+ 0*i = 0. What is i?
-1, 1
Suppose 5*k + 23 + 22 = 0. Let z be (-2)/k - 10/(-36). Suppose z - 1/4*l - 1/4*l**2 = 0. What is l?
-2, 1
Let r = -557 - -3917/7. Solve -12/7*x + 2/7*x**2 + r = 0 for x.
3
Let n(p) be the second derivative of -1/27*p**3 - 5*p - 2/9*p**2 + 0 + 1/54*p**4. Factor n(a).
2*(a - 2)*(a + 1)/9
Let w(r) be the second derivative of -r**10/10080 + r**8/1120 - r**6/240 - r**4/6 + r. Let k(j) be the third derivative of w(j). Factor k(n).
-3*n*(n - 1)**2*(n + 1)**2
Let b(n) be the first derivative of n**6/15 - 2*n**5/25 - n**4/5 + 22. Factor b(p).
2*p**3*(p - 2)*(p + 1)/5
Let s(i) = 2*i - 1. Let o(n) = 3*n - 3. Let h(b) = 2*o(b) - 5*s(b). Let y be h(-1). Factor w**4 + 0*w**4 - 4*w**2 + 3*w**2 + w**5 - w**y.
w**2*(w - 1)*(w + 1)**2
Let n(y) be the second derivative of y**7/147 - y**6/105 - y**5/70 + y**4/42 + 3*y. Factor n(j).
2*j**2*(j - 1)**2*(j + 1)/7
Let b be (18/8 + 0)*-12. Let j = b - -27. Factor j*d + 1/3*d**2 + 0.
d**2/3
Let f = 5183/8 + -647. Let d(t) be the first derivative of 0*t**2 + 3 - 3/2*t**5 + 3/4*t**6 + 0*t + f*t**4 - 1/6*t**3. Suppose d(z) = 0. What is z?
0, 1/3, 1
Let g be 14/(-21)*6/(-8). Let y(k) be the first derivative of 1/10*k**5 - 1/2*k - 1/4*k**4 + 0*k**3 + g*k**2 + 3. Factor y(o).
(o - 1)**3*(o + 1)/2
Let j = -2 + 4. Let q = -1141/9 + 127. Find r such that 0 - q*r - 2/9*r**j = 0.
-1, 0
Let c(r) be the second derivative of r**6/6 + r**5/2 - 5*r**4/4 + 18*r. Factor c(x).
5*x**2*(x - 1)*(x + 3)
Let o(m) = -m**2 + 6*m + 2. Let h be o(6). Suppose 3*n + 5*t - 37 = 0, 2*n - h*t - t = -7. Determine d, given that -5*d + 4 + 3*d + 2*d**2 - n*d**2 = 0.
-2, 1
Let d = -4 + 9. Let q(j) = j**3 - 17*j**2 - 17*j + 1. Let r(g) = -2*g**3 + 42*g**2 + 42*g - 2. Let k(a) = d*r(a) + 12*q(a). Factor k(v).
2*(v + 1)**3
Let m(y) be the first derivative of y**4/36 - y**2/6 + 6*y - 2. Let x(i) be the first derivative of m(i). Factor x(q).
(q - 1)*(q + 1)/3
Let k(t) be the third derivative of t**7/8820 - t**6/1260 + t**5/420 + t**4/12 - t**2. Let d(g) be the second derivative of k(g). Find y such that d(y) = 0.
1
Let p(s) be the third derivative of s**7/70 - s**5/20 + 3*s**2. Factor p(m).
3*m**2*(m - 1)*(m + 1)
Let n = 6259093/3312 + 2723/368. Let g = 1901 - n. Let -g*m**3 + 0 - 32/9*m**2 - 10/9*m**4 - 8/9*m = 0. What is m?
-2, -1, -2/5, 0
Let r(l) = 3*l**2 + l. Let s be r(-1). Let 1/4*d**s - 1/4 + 0*d = 0. What is d?
-1, 1
Suppose -9 - 9 = 2*u. Let w be 38/30 - u/(-15). Solve -2/3 - 4/3*v - w*v**2 = 0 for v.
-1
Let c(i) be the first derivative of -i**6/420 - i**5/210 + 5*i**2/2 + 6. Let l(a) be the second derivative of c(a). Determine t, given that l(t) = 0.
-1, 0
Let q(g) = g**2 + 3*g + 1. Let m be q(-4). Let a(p) = -p**2 - 4*p + 14. Let j be a(2). Factor -11/4*h - 7/2*h**j - 1/2 + 4*h**4 + 7/4*h**m + h**3.
