 + 176/(-99). Let n be 4/(8/10) + o. Find g such that -2*g**5 + 2*g**4 - 4*g**n + 8*g**4 + 0*g**3 - 4*g**4 = 0.
0, 1, 2
Let b(i) = i**4 + 13*i**3 + 15*i**2 - 15*i - 16. Let p(v) = 5*v**4 + 64*v**3 + 76*v**2 - 75*v - 81. Let w(s) = 11*b(s) - 2*p(s). Solve w(f) = 0 for f.
-14, -1, 1
Let 9*q**2 + 6*q**3 - 15*q**3 + 2*q + 6*q**3 - 8*q = 0. Calculate q.
0, 1, 2
Let f = -4/1951 - -3970/33167. Determine v, given that f*v**2 + 24/17 - 16/17*v = 0.
2, 6
Factor 2*q**3 - 98*q + 85*q**2 - 3*q**3 + 188*q - 8*q**3 + 4*q**3.
-5*q*(q - 18)*(q + 1)
Suppose o = -18 + 30. Factor -7*q**2 + 15*q - 20 + 24*q**2 - o*q**2.
5*(q - 1)*(q + 4)
Let y(d) = -195*d + 192*d - d**4 - 4*d**2 + 9*d**2 - d**3. Let j(u) = -u**2 + u. Let a(o) = -4*j(o) - y(o). Let a(r) = 0. What is r?
-1, 0, 1
Let r be (36/(-27))/(3/(-9)). Suppose -c = c. Factor 2*n - 2*n**2 + c*n**2 + 2*n**4 - n**2 - n**r.
n*(n - 1)**2*(n + 2)
Let f(b) be the first derivative of -1 + 7*b**2 + 4/3*b**3 - 3*b**4 - 1/3*b**6 - 2*b**5 + 6*b. Find z, given that f(z) = 0.
-3, -1, 1
Let s(f) be the first derivative of 24/5*f + 8 + 2*f**2 + 4/15*f**3. Factor s(d).
4*(d + 2)*(d + 3)/5
Let z(s) be the second derivative of -s**6/30 - s**4/12 - 28*s. Let p(h) = -6*h**4 - 8*h**3 + 2*h**2 - 4*h. Let j(f) = p(f) - 8*z(f). Let j(v) = 0. Calculate v.
0, 1, 2
Suppose 102/13*t + 50/13 + 2/13*t**3 + 54/13*t**2 = 0. Calculate t.
-25, -1
Let n(v) = 8*v**2 + 1 + v - 20*v**2 + 10*v**2. Let l(k) = -3*k**2 + k + 2. Suppose -3*a + 8 = -5*a. Let t(z) = a*n(z) + 3*l(z). What is h in t(h) = 0?
-2, 1
Let h(m) be the first derivative of -1/12*m**6 + 3*m**2 + 6 + 0*m**3 + 0*m - 1/12*m**4 + 1/5*m**5. Let d(x) be the second derivative of h(x). Factor d(y).
-2*y*(y - 1)*(5*y - 1)
Find p, given that 5/3*p**4 - 55/3*p**2 + 500/3 + 10*p**3 - 100*p = 0.
-5, 2
Let x(i) = -4*i**2 + i + 1. Let j(c) = -14*c**2 + 20*c + 34. Let b(u) = j(u) - 4*x(u). Determine k so that b(k) = 0.
-5, -3
Let w(v) be the second derivative of 49*v**6/15 - 77*v**5/10 + 16*v**4/3 - 4*v**3/3 - v - 96. Factor w(j).
2*j*(j - 1)*(7*j - 2)**2
Let f(a) be the third derivative of a**8/504 - 2*a**7/315 + a**5/45 - a**4/36 - 16*a**2 - 16. Factor f(q).
2*q*(q - 1)**3*(q + 1)/3
Let d(n) be the first derivative of 3*n**7/14 + n**6/4 - 5*n**5/3 + 5*n**4/3 - 5*n**2 + 24. Let t(v) be the second derivative of d(v). Solve t(o) = 0 for o.
-2, 0, 2/3
Let n(z) = 11*z**2 - 173*z - 572. Let s(l) = -300*l**2 + 4670*l + 15445. Let t(d) = 55*n(d) + 2*s(d). Suppose t(i) = 0. Calculate i.
-3, 38
Let f(p) be the third derivative of 3375*p**5/14 - 75*p**4/7 + 4*p**3/21 + 101*p**2. Let f(g) = 0. Calculate g.
2/225
Let t be 2 + (-3 - 22/(-10) - 28/(-35)). Let 0*d - 1/4*d**t + 1/4*d**3 + 0 = 0. Calculate d.
