+ 0*a**3 + 0 + 1/2*a**2 - 1/2*a**4 = 0.
-1, 0, 1
Let v be 10 + (-12)/((-1008)/(-804)). Let f(l) be the third derivative of -7*l**2 + 0 + 0*l - v*l**3 - 1/210*l**5 + 1/14*l**4. Solve f(u) = 0.
3
Suppose 2*g + 4 - 6 = 0. Let w(r) = -r**3 + r**2 + r. Let b(y) = -15*y**4 - 5*y**3 + 2*y**2 - 4*y. Let k(u) = g*b(u) + 4*w(u). Determine f, given that k(f) = 0.
-1, 0, 2/5
Let h(q) be the second derivative of q**6/80 + 39*q**5/160 + 3*q**4/2 + 9*q**3/4 + 100*q + 2. Factor h(b).
3*b*(b + 1)*(b + 6)**2/8
Let z be (20/30)/((-2)/(6/(-7))). Let q be (-48)/14 + 6 + -1 + -1. Factor z*k**3 - 6/7*k**2 + 0 + q*k.
2*k*(k - 2)*(k - 1)/7
Let x = 12/11 + -37/44. Let k be (-60)/(-50)*(-35)/(-56). Determine f so that -f + x*f**2 + k = 0.
1, 3
Let p(a) be the second derivative of -a**8/15960 + a**7/3990 - a**6/3420 - a**3/3 + 5*a. Let w(n) be the second derivative of p(n). Factor w(q).
-2*q**2*(q - 1)**2/19
Let f(w) be the first derivative of 2*w**3/39 + 4*w**2/13 + 6*w/13 + 106. What is d in f(d) = 0?
-3, -1
Let s(x) be the second derivative of x**4/12 - x**3/6 - x. Let n be -2 - (-1 + 0 - -2). Let h(u) = -12*u**2 - 9*u - 3. Let r(t) = n*s(t) - h(t). Factor r(k).
3*(k + 1)*(3*k + 1)
Let w(d) = -15*d**2 + 8*d + 10. Let s(t) = 30*t**2 - 17*t - 20. Let u be (-2)/2 + 8/2. Let a(j) = u*s(j) + 7*w(j). Factor a(v).
-5*(v - 1)*(3*v + 2)
Let r(j) be the first derivative of 0*j + 5*j**2 + 1/20*j**5 + 8 + 3/2*j**3 + 1/2*j**4. Let g(d) be the second derivative of r(d). Factor g(t).
3*(t + 1)*(t + 3)
Factor 12*n - 34*n + 6 + 40*n**2 - 11*n - 25*n**2.
3*(n - 2)*(5*n - 1)
Let o(k) be the third derivative of -k**5/30 + k**4/2 - 3*k**3 - 2*k**2 + 5. Factor o(q).
-2*(q - 3)**2
Let m = -2149 - -2151. Factor 0*k + 0 - 1/2*k**5 - 1/2*k**3 + k**4 + 0*k**m.
-k**3*(k - 1)**2/2
Let m = 106 - 92. Suppose m*q = 10*q + 5*b + 20, 2*q = -3*b - 12. Let 1/4*o + q*o**2 + 0 - 1/4*o**3 = 0. What is o?
-1, 0, 1
Let n(u) = -3*u - 4. Let a be n(-3). Let g = -610 + 610. Factor 2*c**3 + 32/5*c**a + 0 - 32/5*c**4 + g*c - 1/5*c**2.
c**2*(2*c - 1)*(4*c - 1)**2/5
Let 18/7*t - 12/7*t**2 + 0 + 2/7*t**3 = 0. What is t?
0, 3
Let i(m) = -14*m**2 + 86*m - 8. Let a(v) = 5*v**2 - 28*v + 3. Let w(h) = 8*a(h) + 3*i(h). Factor w(j).
-2*j*(j - 17)
Suppose -a - 3*a = -48. Let f(v) = -v**2 + 11*v + 21. Let b be f(a). Factor 5*t**4 + t**3 + 9*t**2 + 2*t**3 - b*t**4 + 2*t.
-t*(t - 2)*(t + 1)*(4*t + 1)
Suppose 4*b - 13 = -5*o + 2, 3*b = 3*o - 9. Let c(a) = 0 + 3 + a**2 + a**3 - 4. Let y(g) = -2*g**2 + 4*g + 1. Let z(p) = o*c(p) - y(p). Factor z(u).
(u - 1)*(u + 2)*(3*u + 2)
Let h(y) be the second derivative of 2/15*y**6 + 0*y**3 + 0*y**5 + 0*y**2 - 13*y - 1/21*y**7 + 0*y**4 + 0. What is i in h(i) = 0?
