10*t = 0. Calculate t.
-1/6, 1
Let y(c) be the third derivative of -c**7/2415 - c**6/1380 + 2*c**2. What is g in y(g) = 0?
-1, 0
Let o(k) = -k**3 - k**2 + 2*k - 3. Let a(x) = x**3 + x**2 - 2*x**2 + 1 + 0*x**3. Let l(b) = b + 7. Let i be l(-4). Let y(v) = i*a(v) + o(v). Factor y(t).
2*t*(t - 1)**2
Let m(x) = -7*x**2 + 3. Let j(p) = -p**2 + 1. Let q(y) = 3*j(y) - m(y). Factor q(k).
4*k**2
Let c = 4/5 - 3/10. Determine o so that 0 + 1/2*o**3 + o**2 + c*o = 0.
-1, 0
Suppose -4*i - 5*r - 13 = 0, i + 17 = -5*r - 5. Factor -9*g**2 + 21*g**2 - 7*g + 13*g + 4*g**4 + 12*g**i - 2*g.
4*g*(g + 1)**3
Let r(x) be the third derivative of -x**6/420 + x**5/210 + x**4/84 - x**3/21 + 2*x**2. Solve r(g) = 0 for g.
-1, 1
Let r(i) = -2*i**5 - 5*i**4 + 2*i**3 - i**2 + 3*i. Let d(z) = 6*z**5 + 14*z**4 - 6*z**3 + 2*z**2 - 8*z. Let h(w) = 3*d(w) + 8*r(w). Factor h(v).
2*v**2*(v - 1)*(v + 1)**2
Let i(f) = f**2 - 9*f + 19. Let z(p) = 2*p - 4. Let j(y) = 4*i(y) + 22*z(y). Factor j(n).
4*(n - 1)*(n + 3)
Let q = -193/5 + 39. Factor 0 + 0*a - q*a**2.
-2*a**2/5
Let b(r) be the third derivative of -r**5/90 + 8*r**2. Find h, given that b(h) = 0.
0
What is i in -4 + 0 - 3*i**2 - 3*i + 0*i - 10*i = 0?
-4, -1/3
Let c = -109/42 + -1/14. Let o = 3 + c. Solve 0*w - 1/3*w**2 - w**5 + w**3 + o*w**4 + 0 = 0.
-1, 0, 1/3, 1
Find p such that 1/5 - 2/5*p**2 + 1/5*p**4 + 0*p + 0*p**3 = 0.
-1, 1
Let -46 + 17 + 2*f**2 + 15 + 12 + f - f**3 = 0. Calculate f.
-1, 1, 2
Solve 0 + 2/5*g + 0*g**3 - 2/5*g**5 - 4/5*g**2 + 4/5*g**4 = 0.
-1, 0, 1
Let z(c) be the first derivative of -c**5 + 5*c**4/4 + 5*c**3/3 - 5*c**2/2 + 7. What is u in z(u) = 0?
-1, 0, 1
Let q(p) be the third derivative of -1/210*p**5 - 2*p**2 + 0 + 0*p**3 - 1/245*p**7 + 1/84*p**4 + 0*p - 1/84*p**6. Factor q(b).
-2*b*(b + 1)**2*(3*b - 1)/7
Let x(b) be the third derivative of b**6/120 + 13*b**5/180 + 2*b**4/9 + 2*b**3/9 - 2*b**2. Find p, given that x(p) = 0.
-2, -1/3
Let w be 35/14*8/30. Let v(s) be the first derivative of w*s**3 - 3*s**2 + 3 + 4*s. Solve v(y) = 0.
1, 2
Solve -3/4*s**5 - 5/4*s**4 + 1/2*s**3 + 3/2*s**2 - 1/4 + 1/4*s = 0.
-1, 1/3, 1
Let j be 0/((2 - 1) + 0). Let a(u) be the third derivative of 0*u - 1/50*u**5 - 1/15*u**3 - u**2 + 1/300*u**6 + j + 1/20*u**4. Determine n so that a(n) = 0.
1
Let t(b) be the third derivative of -1/630*b**6 + 1/84*b**4 + 1/6*b**3 + 0 + 1/420*b**5 - 2*b**2 + 0*b. Let z(q) be the first derivative of t(q). Factor z(u).
-2*(u - 1)*(2*u + 1)/7
Let f be 0/(-1) + (-1)/(-2). Let a = 1403 + -1400. Suppose -5/2*c - f*c**a - 1 - 2*c**2 = 0. Calculate c.
-2, -1
Let a(o) be the third derivative of -o**8/1512 - o**7/945 + o**6/540 + o**5/270 - 18*o**2 + o. Solve a(g) = 0 for g.
-1, 0, 1
Let a(x) = 2*x + 2. Let g be a(6). Suppose 3*m - g - 4 = 0. Factor 4*u**3 + u**2 + 2*u - m*u**3 + 2 - 3*u**2.
