 5
Let a(j) be the first derivative of 2*j**5/65 - 3*j**4/26 + 4*j**2/13 - 3. Let a(u) = 0. What is u?
-1, 0, 2
Suppose -3*i**2 + 20 - 13*i - i**2 - i**2 + 28*i = 0. Calculate i.
-1, 4
Let j(x) = -x**2 - 2*x. Let y(w) = -1. Let q(v) = -j(v) - y(v). Factor q(c).
(c + 1)**2
Let n(y) = 190*y**4 + 350*y**3 - 55*y**2 - 540*y. Let z(q) = -7*q**4 - 13*q**3 + 2*q**2 + 20*q. Let v(s) = -2*n(s) - 55*z(s). Factor v(r).
5*r*(r - 1)*(r + 2)**2
Suppose -3*v - 42 + 51 = 0. Let l(f) be the first derivative of 0*f - 171/4*f**4 + 19*f**3 - 8*f**6 - 3*f**2 + 168/5*f**5 - v. Suppose l(y) = 0. What is y?
0, 1/4, 1, 2
Determine v, given that -35/2*v**2 + 5/2*v**3 + 40*v**4 + 5*v + 0 - 30*v**5 = 0.
-2/3, 0, 1/2, 1
Let a(r) = -4*r**2 + 7. Let y(p) = 15*p**2 + 3*p - 29. Let f(j) = -61*j**2 - 11*j + 117. Let v(n) = 6*f(n) + 22*y(n). Let z(u) = 28*a(u) - 3*v(u). Factor z(x).
-4*(x - 1)*(x + 1)
Let k be 8/2 - 351/90. Let a(s) be the second derivative of 0*s**2 + 0*s**3 + k*s**5 + 1/3*s**4 - 2*s + 0. Factor a(g).
2*g**2*(g + 2)
Let z(w) be the second derivative of -w**6/180 + w**5/30 - w**4/18 - 3*w**2 - 4*w. Let a(d) be the first derivative of z(d). Determine p, given that a(p) = 0.
0, 1, 2
Suppose -28 - 72 = -4*p. Suppose 5*d + 0*d - p = 0. Factor -8*g + 2*g**4 + g**3 + g**d + 8*g.
g**3*(g + 1)**2
Let d(a) = -10*a**2 + 3*a. Let q(o) = -10*o**2 + 3*o - 1. Let u(s) = -5*d(s) + 4*q(s). Let y(x) = -20*x**2 + 7*x + 8. Let r(i) = 5*u(i) + 3*y(i). Factor r(l).
-2*(l - 1)*(5*l + 2)
Let g(p) = -p**2 - p - 7. Let b be g(0). Let n = b + 10. Let 4*s + n*s**2 + 4*s + 8 - s**2 = 0. Calculate s.
-2
Suppose 4*s - 4 = 4*f, -f - f - 1 = -s. Factor x - 2 - x**3 + f + 2.
-x*(x - 1)*(x + 1)
Let h = -1 + 1. Suppose 3*m - 12 + h = 0. Find z such that -2*z**3 + 2*z**m - 5*z**2 - 5*z**4 - z - 5*z**3 = 0.
-1, -1/3, 0
Suppose -1 + 7 = r + 3*j, 4*j = 4. Suppose -4*g = -4*f - 21 - 7, 0 = -4*g + r*f + 24. What is q in -2/3*q + 1/3*q**4 - 1/3 + 2/3*q**g + 0*q**2 = 0?
-1, 1
Let f(b) = -3*b**3 + 3*b**2 - 48*b + 72. Let m(d) = 2*d**3 - 3*d**2 + 48*d - 70. Let v(x) = 5*f(x) + 6*m(x). Suppose v(a) = 0. What is a?
-5, 2
Let l = 44/5 + -161/20. Factor -1/4*d**3 - 1/2 + l*d**2 - 1/4*d**4 + 1/4*d.
-(d - 1)**2*(d + 1)*(d + 2)/4
Let s(z) = 7*z**2 + 5*z - 10. Let y(n) = 50*n**2 + 35*n - 70. Let h(o) = -15*s(o) + 2*y(o). Factor h(f).
-5*(f - 1)*(f + 2)
Let s(n) be the first derivative of 2*n**5/25 + 3*n**4/10 + 4*n**3/15 - 12. Determine k, given that s(k) = 0.
-2, -1, 0
Let g(f) be the second derivative of -f**4/30 - 4*f**3/15 - 4*f**2/5 + 2*f. Let g(o) = 0. Calculate o.
-2
Let g(s) be the second derivative of 2*s**7/147 + s**6/21 - 5*s**4/42 - 2*s**3/21 - 5*s. Find r, given that g(r) = 0.