0, 1
Suppose -25 = 5*b, 3*r - 34 = 6*b - b. Suppose l**2 + 40 + 24*l + 20*l**2 - 36 - 29*l**3 - 20*l**r = 0. What is l?
-2/7, 1
Let y(g) = 18*g**2 + 154*g + 1733. Let t(q) = -15*q**2 - 152*q - 1732. Let s(p) = 5*t(p) + 4*y(p). Suppose s(l) = 0. Calculate l.
-24
Let z = -24 + 36. Let f be 24/5 + z/(-15). Factor -2*c**4 - 10*c**3 + 8*c**3 - 16*c - 10*c**3 - 6 - 24*c**2 - f*c.
-2*(c + 1)**3*(c + 3)
Let d(h) = 3*h + 75. Let q be d(-24). Solve -12*y**2 - 5*y - 6*y**3 + 22*y**2 + y**q = 0 for y.
0, 1
Let v = -4/677 + 1398/7447. Determine m, given that -v*m**2 - 8/11*m - 6/11 = 0.
-3, -1
Let k(t) = -3*t**3 + t**2 - t + 1. Let v(m) = 5*m**3 - m**2 + m - 2. Let i(d) = -3*k(d) - 2*v(d). Determine y so that i(y) = 0.
-1, 1
Let k(s) be the third derivative of -s**5/240 - 5*s**4/48 - 25*s**3/24 + 248*s**2. Factor k(u).
-(u + 5)**2/4
Let u(r) be the first derivative of -1/3*r**2 - 1/2*r**4 + 5*r + 2/3*r**3 + 5. Let s(a) be the first derivative of u(a). Factor s(m).
-2*(3*m - 1)**2/3
Let k = 22 + -30. Let c be k/(-10)*(-105)/(-14). Solve 13 - c*p**2 - 5*p - 2*p**3 + 3*p + 4*p - 7 = 0 for p.
-3, -1, 1
Let l(g) be the second derivative of -3*g**2 - 1/16*g**4 - 6*g - 1/40*g**5 + 1/4*g**3 + 1/80*g**6 + 0. Let h(a) be the first derivative of l(a). Factor h(y).
3*(y - 1)**2*(y + 1)/2
Let c = 2908 + -2905. Solve 9/8*q**2 - 3/8*q**4 - 3/8*q**c + 3/4 + 15/8*q = 0.
-1, 2
Let i(v) be the first derivative of -v**4/14 - 5*v**3/21 - v**2/14 + 2*v/7 + 126. Solve i(a) = 0 for a.
-2, -1, 1/2
Suppose 0 = 2*m + 4*r, -4*r = -3*r + 4. Suppose 0 = -a - 3 + m. Solve -2*c**3 + 1 - 1 + a*c**2 - 3*c**2 = 0.
0, 1
Let b(q) = q + 9. Suppose -2 = d + 5. Let m be b(d). Suppose 3*i**m - i**2 - 4*i**2 - i**2 - 6*i = 0. Calculate i.
-2, 0
Factor 24*h - 40 - 3*h**2 + 22 + 30*h - 117.
-3*(h - 15)*(h - 3)
Let m(f) be the first derivative of f**6/3 - 4*f**5/5 - 7*f**4/2 + 40*f**3/3 - 12*f**2 - 513. Factor m(x).
2*x*(x - 2)**2*(x - 1)*(x + 3)
Let y(m) be the third derivative of m**8/3360 + m**7/420 - m**5/15 + 3*m**4/4 - 10*m**2. Let r(h) be the second derivative of y(h). Find c, given that r(c) = 0.
-2, 1
Let b(k) = k**3 - 28*k**2 + 70*k + 129. Let v be b(25). Suppose -8/9*h**v + 8/9*h**2 - 2/9*h**5 - 2/3*h**3 + 0 + 8/9*h = 0. What is h?
-2, -1, 0, 1
Let l(u) be the second derivative of -1/40*u**6 - 4*u + 0 - 3/20*u**5 + 0*u**2 - 5/16*u**4 - 1/4*u**3. Factor l(m).
-3*m*(m + 1)**2*(m + 2)/4
Suppose 4*k + 57 = -15*k. Let q be 1 + k - (-108)/42. Factor -q*u**4 - 6/7*u**3 + 2/7*u**5 + 8/7*u + 0 + 8/7*u**2.
2*u*(u - 2)**2*(u + 1)**2/7
Suppose 0 = 5*x - 3 - 7. Let a = -1497 - -1500. Suppose 0 + 2/11*l**x - 2/11*l**a + 4/11*l = 0. What is l?
-1, 0, 2
Let g(j) be the second derivative of j**4/38 + 5*j**3/57 + 2*j**2/19 - j + 4. Factor g(r).