-2*(u - 1)*(u + 1)**2
Let 36*k**3 - 11*k + 12 - 14*k + 15*k**2 - 27*k**4 - 11*k = 0. What is k?
-1, 2/3, 1
Determine p, given that -1/5*p**2 + 4/5 + 3/5*p = 0.
-1, 4
Let n(g) be the first derivative of -3 - g**3 - 9/2*g**2 - 6*g. Factor n(p).
-3*(p + 1)*(p + 2)
Suppose w + 2 = 2*l, -3*w - l + 16 = 4*l. Find q, given that 8/5 + 2*q**w + 24/5*q = 0.
-2, -2/5
Suppose 4*k - 8 = -0. Suppose -5*b + 3*b**2 - 5 + 3 + 4*b**k = 0. What is b?
-2/7, 1
Let k(o) be the third derivative of -o**8/336 + 2*o**7/105 - o**6/24 + o**5/30 - 4*o**2. Factor k(x).
-x**2*(x - 2)*(x - 1)**2
Suppose -3*k**3 - 14*k**2 + 2*k**3 - 8 + 0*k**3 + 4*k + 16*k**2 = 0. What is k?
-2, 2
Let t be -3 + (44/12 - 0). Let l(y) be the first derivative of 0*y**2 + 8/9*y**3 + 0*y + t*y**4 - 2 + 2/15*y**5. Factor l(o).
2*o**2*(o + 2)**2/3
Let o(p) = 11*p**4 - 16*p**3 - 2*p**2 - 7*p + 7. Let s(v) = 7*v**4 - 11*v**3 - v**2 - 5*v + 5. Let q(y) = 5*o(y) - 7*s(y). Solve q(w) = 0 for w.
-1/2, 0, 1
Let h(m) be the third derivative of -m**5/300 + m**4/120 + m**3/5 - m**2 - 3*m. Factor h(x).
-(x - 3)*(x + 2)/5
Let g(z) = -3*z**3 - 6*z**2 - 9*z + 6. Let f(o) = -8*o**3 - 19*o**2 - 26*o + 19. Let a(l) = -6*f(l) + 17*g(l). Factor a(v).
-3*(v - 4)*(v - 1)*(v + 1)
Factor -3*k - 5*k + 2*k + k**2 - 3*k**2.
-2*k*(k + 3)
Let x be (4/(-40)*6)/(4/(-10)). What is u in -9/4*u**3 - 3/4*u**2 - 3/4 + x*u**4 + 9/4*u = 0?
-1, 1/2, 1
Let n(y) be the second derivative of 1/20*y**5 - 1/60*y**4 + 0*y**2 + 0 + 0*y**3 + 6*y + 1/70*y**7 - 7/150*y**6. Factor n(r).
r**2*(r - 1)**2*(3*r - 1)/5
Let z(v) be the first derivative of v**4/6 + v + 1. Let q(m) be the first derivative of z(m). Factor q(l).
2*l**2
Solve 5*j**3 + 6*j**3 + 4*j**2 - 14*j**4 + 0*j**2 - j**3 = 0.
-2/7, 0, 1
Let i(y) = -2*y**2 - 2*y + 3. Let b(q) = q**2 + q - 1. Let w(o) = 2*b(o) + 2*i(o). Factor w(z).
-2*(z - 1)*(z + 2)
Suppose 0*r = -3*r + 6. Suppose -12 = -2*l - 2*w, -4*l - 4*w = -w - 20. Let -i**3 + 2*i**3 - i - i**2 - i**4 + l*i**r = 0. Calculate i.
-1, 0, 1
Factor -72/11*x - 648/11 - 2/11*x**2.
-2*(x + 18)**2/11
Let n(j) be the second derivative of j**4/36 + 4*j**3/9 + 7*j**2/6 + 7*j + 6. Find c such that n(c) = 0.
-7, -1
Let k(t) be the first derivative of 3*t**5 - 5*t**4/4 - 1. Factor k(a).
5*a**3*(3*a - 1)
Let g(b) = 8*b**4 + 44*b**3 - 35*b**2 - 17*b - 17. Let p(k) = -3*k**4 - 15*k**3 + 12*k**2 + 6*k + 6. Let h(c) = -6*g(c) - 17*p(c). Suppose h(v) = 0. What is v?
0, 1, 2
Let v(k) = -k**4 + k - 1. Let w(q) = 3*q**2 + 6*q**4 + 3*q**2 - 5*q + 7 - 3*q**2. Let y(z) = 21*v(z) + 3*w(z). Factor y(u).
-3*u*(u - 2)*(u + 1)**2
Let x be -3 + -1 + (11 - 7). Factor 2/7*n**2 + 0*n + x.
