2 + 248). Find a, given that 3/5*a + 1/5 + g*a**3 + 3/5*a**2 = 0.
-1
Let n = 367/3 + -121. Let f(j) be the second derivative of -6*j + n*j**3 + 0 - 6*j**2 + 1/3*j**4. Solve f(s) = 0 for s.
-3, 1
Let s = -46 - -55. Suppose 0 = 4*k - 2*p - 14, s*p - 7*p + 17 = 5*k. Find v such that 0 + 1/3*v**2 + 0*v - 1/3*v**4 + 0*v**k = 0.
-1, 0, 1
Let z(f) = 5*f**3 - 22*f**2 + 14*f - 9. Let c(g) = -g**3 + 4*g**2 + 1. Let b(y) = 3*c(y) + z(y). Determine q so that b(q) = 0.
1, 3
Find n, given that 83*n**4 + 4*n**2 - 251*n**4 - 24*n + 20*n**3 + 81*n**4 + 83*n**4 + 4*n**3 = 0.
-1, 0, 1, 6
Let y(h) be the third derivative of h**7/70 + h**6/20 - h**5/20 - h**4/4 + 3*h**2 + 29*h. Let y(q) = 0. Calculate q.
-2, -1, 0, 1
Let v = -14402/9 + 1603. Factor -10/9*o - 1/9*o**2 - v.
-(o + 5)**2/9
Factor -257*l**3 + 12*l - 6*l**4 - 40*l**2 - 2*l**4 + 293*l**3.
-4*l*(l - 3)*(l - 1)*(2*l - 1)
Suppose -5*o - 4*a = 10, 5*a = -o + 3*o - 29. Let j(m) = m**2. Let w(s) = -s**2. Let g(y) = o*w(y) + j(y). Factor g(d).
-d**2
Let y(j) = -2*j**5 - 26*j**4 + 59*j**3 - 60*j**2 + 24*j. Suppose -7*i - 3*i = 10. Let k(w) = -w**5 - w**4 + w**3. Let a(x) = i*y(x) + 5*k(x). Factor a(m).
-3*m*(m - 2)**3*(m - 1)
Let w(v) = v**2 + v. Let q(n) = -2*n - 2*n**2 + 5*n**2 - 5*n**2. Let u(m) = -4*q(m) - 5*w(m). Factor u(b).
3*b*(b + 1)
Let k(a) be the first derivative of -5*a**4/12 - 80*a**3/3 - 875*a**2/2 + 6250*a/3 - 90. Find m such that k(m) = 0.
-25, 2
Let n(i) = -i**2 + 65*i + 578. Let m(g) = -2*g**2 + 196*g + 1734. Let x(p) = 3*m(p) - 8*n(p). Solve x(y) = 0.
-17
Solve -63*l - 90*l + 177*l - 3*l**2 = 0.
0, 8
Let s be (-28)/(-70) - (-14)/15. Let u(g) be the second derivative of -s*g**4 - 2/21*g**7 + 0*g**3 - 8/5*g**5 + 0 + 0*g**2 - 2/3*g**6 - g. Factor u(x).
-4*x**2*(x + 1)*(x + 2)**2
Let j(s) be the first derivative of s**3/2 - 75*s/2 + 12. Factor j(i).
3*(i - 5)*(i + 5)/2
Let d(x) be the second derivative of -x**7/28 - 7*x**6/30 - 23*x**5/40 - 2*x**4/3 - x**3/3 - 30*x. Determine k, given that d(k) = 0.
-2, -1, -2/3, 0
Let u = -3551/9 - -395. Let w(o) be the first derivative of -1/6*o**4 + o**2 + 0*o + 2 - u*o**3. Factor w(b).
-2*b*(b - 1)*(b + 3)/3
Let n(x) = 3*x**5 - 5*x**4 - 38*x**3 - 50*x**2 - 25*x - 5. Let a(c) = -3*c**5 + 5*c**4 + 38*c**3 + 51*c**2 + 26*c + 5. Let t(i) = 4*a(i) + 3*n(i). Factor t(o).
-(o - 5)*(o + 1)**3*(3*o + 1)
Let x(i) be the second derivative of -121*i**4/60 + 66*i**3/5 - 162*i**2/5 - 204*i. Factor x(q).
-(11*q - 18)**2/5
Let d(v) = v**3 + v**2 - 2*v - 1. Let a(r) = 6*r**3 - 10*r**2 - 8*r - 4. Let w(m) = a(m) - 4*d(m). Factor w(p).
2*p**2*(p - 7)
Factor x**2 - 14*x - 4*x**2 - 33 + 50*x.
-3*(x - 11)*(x - 1)
Let p(o) be the third derivative of 0*o + 0 + 8*o**2 + 25/6*o**3 + 1/6*o**5 + 55/24*o**4. Factor p(x).
