 1
Let f(n) = -81*n**5 - 157*n**4 - 75*n**3 + 13*n**2 + 6*n. Let h(b) = -2*b**5 - b**4 - b**3 + b**2. Let l(r) = f(r) - 2*h(r). Find q such that l(q) = 0.
-1, -2/7, 0, 3/11
Suppose -4*b + 2 = -3*b, -4*u + 56 = -2*b. Let x be 2/(-3) - u/(-9) - 1. Factor -7/5*g**5 + 0*g**2 + 2/5*g**4 + x*g + 0 + 0*g**3.
-g**4*(7*g - 2)/5
Let w(j) be the third derivative of j**5/180 + 37*j**4/144 + j**3/2 + 105*j**2 - j. Let w(d) = 0. Calculate d.
-18, -1/2
Let c be 8/(-10)*(-10)/4. Solve -217*p**2 - 10*p**4 + 227*p**2 - 6*p**3 - p**5 + 9*p**5 - c*p = 0.
-1, 0, 1/4, 1
Let k(h) be the second derivative of -h**6/15 - 38*h**5/5 - 325*h**4 - 17500*h**3/3 - 15625*h**2 + h - 10. Solve k(j) = 0.
-25, -1
Suppose 2*w + 3*f - 37 = 0, -7*f = -w - 12*f + 43. Factor -8/5 - w*m + 22/5*m**2.
2*(m - 2)*(11*m + 2)/5
Let y be 0 + (-6 + 11 - 3). What is u in -1/2*u + 0 + 1/4*u**y = 0?
0, 2
Let t(c) = -c. Let y be t(15). Let x be (10/6)/(y/(-45)). Determine h so that 0*h - 2/3*h**x + 2/3*h**4 + 0 + 2/3*h**3 - 2/3*h**2 = 0.
-1, 0, 1
Let p(w) = -14*w**3 - 72*w**2 - 13*w - 13. Let y be p(-5). Let x be 48/(-140)*(-14)/4. Solve x*v - 2/5*v**y - 4/5 = 0 for v.
1, 2
Let l(h) be the second derivative of 121*h**4/60 + 77*h**3/15 + 49*h**2/10 + 222*h. Solve l(j) = 0.
-7/11
Let b(g) be the second derivative of 0*g**2 - 11/14*g**4 + 0 - 1/35*g**6 + 3/7*g**3 + 19/70*g**5 + 7*g. Factor b(m).
-2*m*(m - 3)**2*(3*m - 1)/7
Suppose -4*z + 90 = -z. Suppose 3*m + z = 8*m. Factor 4*w - 1 + 2*w**3 - 2 + 3 + m*w**2.
2*w*(w + 1)*(w + 2)
Let b(p) = p**5 + p**4 + 49*p**3 + 116*p**2 + 84*p + 37. Let o(c) = 2*c**5 + 2*c**4 + 74*c**3 + 174*c**2 + 124*c + 56. Let u(k) = -8*b(k) + 5*o(k). Factor u(t).
2*(t - 4)*(t + 1)**3*(t + 2)
Let s(c) be the first derivative of 4*c**3/9 + 18*c**2 - 112*c/3 + 35. Factor s(q).
4*(q - 1)*(q + 28)/3
Let d(a) be the second derivative of -a**6/6 + 35*a**5/4 - 335*a**4/12 + 55*a**3/2 - 921*a. Suppose d(q) = 0. Calculate q.
0, 1, 33
Suppose -5*n = 3*v - 60, 4*n + v + 0*v - 48 = 0. Let l be (n/35)/((-42)/(-140)). What is t in l*t + 2/7*t**2 + 8/7 = 0?
-2
Let h be (-3)/(-12) - (-1198)/8. Let s be ((-54)/h)/(-1*3/5). Factor -3/5*b**2 + 6/5 - s*b.
-3*(b - 1)*(b + 2)/5
Let o = -219 + 220. Let a(z) = 1. Let l(x) = -3*x - 2*x**2 - 3*x**2 + 6*x**2. Let q(c) = o*l(c) + 2*a(c). What is r in q(r) = 0?
1, 2
Let h(k) = 22*k**3 - 60*k**2 + 82*k - 30. Let l(v) = -20*v**2 + 10*v**3 + 28*v - v - 3*v**3 - 10. Let n(x) = -2*h(x) + 7*l(x). Let n(y) = 0. What is y?
1, 2
Let r(g) = 2*g**2 + g - 8. Let p be r(4). Suppose -4*v + p = 4*w, -v = 2*w - 14 + 3. Find i such that 1/4*i**3 + 0 + 0*i - 1/8*i**w - 1/8*i**2 = 0.
0, 1
Let b = 836 - 833. Let j(y) be the second derivative of 1/9*y**4 - b*y + 2/3*y**3 + 0 + 4/3*y**2. Factor j(l).