-2, -1, -1/2, 0, 1
Let c(f) be the third derivative of -f**5/60 + f**4/12 - f**3/6 - 20*f**2 - 2. Solve c(t) = 0 for t.
1
Let y be 27/(-36) - 55/(-76). Let i = 83/266 + y. Factor -2/7*w**2 + i*w + 4/7.
-2*(w - 2)*(w + 1)/7
Suppose 0 = b - 8*b + 3*b. Solve -6/5*t**2 - 2/5*t**4 + b + 2/5*t + 6/5*t**3 = 0 for t.
0, 1
Let p(z) = -2*z - 1. Let j be p(-4). Find f, given that -4*f**2 + 5 + 6*f**2 - j = 0.
-1, 1
Solve -14/13*s**5 + 0 - 56/13*s**3 + 94/13*s**4 - 24/13*s**2 + 0*s = 0.
-2/7, 0, 1, 6
Factor -2/17*d + 2/17*d**2 + 0.
2*d*(d - 1)/17
Let o(r) be the third derivative of -r**6/900 + r**4/60 - r**3/3 - 5*r**2. Let y(s) be the first derivative of o(s). Find l, given that y(l) = 0.
-1, 1
Let n be 5/(10/(-6)) + 6. Suppose 1 + n = 2*i. Factor 2/5*l + 2/5*l**3 + 0 + 4/5*l**i.
2*l*(l + 1)**2/5
Suppose m = -9 + 13. Let k(z) be the first derivative of -64/3*z**3 + 0*z + 2 - m*z**2 - 77/2*z**4 - 98/5*z**5. Find g such that k(g) = 0.
-1, -2/7, 0
Suppose 13*s = 6*s. Let d(b) be the second derivative of -1/24*b**4 - 2*b + s + 0*b**2 + 0*b**3. Factor d(h).
-h**2/2
Let v(z) be the first derivative of -1 + z + z**2 - z**3 - 1 - 2. Find b such that v(b) = 0.
-1/3, 1
Let z = -605/7 + 87. Factor 2/7*h - 2/7*h**3 - 4/7*h**2 + z.
-2*(h - 1)*(h + 1)*(h + 2)/7
Let r(y) be the third derivative of y**2 + 1/525*y**7 + 1/600*y**6 + 1/1680*y**8 + 0*y**4 + 0 + 0*y**3 + 0*y + 0*y**5. Factor r(j).
j**3*(j + 1)**2/5
Let p(b) be the second derivative of b**4/96 - b**3/24 - 3*b**2/16 - 3*b - 10. Suppose p(k) = 0. Calculate k.
-1, 3
Let r = -171 - -2579/15. Let -26/5*i**4 - 86/15*i**3 - 6/5*i**5 + r*i**2 + 32/15*i - 8/15 = 0. What is i?
-2, -1, 1/3
Let x(o) be the second derivative of o**6/15 + o**5/5 - 2*o**4 + 14*o**3/3 - 5*o**2 - 18*o + 2. Factor x(h).
2*(h - 1)**3*(h + 5)
Let u(h) be the third derivative of -5/48*h**4 + 3/40*h**5 + 0*h + 1/210*h**7 - h**2 + 0 + 1/12*h**3 - 7/240*h**6. Determine o, given that u(o) = 0.
1/2, 1
Let 2/5 - 4/15*x - 2/15*x**2 = 0. Calculate x.
-3, 1
Let r = 17 + -10. Factor -r*c**2 - 3*c**3 - c - c - 2*c**3.
-c*(c + 1)*(5*c + 2)
Let r = -4 + 9. Let -2*f**3 - f**2 + 0*f**r + f**2 - 4*f**4 - 2*f**5 = 0. What is f?
-1, 0
Let u(x) be the first derivative of -2*x**3/45 + 6*x/5 + 67. Factor u(y).
-2*(y - 3)*(y + 3)/15
Suppose -56*w = -68*w + 48. Solve -1/2*a**3 + 3/2*a**2 + 0 - 3/2*a**w - 1/2*a**5 + a = 0 for a.
-2, -1, 0, 1
Factor -1/5*a**2 + 1/10*a + 1/5 - 1/10*a**3.
-(a - 1)*(a + 1)*(a + 2)/10
Let h(a) be the first derivative of 0*a + 0*a**3 + 5 + 0*a**2 - 8/55*a**5 + 1/33*a**6 + 2/11*a**4. Factor h(z).
2*z**3*(z - 2)**2/11
Let g(m) = -m**3 - 11*m**2 - 11*m - 7. Let b be g(-10). Factor -1/3*h**2 - 1/3*h**b + 1/3 + 1/3*h.
-(h - 1)*(h + 1)**2/3
Let o(g) be the third derivative of 0 + 1/60*g**5 - g**2 + 0*g + 1/4*g**4 + 3/2*g**3. Suppose o(d) = 0. Calculate d.