5*(x + 5)*(2*x + 1)
Let p(r) = r**3 - 6*r**2 + 5*r + 3. Let k be p(5). Let o(i) = 0*i - 1 - 2*i + k*i. Let j(v) = -v**2 + 9*v - 2. Let g(q) = j(q) - 6*o(q). Factor g(h).
-(h - 4)*(h + 1)
Let g(i) be the first derivative of i**4/4 + 4*i**3/3 + 3*i - 5. Let v be g(-4). Factor 7*h + 2*h + 20*h**v - 23*h**3 + 6.
-3*(h - 2)*(h + 1)**2
Let z = 11 - 9. Suppose 0 = 2*p - 3*r - 23, p - z*r + 21 = -7*r. Factor -6*u**2 - p + 0*u - u**2 + 6*u + 5*u**2.
-2*(u - 2)*(u - 1)
Let t(z) be the second derivative of -7*z + 0 + 1/20*z**4 + 0*z**2 - 1/2*z**3. Factor t(b).
3*b*(b - 5)/5
Let 56*i**4 - 33*i**4 - 2*i**3 + 4*i**2 + 0*i**3 - 27*i**4 + 2*i**5 = 0. Calculate i.
-1, 0, 1, 2
Let p = -278 - -150. Let s be p/728*-6 - (-4)/(-14). What is a in -4/13 + 2/13*a**3 - s*a - 6/13*a**2 + 2/13*a**4 = 0?
-1, 2
Factor 67 + 151 - 5*o**2 + 94 - 137 - 10*o.
-5*(o - 5)*(o + 7)
Let t(i) be the first derivative of -64*i + 2/3*i**6 + 4*i**4 - 64/3*i**3 + 4*i**5 + 39 - 64*i**2. Factor t(z).
4*(z - 2)*(z + 1)*(z + 2)**3
Let v(m) = 2*m**4 - 10*m**3 - 10*m**2 + 2*m - 2. Let y(h) = h**5 - 6*h**4 + 31*h**3 + 31*h**2 - 7*h + 7. Let t(w) = 14*v(w) + 4*y(w). Factor t(j).
4*j**2*(j - 2)*(j + 1)*(j + 2)
Find v such that -1/5*v**3 + 0 + 6/5*v + v**2 = 0.
-1, 0, 6
Suppose -6*m + 17 - 5 = 0. Solve -v**2 - 12*v + v**m - 6*v**2 + 3*v**2 = 0 for v.
-4, 0
Let v = -7243/15 - -483. Let d(w) be the first derivative of 3/5*w**2 + v*w**3 - 2 + 4/5*w. Let d(x) = 0. What is x?
-2, -1
Let c(t) be the third derivative of -t**5/80 - 17*t**4/8 - 240*t**2. Determine r so that c(r) = 0.
-68, 0
Factor -1 - 2*v - 24*v + 12*v - 49*v**2.
-(7*v + 1)**2
Let l(y) be the third derivative of -y**6/40 - y**5/30 - y**4/8 - y**3/3 - y**2 - 30*y. Let t be l(-1). Solve -k + 0 - 1/2*k**t = 0 for k.
-2, 0
Let t(x) be the first derivative of -98*x**6/3 - 3080*x**5 - 76717*x**4 - 57200*x**3 - 12168*x**2 - 83. Determine i so that t(i) = 0.
-39, -2/7, 0
Suppose -2*f - 3149 = -4*c - f, -c - 5*f + 782 = 0. Factor 787 - c - 4*w + 4*w**2.
4*w*(w - 1)
Let g = 4376/5 + -874. Let h(y) be the first derivative of 0*y + g*y**2 + 18/25*y**5 + 39/20*y**4 + 12/5*y**3 + 6 + 1/10*y**6. What is p in h(p) = 0?
-2, -1, 0
Let x(i) be the third derivative of -9*i**2 - 5/14*i**3 - 1/4*i**4 + 0 + 0*i + 3/140*i**5. Factor x(u).
3*(u - 5)*(3*u + 1)/7
Factor 83/2*n + 1/4*n**2 + 6889/4.
(n + 83)**2/4
Let f be 4*175/56 - 8. Let l(s) be the first derivative of -7 - f*s**2 + s**3 + 6*s. Let l(n) = 0. Calculate n.
1, 2
Let n(c) = 9*c**3 - 26*c**2 - 79*c - 39. Let w(s) = -s**3 - 2*s**2 - s - 1. Let u(z) = -n(z) - 5*w(z). Factor u(p).
-4*(p - 11)*(p + 1)**2
Let v(a) = 3*a**4 + 5*a**3 + 4*a**2 - 2. Let h(n) = -14*n**4 - 22*n**3 - 17*n**2 + 9. Let z(y) = -2*h(y) - 9*v(y). What is c in z(c) = 0?