4*(l + 1)*(l + 2)/3
Let n(l) be the second derivative of -l**6/15 + 3*l**5/10 + 99*l. Suppose n(j) = 0. Calculate j.
0, 3
Let c be 1/(-3) - 0 - (-528)/72. Let u(l) be the first derivative of -c*l**2 + 4 - 4/3*l**3 + 4*l + 7/2*l**4. Factor u(r).
2*(r - 1)*(r + 1)*(7*r - 2)
Let h(f) = f**3 + f - 105. Let u be h(0). Let y be (4/70)/((-45)/u). Factor -2/15*n - 2/15*n**4 + 0 + 2/15*n**2 + y*n**3.
-2*n*(n - 1)**2*(n + 1)/15
Let k(a) = -a**4 + 10*a**3 + 6*a**2 + 2*a - 5. Let c(g) = -2*g**3 - g**2 + 1. Let v(b) = -6*c(b) - k(b). Suppose v(y) = 0. Calculate y.
-1, 1
Suppose -112*n - 29 = -117*n - 3*h, 4*n = 4*h + 4. Let 10/17*k**3 - 8/17*k**2 + 0 + 6/17*k**n - 8/17*k = 0. Calculate k.
-2, -2/3, 0, 1
Solve 0*y + 6/5*y**2 - 14/5*y**4 + 8/5*y**3 + 0 = 0 for y.
-3/7, 0, 1
Let q be 6/15 - (-3)/5. Let r(d) = -d**3 - d. Let n(g) = 20*g**3 + 16*g**2 + 36*g + 8. Let v(p) = q*n(p) + 16*r(p). Factor v(z).
4*(z + 1)**2*(z + 2)
Let m(z) be the third derivative of z**5/75 - 23*z**4/15 + 1058*z**3/15 - 9*z**2 + 1. Solve m(j) = 0 for j.
23
Let 2*t**3 + 7*t**2 + t - 9*t**2 + 9 - 3 - 3*t**3 - 4*t**2 = 0. Calculate t.
-6, -1, 1
Let g(p) be the first derivative of -p**5/10 + 5*p**4/6 - 8*p**3/3 + 4*p**2 + 4*p + 7. Let o(y) be the first derivative of g(y). Factor o(c).
-2*(c - 2)**2*(c - 1)
Let v(n) be the second derivative of -n**4/90 + 4*n**3/5 - 7*n**2/3 - 39*n + 1. Suppose v(x) = 0. Calculate x.
1, 35
Determine f so that 54 - 164/3*f + 2/3*f**2 = 0.
1, 81
Let x(b) be the second derivative of b**5/4 + 5*b**4/12 - 5*b**3 + 2*b - 34. Determine h so that x(h) = 0.
-3, 0, 2
Let w(m) = 15*m**2 - m - 14. Let s(h) = h - 1. Let k(z) = 4*s(z) - w(z). Factor k(o).
-5*(o - 1)*(3*o + 2)
Let o(c) be the third derivative of c**7/840 - 3*c**6/160 - c**5/80 + 25*c**4/96 + 3*c**3/4 - 2*c**2 - 17. Suppose o(k) = 0. Calculate k.
-1, 2, 9
Suppose 5*u - 3*d = d + 50, -5*u + 2*d = -50. Suppose -25 + 5 = -u*r. Find w such that 0 + 2/3*w - 8/3*w**4 + 6*w**3 - 4*w**r = 0.
0, 1/4, 1
Let t be ((-6)/(-81)*-3)/((-131)/1179). Determine h, given that 0 + 3/8*h - 3/8*h**t = 0.
0, 1
Let s(d) be the first derivative of 55*d**4/14 + 86*d**3/21 + 6*d**2/7 + 82. Determine c so that s(c) = 0.
-3/5, -2/11, 0
Suppose -20 = -w + 3*o, -2*w - 2*o = -0 + 8. Factor 0 - 1/2*u**w - 1/4*u**3 - 1/4*u.
-u*(u + 1)**2/4
Let v = -1 - -6. Suppose -t - 5*r + 2*r + 5 = 0, v*t = 3*r + 7. Factor 5*h**5 - 2 - t*h**4 + 3*h**5 + 2*h - 6*h**5 + 4*h**2 - 4*h**3.
2*(h - 1)**3*(h + 1)**2
Let p(g) = -g**3 - g**2 + 5*g - 3. Let i be p(1). Let r(s) be the second derivative of -1/7*s**2 + i + 2/7*s**3 - 5/42*s**4 - 2*s. Factor r(v).
-2*(v - 1)*(5*v - 1)/7
Let k(a) = 3*a**2 - 8*a - 608. Let z be k(-13). Factor -1/3*f**2 + 1/3*f - 1/3*f**z + 1/3.
