 7)**2/3
Suppose 0*q - 2*q**5 - 7*q**2 + 2*q + 3*q**2 - 54*q**4 + 58*q**4 = 0. What is q?
-1, 0, 1
Factor -3/2*t**2 - 5/2*t**4 + 1/4*t + 0 + 3/4*t**5 + 3*t**3.
t*(t - 1)**3*(3*t - 1)/4
Let g(t) be the first derivative of t**4/12 + 2*t**3/9 + 3. Factor g(o).
o**2*(o + 2)/3
Let s be 4 - (-3 - (0 - 0)). Factor 8*r**2 - s*r**5 + 6*r**5 - 6*r**4 - r**5.
-2*r**2*(r - 1)*(r + 2)**2
Let r = 22 - 22. Suppose -i = -r*i. Let -1/4*s**5 + 0*s**2 + 0 - 1/2*s**4 - 1/4*s**3 + i*s = 0. What is s?
-1, 0
Let l(f) be the first derivative of -f + 7 - 1/4*f**2 + 1/2*f**3 - 1/10*f**5 + 1/8*f**4. Factor l(u).
-(u - 2)*(u - 1)*(u + 1)**2/2
Let 2/3*x**2 + 2*x + 0 = 0. Calculate x.
-3, 0
Let b(k) = -9*k**2 + 9*k - 12. Let r(c) = -10 + c - 10*c**2 + 6*c - 3 + 2*c. Let f(q) = -7*b(q) + 6*r(q). Let f(j) = 0. What is j?
1, 2
Let u(w) be the first derivative of 0*w**2 + 4/33*w**3 - 3/22*w**4 - 7 + 2/55*w**5 + 0*w. Factor u(q).
2*q**2*(q - 2)*(q - 1)/11
Let b(y) be the third derivative of y**8/504 + y**7/315 - y**6/60 - y**5/90 + y**4/18 + 3*y**2. Let b(l) = 0. What is l?
-2, -1, 0, 1
Let k(q) be the third derivative of q**6/900 + q**5/150 + q**4/60 + q**3/6 - 2*q**2. Let w(u) be the first derivative of k(u). Let w(p) = 0. What is p?
-1
Let i(x) be the first derivative of -x**4/2 + 14*x**3/3 - 8*x**2 - 32*x + 50. Factor i(b).
-2*(b - 4)**2*(b + 1)
Let r be -3*(-2)/(-3) + -4. Let h = r - -9. Suppose j**2 + 0*j**2 + j**3 - 3*j**2 - 3*j**h = 0. What is j?
-1, 0
Suppose 27 = -0*r + 3*r. Suppose -m = 5*f + 5, -5*f = -2*m + r - 4. Let m*y + 0 - 2/5*y**2 - 2/5*y**3 = 0. What is y?
-1, 0
Let p(t) be the second derivative of -t**5/70 + t**3/7 + 2*t**2/7 + 5*t. Let p(o) = 0. What is o?
-1, 2
Let w(t) be the second derivative of -t**8/26880 + t**7/5040 - t**6/2880 + t**4/12 - 3*t. Let s(h) be the third derivative of w(h). Factor s(q).
-q*(q - 1)**2/4
Let z = -81/157 + 39969/785. Factor 24*o + z*o**2 + 16/5 + 98/5*o**3.
2*(o + 2)*(7*o + 2)**2/5
Let l(k) be the first derivative of k**4/2 - 2*k**3/3 + 11. Factor l(a).
2*a**2*(a - 1)
Let d be (-48)/(-27) - 3/(81/(-6)). Let c(m) be the second derivative of 1/6*m**3 + 0 - 1/12*m**4 - d*m + 0*m**2. What is r in c(r) = 0?
0, 1
Let k(h) be the first derivative of -9*h**4/26 - 32*h**3/13 - 4*h**2 - 32*h/13 - 6. Solve k(g) = 0 for g.
-4, -2/3
Suppose r - 3*r = 5*x - 15, -4*x + 12 = 5*r. Let d(g) be the second derivative of -3/4*g**4 + g - g**x + 0 - 1/2*g**2. Factor d(a).
-(3*a + 1)**2
Suppose 3*p + 6 + 0*p**2 + 2*p**2 - 11*p = 0. What is p?
1, 3
Let h be ((-8)/(-14))/((-16)/(-56)). Let s = -29 - -59/2. What is p in 1 + 1/2*p - s*p**h = 0?