2*(r + 1)*(3*r + 2)/19
Let r(j) = -j**2 - 16*j - 58. Let h be r(-6). Suppose -u = -2*u + 2. Let 4 - 6*s**2 + 4*s**h - 2*s**u = 0. What is s?
-1, 1
Let w(x) be the second derivative of -x**4/3 - 14*x**3/3 + 60*x**2 + 165*x. Determine g so that w(g) = 0.
-10, 3
Factor 242/9 + 440/9*t + 2/9*t**4 - 40/9*t**3 + 52/3*t**2.
2*(t - 11)**2*(t + 1)**2/9
Let r(v) be the second derivative of -v**6/25 + 19*v**5/25 - 83*v**4/30 + 28*v**3/15 + 4*v**2 + v - 47. Let r(t) = 0. Calculate t.
-1/3, 1, 2, 10
Let j(i) = -22*i + 201. Let z be j(9). Let w(d) be the first derivative of 1 + 1/2*d**2 + 1/3*d**z - 2*d. Suppose w(a) = 0. What is a?
-2, 1
Factor 224/3*l**3 - 64/3*l**4 + 4*l - 100/3*l**2 + 0.
-4*l*(l - 3)*(4*l - 1)**2/3
Let o(f) be the first derivative of -f**4/16 + 19*f**3/12 - 10*f**2 - 25*f + 179. Factor o(i).
-(i - 10)**2*(i + 1)/4
Let x(g) be the second derivative of g**4/3 + 104*g**3 + 12168*g**2 - 374*g. Solve x(w) = 0 for w.
-78
Let f(a) be the first derivative of -a**4/2 + 88*a**3/51 - 37*a**2/17 + 20*a/17 - 242. Find r, given that f(r) = 0.
10/17, 1
Let y be (8/(-10))/(((-3)/5)/3). Suppose -y*q = -14 - 2. Factor 1/5*c**5 + 0*c**2 + 0 + 3/5*c**q + 0*c + 2/5*c**3.
c**3*(c + 1)*(c + 2)/5
Let d(y) be the second derivative of y**4/6 - 20*y**3/3 - 21*y**2 + 38*y - 6. Factor d(n).
2*(n - 21)*(n + 1)
Factor 0*b**4 + 0*b**2 + 0*b**3 + 1/4*b**5 + 0 + 0*b.
b**5/4
Factor -3*z**3 - 127 + 16*z + 94 - 27*z**2 + 47*z.
-3*(z - 1)**2*(z + 11)
Suppose -3*u = 4*w + 143, w + u + 47 = -2*u. Let s be w/(-66) - (-40)/220. Suppose -4/3 + s*k**2 - 2/3*k = 0. What is k?
-1, 2
Let n(t) = t**3 - 11*t**2 - t + 13. Suppose -2*l = -2*p - 3*l + 21, 8 = p + 3*l. Let a be n(p). Factor 4 + 2*k**2 - a*k**3 - 7 + 1 + 2*k.
-2*(k - 1)**2*(k + 1)
Let v(o) be the second derivative of 4/21*o**3 + 0 - 2/7*o**2 - 1/21*o**4 - 9*o. Find n, given that v(n) = 0.
1
Let h(g) = -g**2 - g - 6. Let r(j) = 105*j - j**2 - 6 - 105*j - 1. Let b(y) = 4*h(y) - 3*r(y). Factor b(m).
-(m + 1)*(m + 3)
Let o be 11*(-8)/(-748) + 583/(-5100). Let d(p) be the third derivative of -1/60*p**4 + o*p**5 + 0*p + 1/30*p**3 - 7*p**2 + 0. Solve d(n) = 0 for n.
1
Factor -138/7*g - 2/7*g**2 - 136/7.
-2*(g + 1)*(g + 68)/7
Let u(l) = l + 1. Let q(s) = s**2 + 11*s + 1. Let b(h) = q(h) + 3*u(h). Let a be b(-14). Factor 2*o**5 - o**3 - 5*o**5 + a*o**5.
o**3*(o - 1)*(o + 1)
Factor -18*f**3 + 16*f + 17*f - 48*f**2 + 7*f + 29*f - 101*f - 2*f**4.
-2*f*(f + 1)*(f + 4)**2
Suppose 9*d - 24 = 3*d. Determine s so that 4*s**3 - 44*s + 20 + 28*s**2 - 4*s**3 - d*s**3 = 0.
1, 5
Let p(g) be the first derivative of 25*g**6/6 - 2*g**5 - 125*g**4/4 + 50*g**3/3 + 50*g**2 - 40*g + 53. Let p(f) = 0. Calculate f.
-2, -1, 2/5, 1, 2
Suppose 5*f + p = -3, 2*f + p = -6 + 3. Let k(t) be the second derivative of -1/7*t**3 + 1/28*t**4 + 0 + f