
1
Let z = -7 + 11. Suppose -u = -3*d + 10, -5*u = 3*d - 0*d - 22. Determine t, given that t**2 + 4*t**u - 7*t**2 + z*t**3 - 2*t**4 = 0.
0, 1
Suppose 2*o = -2*o + 24. Let t(g) = 2*g**5 + 8*g**3 - 5*g**2. Let j(c) = -3*c**5 - 9*c**3 + 6*c**2. Let d(u) = o*t(u) + 5*j(u). Factor d(f).
-3*f**3*(f - 1)*(f + 1)
Let t(u) = 5*u**3 + 10*u**2 - 15*u - 7. Let s(d) = 2*d**3 + 5*d**2 - 7*d - 3. Let z(n) = -7*s(n) + 3*t(n). Let z(j) = 0. What is j?
0, 1, 4
Let s(j) be the first derivative of 32*j**5/45 - 20*j**4/3 + 386*j**3/27 + 40*j**2/3 + 32*j/9 - 4. Solve s(i) = 0 for i.
-1/4, 4
Let w(b) = 3*b**4 - 10*b**3 + b**2 + 11*b. Let f(m) = m**4 - m**2 - m. Let r(g) = -5*f(g) - w(g). Factor r(h).
-2*h*(h - 1)**2*(4*h + 3)
Factor -4*w + 4*w**4 - 8/3*w**2 - 4/3 + 4/3*w**5 + 8/3*w**3.
4*(w - 1)*(w + 1)**4/3
Let p be 21/6*-1 - -5. Solve 1/2*n**4 + 3/2*n + p*n**5 - 3*n**3 + 1/2 - n**2 = 0.
-1, -1/3, 1
Let k(s) = -7*s**3 + 4*s**2 + 7*s + 4. Let j(o) = 8*o**3 - 5*o**2 - 8*o - 5. Let w(q) = -4*j(q) - 5*k(q). Factor w(t).
3*t*(t - 1)*(t + 1)
Let n(r) be the third derivative of -r**10/75600 + r**9/37800 + r**8/8400 - r**4/8 + r**2. Let c(w) be the second derivative of n(w). Factor c(o).
-2*o**3*(o - 2)*(o + 1)/5
Suppose -76 = -35*y + 29. Factor 1/3*w**y - 1/3 + 1/3*w**2 - 1/3*w.
(w - 1)*(w + 1)**2/3
Let x(c) = -4*c**4 - 56*c**3 - 52*c**2 - 24*c + 8. Let w(b) = -b**4 - 19*b**3 - 17*b**2 - 8*b + 3. Let t(r) = -8*w(r) + 3*x(r). Let t(g) = 0. Calculate g.
-2, -1, 0
Suppose -10*t + 7*t + 9 = 0. Find b, given that -2*b**5 - 7*b**4 + 6*b**4 - 12*b**t + 9*b**4 - 2*b + 8*b**2 = 0.
0, 1
Let y(r) be the second derivative of -5*r**7/42 - r**6/6 + 3*r**5/4 + 25*r**4/12 + 5*r**3/3 - 17*r. Factor y(m).
-5*m*(m - 2)*(m + 1)**3
Suppose -256 + 254 + v + 7*v - v - 5*v**2 = 0. Calculate v.
2/5, 1
Let r(h) be the first derivative of 2/5*h - 1/20*h**4 + 1/10*h**2 - 2/15*h**3 + 8. What is f in r(f) = 0?
-2, -1, 1
Let u(h) = -35*h**4 + 29*h**3 + 6*h**2. Let x(f) = -6*f**4 + 5*f**3 + f**2. Let y = -18 - -52. Let o(c) = y*x(c) - 6*u(c). Solve o(z) = 0.
-1/3, 0, 1
Suppose -3*c = -0*c - 12. Find a, given that -4*a**3 + 4*a + 8*a**2 - a**4 - 4 + 2 - 4*a**4 - a**c = 0.
-1, 1/3, 1
Let n be 24/(-9)*1/(-12). Solve -n*z**2 - 4/9 + 2/3*z = 0.
1, 2
Let c(z) = 4*z**2 - 1. Let n be c(1). Suppose 2*i - n*i**2 + 4*i**4 + 4*i**5 - i**2 - 6*i**5 = 0. Calculate i.
-1, 0, 1
Let h(c) = c**4 - 2*c**3 - 2*c**2 + 2*c + 1. Let j(v) = 8*v**4 - 17*v**3 - 16*v**2 + 17*v + 8. Let l(p) = 51*h(p) - 6*j(p). What is s in l(s) = 0?
-1, 1
Let b(n) be the third derivative of -14/25*n**6 + 0*n + 7/75*n**7 - n**2 + 16/15*n**3 + 44/75*n**5 + 0 + 8/5*n**4. Determine q, given that b(q) = 0.