-3
Let p(d) = d + 1. Let j = -9 + 12. Let r(s) = -s**2 - s - 6. Let o(t) = j*r(t) + 12*p(t). Find k such that o(k) = 0.
1, 2
Suppose -8/5*b**2 - 12/5 - 4*b = 0. Calculate b.
-3/2, -1
Let n(z) = z**2 - 2*z - 8. Let p be n(-2). Factor 2/11*y**2 - 16/11*y**3 + 4/11*y + 10/11*y**4 + p.
2*y*(y - 1)**2*(5*y + 2)/11
Let v(r) be the third derivative of -r**8/3360 + r**6/720 + 2*r**3/3 - 4*r**2. Let j(m) be the first derivative of v(m). Factor j(y).
-y**2*(y - 1)*(y + 1)/2
Suppose -2*p = n, 0 = 4*n - 3*n - p - 3. Factor -12*s**n - 3*s - 3*s**4 + 32*s**2 + 3*s**3 - 17*s**2.
-3*s*(s - 1)**2*(s + 1)
Let b be -1*(3 - (12 - 4)). Let r(d) be the second derivative of 0 + 0*d**2 - 1/3*d**4 + 1/3*d**3 - 3*d + 1/10*d**b. Factor r(u).
2*u*(u - 1)**2
Let t(s) be the second derivative of 0 + 1/9*s**2 - 7*s + 1/54*s**4 + 2/27*s**3. Solve t(h) = 0 for h.
-1
Let v(u) be the third derivative of u**6/420 - u**5/105 - u**4/28 + 8*u**2. Find p such that v(p) = 0.
-1, 0, 3
Solve 0 + 0*t**2 + 0*t + 2/3*t**3 + 4/3*t**4 + 2/3*t**5 = 0.
-1, 0
Factor -k**2 + 1 - 15 - 2*k + 7 + 6.
-(k + 1)**2
Let x be 69/387 + (-12)/18. Let h = x - -445/559. Find s, given that -8/13*s**3 - 2*s**2 - 22/13*s - h = 0.
-2, -1, -1/4
Let f be (-238)/(-1188) + (-8)/44. Let i(v) be the second derivative of v + f*v**4 + 0 - 2/9*v**2 + 1/27*v**3. Factor i(b).
2*(b - 1)*(b + 2)/9
Suppose -4*o - 3 + 7 = 0. Suppose -3*b - 5*c = 5, 5*c - 6*c = 5*b + o. Factor -1/2*i + b + 1/2*i**2.
i*(i - 1)/2
Factor 0 - 14/3*f**2 - 10*f**3 - 2/3*f - 6*f**4.
-2*f*(f + 1)*(3*f + 1)**2/3
Let v(q) be the first derivative of 4*q**5/5 - 3*q**4 - 28*q**3/3 + 30*q**2 + 72*q - 49. Determine j so that v(j) = 0.
-2, -1, 3
Let s be (-14)/72*13/(-91). Let f(d) be the third derivative of d**2 - 1/180*d**6 - 1/45*d**5 + 0 + 0*d + 0*d**3 - s*d**4. Determine u so that f(u) = 0.
-1, 0
Factor 8/5*a**4 - 6/5*a**2 - 7/5*a + 3/5*a**5 + 4/5*a**3 - 2/5.
(a - 1)*(a + 1)**3*(3*a + 2)/5
Suppose 2*w + w + 2*p - 3 = 0, -2*p = w - 1. Let j(v) = v**3 + v + 1. Let d(g) = -g**3 + g**2 - 7*g - 5. Let i(t) = w*d(t) + 4*j(t). Solve i(s) = 0.
-1, -1/3, 1
Let l(u) be the first derivative of u**6/135 + u**5/30 + u**4/27 - 5*u - 10. Let z(q) be the first derivative of l(q). Factor z(f).
2*f**2*(f + 1)*(f + 2)/9
Let u(b) be the second derivative of b**6/6 + 7*b**5/20 - b**4/4 - 7*b**3/6 - b**2 - 22*b. Solve u(y) = 0 for y.
-1, -2/5, 1
Suppose x - 2*x + 33 = -5*a, 2*a + 27 = 5*x. Let i(c) = c + 6. Let j be i(a). Factor j - 1/3*s**3 + 0*s**2 + 1/3*s.
-s*(s - 1)*(s + 1)/3
Let j(i) be the third derivative of 0*i + 0*i**5 - 3*i**2 + 0*i**4 - 1/40*i**6 + 0 + 0*i**3. Determine q so that j(q) = 0.
0
Let g = -38 + 38. Suppose -2/11*y**5 + 0*y**2 + 4/11*y**3 + 0*y + g + 2/11*y**4 = 0. What is y?
-1, 0, 2
Let