-1, 0, 2
Let t = -9 - -13. Factor -4*c**2 - 3*c**3 - 2*c + t + c**3 + 3*c**3 + c**3.
2*(c - 2)*(c - 1)*(c + 1)
Suppose 3*t = 9 - 0. Let w = 15 - t. Suppose -3*m**3 - w + 4*m**3 - 4*m**3 + 12*m**2 - 3*m**2 = 0. Calculate m.
-1, 2
Suppose 2865 - 4*s + 3*s**2 - 2*s**2 + 22*s - 2884 = 0. What is s?
-19, 1
Let h(p) be the first derivative of 4*p**5/5 + 7*p**4 + 68*p**3/3 + 34*p**2 + 24*p - 429. Solve h(c) = 0 for c.
-3, -2, -1
Let l = 2157 - 2155. Let 2/7*g**3 + 4/7 + 10/7*g + 8/7*g**l = 0. What is g?
-2, -1
Let h be (6/(-9))/(-5 + 2 + 1). Find q, given that -2/3*q - h*q**2 - 1/3 = 0.
-1
Let q(o) = -o**3 + o**2 + o - 3. Let u be q(0). Let m be 3 - 4 - (u + (-52)/16). Factor -15/4*w**3 + m*w**2 - 3/2*w + 0.
-3*w*(w - 1)*(5*w - 2)/4
Let c = -20 + 29. Let w be 52/6 + 3/c. Factor -5*i + w + i**2 - 11 + i - 3*i**2.
-2*(i + 1)**2
Let a(x) be the third derivative of x**5/20 + 23*x**4/8 - 12*x**3 + 33*x**2 + 2*x. Factor a(p).
3*(p - 1)*(p + 24)
Let t(i) be the second derivative of i**5/40 - i**4/16 + 4*i**2 + 2*i. Let a(q) be the first derivative of t(q). Factor a(n).
3*n*(n - 1)/2
Let v(y) be the first derivative of -y**7/14 + y**6/10 + 3*y**5/20 - y**4/4 - 6*y - 11. Let d(o) be the first derivative of v(o). Suppose d(b) = 0. Calculate b.
-1, 0, 1
Let g(b) = -6*b**3 - 2*b. Let n(o) = -o**4 + o**3 - o**2 + o. Suppose 3*c - 9 = -3. Let f(z) = c*n(z) + g(z). Let f(t) = 0. What is t?
-1, 0
Let q = -1 + 3. Suppose -3*o**q - 17*o**3 - 2*o**2 + 22*o**3 = 0. What is o?
0, 1
Factor -85*k**3 - 30 + 30*k**2 + 0*k - 5*k + 90*k**3.
5*(k - 1)*(k + 1)*(k + 6)
Let j(v) be the third derivative of 1/630*v**7 - 18*v**2 - 1/18*v**4 - 1/60*v**6 + 1/20*v**5 + 0*v + 0*v**3 + 0. Determine f so that j(f) = 0.
0, 1, 4
Let q be 0*(90/(-12) - -8). Factor f + q + 2*f**3 + 1/2*f**4 + 5/2*f**2.
f*(f + 1)**2*(f + 2)/2
Let c(n) = n**3 - n**2 - 2*n + 3. Let k be c(2). Let a(m) = -m + 7. Let g be a(k). Factor -3*x**2 - 2*x**g + 2*x**4 + 2*x**2 - 6*x**3 + 2*x**5 + 2*x - x**4.
x*(x - 2)*(x + 1)**2*(2*x - 1)
Let n be 3 - 12/14*(-7)/(-4) - 0. Solve -3/2*l**3 + n*l + 0*l**2 + 0 = 0 for l.
-1, 0, 1
Let i(l) = -2*l**3 + l**2 + l + 1. Let w(q) = q**3 - 9*q**2 - 6*q + 49. Let o(a) = -i(a) - w(a). Factor o(c).
(c - 2)*(c + 5)**2
Let v(p) be the first derivative of p**6/33 + 32*p**5/55 + 36*p**4/11 - 432*p**2/11 + 91. Factor v(x).
2*x*(x - 2)*(x + 6)**3/11
Let s(b) be the second derivative of 1/36*b**4 + 32/3*b**2 - 8/9*b**3 + 2*b - 3. Factor s(w).
(w - 8)**2/3
Let v be (57/18 - 3)/(1/1552). Let b = -258 + v. What is s in -1/6*s + 2/3*s**4 + b*s**2 - s**3 + 0 - 1/6*s**5 = 0?
0, 1
Let j(r) be the first derivative of -98*r**3/3 + 126*r**2 - 162*r - 33. Factor j(l).
-2*(7*l - 9)**2
Let q(t) = -t**3 - 2*t - 2. Let k(b) = -b**3 - 27*b**2 + 37*b + 67. Let w(