-2/7, 2
Let s(c) be the third derivative of c**9/241920 - c**8/80640 - c**5/60 - 2*c**2. Let i(h) be the third derivative of s(h). Let i(b) = 0. Calculate b.
0, 1
Let f = -4 + 8. Let a(l) = -l**4 - l + 1. Let m(w) = -7*w**4 + 5*w**3 - 3*w**2 - 16*w + 10. Let q(j) = f*m(j) - 44*a(j). Find h, given that q(h) = 0.
-1, -1/4, 1
Let p(d) be the first derivative of -d**6/3 + 12*d**5/5 - 2*d**4 - 4*d**3 + 5*d**2 + 6. Solve p(m) = 0 for m.
-1, 0, 1, 5
Suppose 6 = -497*c + 499*c. Find u, given that -13/5*u**c + 2/5 - 4*u**4 + 18/5*u**2 + 13/5*u = 0.
-1, -2/5, -1/4, 1
Find h, given that 15*h**4 - 27/2*h**3 + 9/2*h + 0 - 6*h**2 = 0.
-3/5, 0, 1/2, 1
Let j(i) be the second derivative of 0*i**2 - 1/90*i**6 + 1/18*i**3 + 1/36*i**4 + 3*i + 0 - 1/60*i**5. Suppose j(d) = 0. Calculate d.
-1, 0, 1
Let c(f) = f - 1. Let h be c(2). Let a(p) be the first derivative of 2/27*p**3 + 0*p - h + 0*p**2. Factor a(u).
2*u**2/9
Let y(k) be the second derivative of -k**7/42 + k**6/45 + k**5/10 - k**4/9 - k**3/6 + k**2/3 - 2*k + 4. Find n such that y(n) = 0.
-1, 2/3, 1
Solve -1/6*a**3 + 1/6*a**5 + 1/6*a**4 + 0*a - 1/6*a**2 + 0 = 0 for a.
-1, 0, 1
Let j be (-7)/(-14)*(-9)/(-6). Solve -3/4*x**3 + 3/4*x + j*x**2 - 3/4 = 0.
-1, 1
Solve 0 - 1/3*x**2 + 0*x - 1/3*x**3 = 0 for x.
-1, 0
Let p(q) be the third derivative of -q**5/90 + q**4/36 + 2*q**3/9 + 8*q**2. Factor p(f).
-2*(f - 2)*(f + 1)/3
Let f(r) = -8*r**4 - 16*r**3 - 8*r**2 + 5*r + 5. Let n(k) = 4*k**4 + 8*k**3 + 4*k**2 - 2*k - 2. Let c(m) = 2*f(m) + 5*n(m). Find s, given that c(s) = 0.
-1, 0
Let h(f) be the third derivative of -f**5/180 - f**4/36 + f**3/6 + 34*f**2. Determine o so that h(o) = 0.
-3, 1
Suppose -2/3 + 2/3*x**4 + 4/3*x**3 - 4/3*x + 0*x**2 = 0. What is x?
-1, 1
Let l be (2 - (-1 - 1)) + -1. Let n(y) be the first derivative of -l*y**5 - 6*y + 4 + 9/4*y**4 + 7*y**3 - 9/2*y**2. Find x, given that n(x) = 0.
-1, -2/5, 1
Suppose 0 = 5*i - 3*n - 6, n - 9 = -i - i. Factor -2*m**i + 0*m - 2*m - 2*m**2 + 2 + 2*m**3 + 2*m**3.
2*(m - 1)**2*(m + 1)
Let r(w) be the third derivative of w**5/210 + 4*w**4/21 + 64*w**3/21 + 6*w**2. Solve r(v) = 0 for v.
-8
Let a(b) be the second derivative of 0*b**3 - 1/150*b**5 + 3*b + 0 - 1/30*b**4 + b**2. Let k(s) be the first derivative of a(s). Factor k(t).
-2*t*(t + 2)/5
Let f(w) be the third derivative of -w**6/180 + w**5/30 + 3*w**2. Let f(y) = 0. What is y?
0, 3
Let y = 8 - 6. Factor 8*w + 0 - 8 - 2*w**y + 2 - 2.
-2*(w - 2)**2
Let o(h) be the second derivative of h**4/12 - 8*h**3/3 + 32*h**2 + 11*h. Find q, given that o(q) = 0.
8
Let v = -13 - -9. Let d be (273/130)/((-2)/v). Let d*u**4 - 6/5*u**3 - 3/5*u**2 - 12/5*u**5 + 0 + 0*u = 0. What is u?
-1/4, 0, 1
Let u(o) = o**3 + 2*o - 1. Let q be u(1). Let g(w) be the second derivative of -w + 1/12*w**4 + 0 - 1/24*w**3 + 0*w**q. Find v such that g(v) = 0.