2*n**2/7
Let n be (-40)/(-45)*(-2)/(-8). Let r(z) be the first derivative of -2/5*z**5 + 0*z + 5/6*z**4 + 1 - 1/3*z**2 - n*z**3. Find s such that r(s) = 0.
-1/3, 0, 1
Let t(i) be the third derivative of -2*i**7/105 - i**6/10 - 2*i**5/15 + 11*i**2. Suppose t(l) = 0. What is l?
-2, -1, 0
Let x(k) be the second derivative of -k**6/180 - k**5/120 + k**4/18 + k**3/9 - 19*k. Suppose x(i) = 0. What is i?
-2, -1, 0, 2
Let s(p) be the second derivative of p**4/12 - p**3/6 + 3*p. Factor s(z).
z*(z - 1)
Solve -d**2 + 4*d**2 + d**2 - 8*d = 0 for d.
0, 2
Factor 1/7 - 2/7*u**2 + 0*u**3 + 0*u + 1/7*u**4.
(u - 1)**2*(u + 1)**2/7
Factor 0*x**2 - 2*x - x - x - 4*x**2 + 24.
-4*(x - 2)*(x + 3)
Let d = 2 - 3. Let h = d + 2. Determine z, given that 1/2*z - 1/2*z**2 + h = 0.
-1, 2
Let g(x) be the first derivative of -x**5/3 - 5*x**4/12 + 20*x**3/9 + 10*x**2/3 + 30. Factor g(p).
-5*p*(p - 2)*(p + 1)*(p + 2)/3
Let p(x) be the first derivative of -x**6/9 + 2*x**5/15 + x**4/6 - 2*x**3/9 + 1. Factor p(v).
-2*v**2*(v - 1)**2*(v + 1)/3
Let b = -6 + 11. Solve -1/3 - 2/3*q**2 - 1/3*q**b + q - 2/3*q**3 + q**4 = 0.
-1, 1
Let g(c) = -c**3 + 7*c**2 + 10*c - 11. Let r be g(8). Suppose -r*d - 4*b = b, -d + 20 = -4*b. Let z**4 + 4*z**2 - 3*z**2 - d*z**3 + 2*z**3 = 0. What is z?
0, 1
Let m be (12/(-54) + 0)/((-20)/6). Let s(r) be the first derivative of -2/3*r**2 + 0*r**3 + 0*r + 1/4*r**4 - 1 + m*r**5. Factor s(l).
l*(l - 1)*(l + 2)**2/3
Let d(p) be the second derivative of -5*p**4/12 - 5*p**3/3 + 3*p. Factor d(n).
-5*n*(n + 2)
Suppose 3*i - 8 = i. Suppose -2*h - i*o = 6, h = 3*o - o + 13. Factor 9/5*s + 14/5*s**3 - 2/5 - 16/5*s**2 + 1/5*s**h - 6/5*s**4.
(s - 2)*(s - 1)**4/5
Let m be (-6)/1 - (-9 - -13 - 10). Factor -3/8*x + 3/8*x**2 + m.
3*x*(x - 1)/8
Let i = 59 + -59. Factor 2/7*w**2 + 4/7*w + i.
2*w*(w + 2)/7
Let c(o) be the second derivative of 3*o**5/4 - 3*o**4 + 2*o**3 - 7*o. Factor c(l).
3*l*(l - 2)*(5*l - 2)
Let f be 8/(-4)*(0 + -4). Suppose v = -3*v + f. Factor 3*n**4 + 2*n**3 - v*n**2 - 5*n**4 - 6*n**3.
-2*n**2*(n + 1)**2
Let b(c) be the first derivative of 0*c**3 - 2 + 1/8*c**4 - 1/4*c**2 + 0*c. Factor b(s).
s*(s - 1)*(s + 1)/2
Let a = 14 + -12. Factor -3*o**2 - 5 + 0*o**a + 3*o + 5.
-3*o*(o - 1)
Let k(g) be the first derivative of -4*g**3/3 + 14*g**2 - 49*g + 55. Determine a so that k(a) = 0.
7/2
Solve 2/7*s**2 + 0 - 2/7*s**3 + 0*s = 0.
0, 1
Factor 2*d + 4/3 + 0*d**2 - 2/3*d**3.
-2*(d - 2)*(d + 1)**2/3
Let i(f) be the second derivative of f**7/1008 - 7*f**6/1440 + f**5/120 + f**4/4 - 2*f. Let u(c) be the third derivative of i(c). Find m, given that u(m) = 0.
2/5, 1
Factor -1/3*g**2 + 2/3*g - 1/3.
-(g - 1)**2/3
Suppose -q - 5*k = 23, 3 = 4*q - 0*q + k. Let b(a) be the first derivative of 4 + 2/3*a**q + 2/27*a**3 + 2*a. Factor b(j).
2*(j + 3)**2/9
Suppose 0 = -3*s - 4*b + 21, -4 = -