-(f - 1)*(f + 1)**2/3
Let q(f) = -4*f**2 + 184*f + 11. Let t(u) = -u**2 + 61*u + 4. Let r(h) = -4*q(h) + 11*t(h). Suppose r(w) = 0. Calculate w.
0, 13
Suppose g + 2*k = 22, 4*g - 5*k + 10*k = 79. Suppose -13 = u - g. Factor -1/6*i**u + 0 + 1/2*i**2 - 1/3*i.
-i*(i - 2)*(i - 1)/6
Let p(b) be the second derivative of 0 + 0*b**2 - 1/5*b**5 - 2/3*b**4 + 5*b - 2/3*b**3. Factor p(t).
-4*t*(t + 1)**2
Let f(d) = -d**5 - 6*d**3 - d. Let w be (-5)/15*(-1 - 8). Let x be ((-8)/6)/((-8)/(-24)). Let k(r) = -6*r**3. Let b(l) = w*f(l) + x*k(l). Factor b(i).
-3*i*(i - 1)**2*(i + 1)**2
Let q(m) be the second derivative of m**7/441 + m**6/315 - 99*m. Factor q(t).
2*t**4*(t + 1)/21
Factor 9327*j + 9283*j - 57*j**2 - 18550*j - 3*j**3.
-3*j*(j - 1)*(j + 20)
Let n = -33 + 39. Factor 15*x**3 - n*x**2 - 12*x + 0*x**2 - 16*x**3 - 8.
-(x + 2)**3
Let j be -2 + (-1 - 1) + 6. Solve -18*z + 14*z + 10*z - 3 - 3*z**j = 0.
1
Let k(m) be the second derivative of m**6/15 + 19*m**5/10 + 13*m**4 - 140*m**3/3 - 200*m**2 - m + 1. Suppose k(w) = 0. Calculate w.
-10, -1, 2
Suppose -15*c - 16 = -19*c. Let i(l) be the first derivative of -8/3*l**3 - 1 - 9*l**2 - c*l. Determine h so that i(h) = 0.
-2, -1/4
Factor 4/21*r**4 + 2/21*r**3 + 2/21*r**5 + 0 + 0*r**2 + 0*r.
2*r**3*(r + 1)**2/21
Suppose -5*m + 275 = 85. Find k, given that -8 + m*k**3 - 12*k + 47*k**3 - 81*k**3 = 0.
-1, 2
Let r(i) be the first derivative of -i**4/12 + 7*i**2/6 - 2*i - 54. Suppose r(x) = 0. What is x?
-3, 1, 2
Let f be 4/(-10 + 10 + 8 + -2). Factor 1/6*v**2 + 1/2 + f*v.
(v + 1)*(v + 3)/6
Let g = 115 - 66. Determine b so that 100*b**4 - 54*b**4 + 3*b**2 - g*b**4 = 0.
-1, 0, 1
Let w be (1 + 65/(-35))*14/(-3). Suppose 4*b - 8 - w = 0. Factor -1/2 + k**2 - 1/2*k**4 + k**b - 1/2*k - 1/2*k**5.
-(k - 1)**2*(k + 1)**3/2
Let g(k) be the first derivative of 5*k**8/336 + 2*k**7/21 + k**6/4 + k**5/3 + 5*k**4/24 + 12*k**2 + 15. Let q(a) be the second derivative of g(a). Factor q(c).
5*c*(c + 1)**4
Let w(x) = -24*x**4 + 56*x**3 - 54*x**2 + 10*x + 6. Let n(z) = z**4 + z**3 - z**2 + z - 1. Let c(h) = 6*n(h) + w(h). Factor c(o).
-2*o*(o - 2)*(o - 1)*(9*o - 4)
Let v(f) = 80*f**2 - 730*f. Let t(g) = 3*g**2 - 27*g. Let m be ((-7)/2)/7*-4. Let y(s) = m*v(s) - 55*t(s). Let y(q) = 0. Calculate q.
0, 5
Let f = 60233/4 + -15056. Find q such that 0 - 7/4*q**2 + f*q**3 - 1/2*q = 0.
-2/9, 0, 1
Suppose -23*a - 5*m + 25 = -20*a, m - 5 = 0. Let n(o) be the third derivative of -1/120*o**5 + 1/48*o**4 - 11*o**2 + 0*o**3 + 0*o + a. Solve n(u) = 0.
0, 1
Let c(j) be the second derivative of 0*j**3 + 0 - 1/3*j**2 + 1/18*j**4 - 5*j. Suppose c(i) = 0. What is i?
-1, 1
Determine v, given that -1 + 65*v - 242*v**2 - 2 + 7*v**3 + 178*v**2 - 5 = 0.
1/7, 1, 8
Determine w, given that 4/7*w**2 - 32*w + 448 = 0.
28
Let y be (((-8)/(-12))/(1/(-12)))