(h - 1)*(h + 1)**3*(7*h + 2)/4
Suppose -20 = 240*h - 245*h. Factor -4/3*j**2 - 2/3*j + 0 + 4/3*j**h + 2/3*j**5 + 0*j**3.
2*j*(j - 1)*(j + 1)**3/3
Let k be 1/(66/9)*(-8 - -12). Let 0 + k*c**3 - 6/11*c**2 - 2/11*c**4 + 2/11*c = 0. What is c?
0, 1
Suppose -128/7 + 32/7*w - 2/7*w**2 = 0. Calculate w.
8
Factor 2/11*n**2 + 4/11*n + 2/11.
2*(n + 1)**2/11
Let y be (-2)/((-3 + 5)/(-10)). Let p = -7 + y. Factor -3*o**2 + 0*o**p + 6*o**3 - 3*o**3 + 3*o**3.
3*o**2*(2*o - 1)
Let b(v) be the first derivative of 5*v**5 + 5*v**4/2 - 25*v**3/3 - 5*v**2 + 17. Find a, given that b(a) = 0.
-1, -2/5, 0, 1
Factor 0*l**2 - 1/6*l**3 + 0 + 1/6*l.
-l*(l - 1)*(l + 1)/6
Let q(b) be the third derivative of -b**9/211680 - b**8/35280 - 7*b**5/60 + 10*b**2. Let z(a) be the third derivative of q(a). Determine p, given that z(p) = 0.
-2, 0
Let l(v) be the first derivative of -v**3/3 + v**2 + 2*v + 1. Let w(r) = -2*r - 7 - 1 + 5 + r**2. Let j(h) = -4*l(h) - 3*w(h). Factor j(z).
(z - 1)**2
Let y = 10 + -6. Suppose -y*d = -3*d. What is f in 1/4*f**5 - 1/4*f**3 - 1/4*f**2 + 1/4*f**4 + 0 + d*f = 0?
-1, 0, 1
Let t be 45/18*(-12)/(-5). Let i be 4/(-9)*t/(-8). Find o, given that 0 + 1/3*o**2 - i*o = 0.
0, 1
Let u(b) be the second derivative of -b**6/288 + b**5/160 + b**4/48 + b**3/2 - b. Let o(m) be the second derivative of u(m). Let o(v) = 0. Calculate v.
-2/5, 1
Let u be ((-9)/(-2) - 1)*4. Suppose 3*i = 2*t - 4, 3*i + 0*i = 0. Determine q, given that 8*q**5 - 4*q**3 - u*q**4 - t - 2*q + 16*q**2 - 6*q + 4*q = 0.
-1, -1/4, 1
Let t(d) = 8*d**4 + 8*d**3 + 2*d**2. Let w(h) = 7*h**4 + 8*h**3 + 3*h**2. Let q(p) = 5*t(p) - 6*w(p). Factor q(o).
-2*o**2*(o + 2)**2
Let k(z) be the second derivative of 0 + 5*z + 1/4*z**2 - 1/120*z**6 + 1/16*z**4 - 1/80*z**5 + 5/24*z**3. Let k(f) = 0. What is f?
-1, 2
What is f in 3/2*f - 9/2*f**3 - 3*f**2 + 0 = 0?
-1, 0, 1/3
Suppose 1/2*h**2 - 4*h - 9/2 = 0. What is h?
-1, 9
Let b(s) be the second derivative of -5/24*s**3 + 3*s - 1/16*s**4 - 1/4*s**2 + 1/120*s**6 + 1/80*s**5 + 0. Factor b(o).
(o - 2)*(o + 1)**3/4
Suppose -3*l + c - 5*c = -32, -l = -5*c + 21. Let f(x) be the second derivative of 0 + x + 0*x**3 + 0*x**2 - 1/30*x**l - 1/100*x**5. Solve f(h) = 0.
-2, 0
Let m(y) = 6 - 4*y - 4 + 3*y. Let r be m(0). Let -2*i**2 + 0*i**2 - 2*i**5 - 8*i**4 - 12*i**3 - r*i - 6*i**2 = 0. Calculate i.
-1, 0
Let l = -191/4 + 48. Let b(j) be the first derivative of l*j + 1/16*j**4 + 1/4*j**3 + 3/8*j**2 - 3. Factor b(q).
(q + 1)**3/4
Let u be (-1)/(-2) - (0 + 0). Suppose -3*f = 2*f. Find n, given that f + u*n - 1/2*n**2 = 0.
0, 1
Let x = -77 - -1079/14. Let v(g) be the second derivative of 1/7*g**2 + 0 + 1/70*g**5 + x*g**4 + 1/7*g**3 - g. Solve v(m) = 0.