-1, 2
Suppose 3*j + 2 = 8. Factor 3*f**2 - 2*f**4 + 2*f**3 - 4*f**3 - f**2 + j*f + 0*f**4.
-2*f*(f - 1)*(f + 1)**2
Let j(u) be the second derivative of u**4/30 - u**3/15 - 2*u**2/5 - 2*u. Factor j(b).
2*(b - 2)*(b + 1)/5
Let g(a) be the third derivative of 1/6*a**3 + 1/60*a**5 + 3*a**2 + 0 + 0*a - 1/12*a**4. Find s such that g(s) = 0.
1
Let p(m) be the first derivative of 3*m**4/2 + 7*m**3/3 + m**2/2 - 7*m - 4. Let s(b) = -2*b**3 - 2*b**2 + 2. Let f(o) = 2*p(o) + 7*s(o). Solve f(n) = 0 for n.
-1, 0, 1
Suppose 4*j = j. Suppose -5*h - 2*u + 13 = 0, j = -h + u - 0 + 4. Factor 5*a**2 - 1 - 3*a**2 - a**4 - 3 + h.
-(a - 1)**2*(a + 1)**2
Let l be 1 + 3 + ((-34)/10 - -1). Solve 0 - l*g**3 + 0*g**2 + 0*g + 8/5*g**4 - 2/5*g**5 = 0.
0, 2
Let z be 2*((-10)/(-5))/2. Find p such that 2/5*p + 0*p**z + 0 - 2/5*p**3 = 0.
-1, 0, 1
Let t(k) = 39*k - 150. Let x(g) = -g**2 - 38*g + 151. Let j(z) = -4*t(z) - 3*x(z). Suppose j(r) = 0. Calculate r.
7
Let o(f) = f + 13. Let a be o(-7). Suppose 3*s + 9 = -3*m + a*s, 3 = s. Find w, given that 0 - w**2 - 7/2*w**3 + m*w = 0.
-2/7, 0
Let d be (1/(-32))/(40/(-16)). Let s(u) be the third derivative of -1/24*u**3 - d*u**5 - 1/480*u**6 + 0*u + 0 + u**2 - 1/32*u**4. Factor s(o).
-(o + 1)**3/4
Factor 2/11*c**2 + 2/11*c - 4/11.
2*(c - 1)*(c + 2)/11
Let m = -3/122 + 997/854. Suppose 2/7*c**3 - 8/7*c**4 + 0 + m*c**2 - 2/7*c = 0. What is c?
-1, 0, 1/4, 1
Suppose z - 4*v - 8 = -z, 4*z - 12 = 4*v. Let n(s) be the second derivative of 1/18*s**4 - 4/9*s**3 + s + 4/3*s**z + 0. What is a in n(a) = 0?
2
Let v = -4906/13 + 24033/91. Let k = -113 - v. Factor 0*q + 0 + k*q**2.
2*q**2/7
Let r(y) = -2*y**4 - 2*y**3 + 4*y**2 + 6*y + 6. Let a = 19 - 13. Let n(k) = -k**3 + k**2 + k + 1. Let g(f) = a*n(f) - r(f). Factor g(h).
2*h**2*(h - 1)**2
Let j(x) be the third derivative of -x**8/448 - x**7/280 + x**6/160 + x**5/80 + 2*x**2. Let j(f) = 0. Calculate f.
-1, 0, 1
Let d(u) = u**2 - 3*u - 6. Let a be d(5). Determine g, given that -3*g**a - 7*g**3 - 3*g**2 - 4*g + 4*g + g**3 = 0.
-1, 0
Suppose 4*l + 2*h - 8 - 2 = 0, -h + 9 = 4*l. Suppose 3*g = 4*g - l. Factor -5 + m**g + 4 + 2*m**3 - 2*m + m - m.
(m - 1)*(m + 1)*(2*m + 1)
Let l be 7*-1*(-74)/259. Determine d so that 1/3*d**l - 1 - 2/3*d = 0.
-1, 3
Let p(j) = j**2 + j. Let d(t) = -3*t**2 - 6*t - 3. Let r(z) = -d(z) - 6*p(z). Let r(n) = 0. What is n?
-1, 1
Let r be (-9)/(-6) - (-9)/6. Determine d so that 0 - r*d**2 + 3/2*d + 3/2*d**3 = 0.
0, 1
Factor -9/2*a + 5/2*a**2 + 2.
(a 