0, 2
Let -88*t**2 - 97*t**2 - 17*t - 90*t**2 + 364*t**2 - 88*t**2 = 0. What is t?
0, 17
Let x(b) = -3*b**2 + 7*b. Let f(c) = -5*c**2 + 11*c. Let z(q) = 5*f(q) - 8*x(q). Let l(s) = -3*s**2 + 10*s - 36. Let n(i) = -l(i) + 2*z(i). Factor n(u).
(u - 6)**2
Let q(x) be the first derivative of 4*x**3/3 + 38*x**2 + 136*x - 181. Find t such that q(t) = 0.
-17, -2
Let 97/3*t - 1/3*t**2 - 32 = 0. Calculate t.
1, 96
Find g such that -218*g**2 - 959*g**3 - 35*g**5 + 158 - 1312*g**2 - 405*g - 201*g**3 + 112 - 340*g**4 = 0.
-3, -1, 2/7
Let z be (0 - 6/(-5))/(28/140). Find g, given that -g**2 + z*g + 9 - 5 - 7 - 2*g**2 = 0.
1
Suppose 4*z + 2*g - 30 = 0, 5*z + 5*g - 26 = 2*z. Let i(r) = r**3 - 8*r**2 + 8*r - 7. Let s be i(z). Factor -1/3*k**4 + s*k + 2/3*k**3 + 0 - 1/3*k**2.
-k**2*(k - 1)**2/3
Factor -2*j**2 + 16*j - 113 - 107 + 188.
-2*(j - 4)**2
Let h(d) be the third derivative of d**6/84 + 6*d**5/35 + 19*d**4/28 + 10*d**3/21 - 14*d**2 + 1. Determine s so that h(s) = 0.
-5, -2, -1/5
Suppose 5*d - 4*h - 8 = 0, -30*h + 27*h - 6 = -d. Factor -1/3*l**2 + d - 2/3*l.
-l*(l + 2)/3
Let j be (-2)/(-28) + 9/42. Let h be 20/(-28)*(-2)/5. Factor 2/7*w**2 - 2/7*w**4 + 0*w + 0 - j*w**3 + h*w**5.
2*w**2*(w - 1)**2*(w + 1)/7
Let w(l) be the third derivative of 1/40*l**5 + 0*l + 0 + 1/80*l**6 - 1/4*l**3 + 13*l**2 - 1/16*l**4. Suppose w(n) = 0. What is n?
-1, 1
Let u(j) = j**4 + 2*j**3 - 24*j**2 + 22*j - 9. Let k(y) = y**4 + 3*y**3 - 24*y**2 + 23*y - 9. Let t(a) = 4*k(a) - 3*u(a). Factor t(w).
(w - 1)**3*(w + 9)
Let 2200/7*h + 3750/7 - 1444/7*h**2 - 2/7*h**4 + 104/7*h**3 = 0. Calculate h.
-1, 3, 25
Let i be 12/8 - 9/(-6). Factor 3*o**4 - 15*o**4 - 3*o**3 - 4*o**5 - 4*o**2 - 5*o**3 - 4*o**i.
-4*o**2*(o + 1)**3
Let o be (-8 + -83)/(-7) + -7. Let l(f) be the first derivative of -7 + 8/5*f**5 + 8/3*f**3 + 3*f**4 + 0*f + 1/3*f**o + f**2. Factor l(h).
2*h*(h + 1)**4
Factor 2/3*b**3 + 2/3*b + 4/3*b**2 + 0.
2*b*(b + 1)**2/3
Let a = 1957/4 + -489. Let y(h) be the third derivative of 0 + 0*h**3 + 1/4*h**5 + 0*h + a*h**4 - 3*h**2. Factor y(d).
3*d*(5*d + 2)
Let y(f) be the second derivative of f**5/120 + f**4/12 - 8*f**2/3 + 3*f - 20. Solve y(v) = 0 for v.
-4, 2
Let y(v) be the first derivative of -3*v**4/4 - 20*v**3/3 - 6*v**2 - 20. Factor y(u).
-u*(u + 6)*(3*u + 2)
Factor 15*g**4 + 16*g**4 + 28*g**2 - 10*g**4 - 49*g**4 + 8*g - 8*g**3.
-4*g*(g - 1)*(g + 1)*(7*g + 2)
Let o(t) be the first derivative of 2*t**5/105 - 5*t**4/42 + 4*t**3/21 + 60. Factor o(a).
2*a**2*(a - 3)*(a - 2)/21
Suppose 2/11*s**3 + 0*s**2 + 2/11*s**4 + 0 + 0*s = 0. What is s?