-1
Let v be 1/(-2)*4*-1. Suppose 0 = -0*o - v*o + 4. Factor -4*i**2 + 4*i**o + 2*i**3 - 2*i.
2*i*(i - 1)*(i + 1)
Let v(u) = u + 6. Suppose q = -q - 8. Let a be v(q). Factor -8/5 + 8/5*b - 2/5*b**a.
-2*(b - 2)**2/5
Let k(t) be the second derivative of 0 + 3/2*t**2 + 3*t - 1/8*t**4 - 1/4*t**3. Factor k(s).
-3*(s - 1)*(s + 2)/2
Factor 0 - 4/9*q**2 - 2/9*q**3 - 2/9*q.
-2*q*(q + 1)**2/9
Let z(y) be the third derivative of -y**5/45 + 7*y**4/18 - 8*y**3/3 - 15*y**2. Suppose z(t) = 0. What is t?
3, 4
Suppose h + 5*r = -3*h + 3, 5*h = 5*r + 15. Find a, given that 0 - 1/2*a + 1/2*a**h = 0.
0, 1
Let t(f) be the third derivative of 1/70*f**7 + 1/10*f**5 + f**2 + 0*f**3 + 3/40*f**6 + 0*f + 0*f**4 + 0. Factor t(h).
3*h**2*(h + 1)*(h + 2)
Let b(s) be the first derivative of s**4/12 - s**3/3 + s**2/2 - 5*s + 1. Let m(k) be the first derivative of b(k). Let m(n) = 0. Calculate n.
1
Let v(d) = 7*d**2 + 4*d + 5. Let h(s) = -3*s**2 - 2*s - 2. Let x = 5 + 16. Suppose -2*t - 3 - 25 = 4*f, t - x = 5*f. Let l(z) = f*h(z) - 2*v(z). Factor l(c).
c*(c + 2)
Let f(b) = -b**3 - 5*b**2 + 5*b - 7. Let h be f(-6). Let m be 3 - (h + (1 - -1)). Solve -6*s**2 + 25/2*s**5 + 15*s**4 + m*s + 0 - 11/2*s**3 = 0 for s.
-1, 0, 2/5
Let n(w) be the third derivative of w**9/90720 + w**8/30240 - w**7/3780 - w**5/60 + 4*w**2. Let s(l) be the third derivative of n(l). Let s(f) = 0. Calculate f.
-2, 0, 1
Let a(y) be the first derivative of 1/6*y**6 - 1/3*y**3 + 0*y - 1/4*y**4 + 1/5*y**5 + 2 + 0*y**2. Determine s so that a(s) = 0.
-1, 0, 1
Let k(r) = -r**2 - r + 1. Let d = -1 + 3. Let f(x) = -6*x - 3*x + x + 0*x**2 - x**d. Let y(u) = -f(u) + 4*k(u). Find l such that y(l) = 0.
-2/3, 2
Let m(b) be the third derivative of 0 + 1/720*b**6 + 1/504*b**8 + 0*b**4 - 1/315*b**7 + 0*b**3 - 2*b**2 + 0*b + 0*b**5. Factor m(i).
i**3*(2*i - 1)**2/6
Let i(l) = 19*l**2 - 19*l - 3. Let r(d) be the third derivative of -d**5/3 + 3*d**4/4 + d**3/3 + 7*d**2. Let x(c) = 6*i(c) + 5*r(c). Factor x(a).
2*(a - 2)*(7*a + 2)
Let h(i) be the third derivative of i**5/105 - 11*i**4/28 - 17*i**3/21 + 19*i**2. Find c, given that h(c) = 0.
-1/2, 17
Find y such that 44/3*y - 25/3*y**4 + 5/3*y**3 + 8/3 + 22*y**2 = 0.
-1, -2/5, 2
Let h(g) = -g**3 - 6*g**2 + g + 8. Let o be h(-6). Factor 2/5*z**3 + 2/5*z**4 - 2/5*z - 2/5*z**o + 0.
2*z*(z - 1)*(z + 1)**2/5
Let w(i) be the third derivative of i**5/100 + i**4/20 + i**3/10 - 4*i**2. Suppose w(q) = 0. What is q?
-1
Let g(o) be the first derivative of o**8/2016 - o**7/630 + o**5/180 - o**4/144 + 2*o**2 - 5. Let r(t) be the second derivative of g(t). Let r(v) = 0. What is v?
-1, 0, 1
Let z(x) be the third derivative of 0 + 0*x**4 + 8*x**2 - 1/9*x**3 + 1/90*x**5 + 0*x. Solve z(f) = 0.
-1, 1
Let w(j) be the third derivative of 5*j**7/42 - 17*j**6/24 +