0, 1/4
Suppose -2*x - f = 99, -f + 228 = -5*x + 3*f. Let v be (-30)/(-9)*x/(-280). Factor -2/7 - 2/7*y**2 - v*y.
-2*(y + 1)**2/7
Let w be (777/(-18))/7*2. Let h = w + 13. Find u, given that 0 + h*u**3 + 2/3*u + 4/3*u**2 = 0.
-1, 0
Let k = 2 + 2. Determine z, given that 3*z + z**2 - k*z - 2*z**2 = 0.
-1, 0
Let g(z) be the third derivative of -z**9/15120 - z**8/6720 + z**7/2520 + z**6/720 + z**4/8 + z**2. Let l(i) be the second derivative of g(i). Factor l(v).
-v*(v - 1)*(v + 1)**2
Let b(p) be the third derivative of p**6/48 - p**5/30 - 11*p**4/48 - p**3/6 + 34*p**2. Factor b(s).
(s - 2)*(s + 1)*(5*s + 1)/2
Let q(w) = w**2 - 1. Let k = -8 + 26. Let s(y) = 3*y**5 + 9*y**4 + 9*y**3 + 21*y**2 - 18. Let f(r) = k*q(r) - s(r). Factor f(o).
-3*o**2*(o + 1)**3
Let k(p) be the second derivative of p**6/1800 - p**5/100 + 3*p**4/40 - p**3/2 + 4*p. Let d(y) be the second derivative of k(y). Factor d(o).
(o - 3)**2/5
Let u(d) be the second derivative of 2*d**7/273 - d**6/39 + 3*d**5/130 + d**4/78 - d**3/39 - 3*d. Factor u(w).
2*w*(w - 1)**3*(2*w + 1)/13
Let n = -5 + 27. Let r(u) = u**2 - u + 4. Let y be r(0). Factor 2*v + n*v**2 - 6*v**4 - 10*v**y + 24*v**3 - 7*v**2.
-v*(v - 2)*(4*v + 1)**2
Let n(z) be the first derivative of z**4/24 + z**3/6 + z**2/4 - 3*z - 1. Let f(h) be the first derivative of n(h). Factor f(i).
(i + 1)**2/2
Let i(t) be the third derivative of t**6/200 - 9*t**5/20 + 135*t**4/8 - 675*t**3/2 + 3*t**2 - 3. Determine s so that i(s) = 0.
15
Let m(p) be the first derivative of p**3/18 - p/6 + 3. Solve m(c) = 0 for c.
-1, 1
Let q(f) be the second derivative of -5*f**7/42 - f**6/3 + 3*f**5/4 + 34*f. Suppose q(l) = 0. Calculate l.
-3, 0, 1
Suppose 0 = 5*m + 3*t, -2*m + 8 = -3*m + t. Let p = -2 - m. Let d(z) = -z**3. Let c(w) = w**5 - 3*w**4 + 9*w**3 - w**2. Let q(o) = p*c(o) + 6*d(o). Factor q(v).
v**2*(v - 1)**3
Let u be 103/150 + 12/(-18). Let g(f) be the second derivative of f + 1/15*f**3 - 1/15*f**4 + 0*f**2 + u*f**5 + 0. Determine m, given that g(m) = 0.
0, 1
Let i(u) = -u**3 + 6*u**2 + 9*u - 10. Let r be i(7). Suppose -4*a - 4*m - 26 = -9*a, 0 = 5*a + 3*m + 2. Find b, given that -4*b**2 + r*b**2 + b + b**a = 0.
-1, 0
Factor -9 + 0 + 2*z**2 + 3*z**2 - 11.
5*(z - 2)*(z + 2)
Factor 0*d + 2/11*d**2 + 0.
2*d**2/11
Let g(v) be the third derivative of v**7/14 - 7*v**6/40 + v**5/10 + 11*v**2. Factor g(t).
3*t**2*(t - 1)*(5*t - 2)
Suppose -3*u - 4 = -5*u. Factor 1/2*y**5 + 0 + 0*y**4 + 1/2*y + 0*y**u - y**3.
y*(y - 1)**2*(y + 1)**2/2
Let l(w) be the second derivative of 1/42*w**4 + 0*w**3 + 0 - 1/7*w**2 - 2*w. Factor l(j).
2*(j - 1)*(j + 1)/7
What is w in -12/5*w**3 - 18/5 + 2/5*w**4 + 12/5*w + 16/5*w**2 = 0?
-1, 1, 3
Let z(b) = 4*b**5 - 19*b**4 + 19*b**3 - 11*b**2 + 7*b - 7. Let n(i) = -2*i**5 + 9*i*