-1, 0
Factor 2/7*u**3 - 32/7 - 18/7*u**2 + 48/7*u.
2*(u - 4)**2*(u - 1)/7
Let p(w) be the second derivative of 1/210*w**7 + 1/3*w**4 - 19/30*w**3 - 1/75*w**6 + 0 + 3/5*w**2 - 3/50*w**5 - 13*w. Factor p(a).
(a - 2)*(a - 1)**3*(a + 3)/5
Let k(r) be the first derivative of -r**6/45 - 8*r**5/75 + r**4/30 + 8*r**3/45 - 20. Find v such that k(v) = 0.
-4, -1, 0, 1
Let l be 0/(2/8*4). Determine c so that -8*c**2 + 20 + 13*c**2 + l*c**2 + 20*c = 0.
-2
Let -2*b**3 + 2*b**2 + 0*b**2 - 6*b + 2*b - 8 + 3*b**3 = 0. What is b?
-2, 2
Let i be (-2968)/(-212) + 32/(-3). Solve -m**2 - 1 + i*m = 0 for m.
1/3, 3
Let q be (-141)/940*(30/4)/(-3). Let 3/8*a**4 + 0 - q*a**2 - 3/8*a**3 + 3/8*a**5 + 0*a = 0. What is a?
-1, 0, 1
Find o such that 8 - 2/3*o**2 - 2/3*o = 0.
-4, 3
Suppose 0 = 6*m + 3 - 15. Suppose m*l - l**2 - 3*l**4 + 4*l**4 + 4*l**2 - 2*l**4 = 0. Calculate l.
-1, 0, 2
Let o(g) be the second derivative of 5/2*g**2 + 0 + 5/3*g**3 + 5/12*g**4 - 16*g. Factor o(i).
5*(i + 1)**2
Let -1/2*q**3 - 3/2*q - 5/2*q**2 + 9/2 = 0. Calculate q.
-3, 1
Let d(l) be the third derivative of 5*l**8/336 - 5*l**7/42 - 17*l**6/24 + 49*l**5/12 + 100*l**4/3 + 250*l**3/3 + l**2 - 144. Solve d(n) = 0.
-2, -1, 5
Let b(u) be the third derivative of u**7/840 - 13*u**6/240 - 17*u**5/48 - 29*u**4/48 + 11*u**2 + 6. Find j such that b(j) = 0.
-2, -1, 0, 29
Let y be ((-39)/(-27) - 4/(-18))*57. Factor 12*n**4 - 17*n + y*n - 52*n**3 + 54*n + 72 - 4*n**2.
4*(n - 3)**2*(n + 1)*(3*n + 2)
Factor j**3 + j**3 - 24 + 221*j**2 - 239*j**2 - 5*j**3 - 36*j.
-3*(j + 2)**3
Let g be 56 - 49 - 68/10. Determine v so that 2/5 + 4/5*v**2 - g*v**3 - v = 0.
1, 2
Let q(r) be the second derivative of 16*r + 2*r**4 - 1/5*r**5 - 8*r**3 + 16*r**2 + 0. Factor q(c).
-4*(c - 2)**3
Let l(m) be the first derivative of m**6/720 - m**5/48 - m**4/8 - 19*m**3/3 + 24. Let a(h) be the third derivative of l(h). Factor a(j).
(j - 6)*(j + 1)/2
Suppose 2*o = -0*o - 3*o. Let f = -6 - -8. Factor 6/7*y + 3/7*y**f - 3/7*y**3 + o.
-3*y*(y - 2)*(y + 1)/7
Let s(u) be the second derivative of -u**4/3 - 8*u**3/3 + 42*u**2 + 162*u - 2. Factor s(t).
-4*(t - 3)*(t + 7)
Let x(f) = f**5 - f**2. Let b(j) = 7*j**5 + 37*j**4 + 89*j**3 + 73*j**2 + 18*j. Let m(o) = -b(o) + 2*x(o). Determine i, given that m(i) = 0.
-3, -1, -2/5, 0
Let b(k) be the first derivative of 2*k**3/3 - 10*k**2 + 32*k - 7. Factor b(a).
2*(a - 8)*(a - 2)
Let w(j) = -5*j**2 + 29*j + 26. Let x(p) = 5*p**2 - 30*p - 25. Let k(v) = -5*w(v) - 4*x(v). Find t, given that k(t) = 0.
-1, 6
Let k be (5 - (-1 - -5))/((-1)/4). Let j be 26/8 + 1/k. Suppose 0 + 0*i - 3/4*i**2 - 3/4*i**4 + 3/2*i**j = 0. What is i?
0, 1
Let k(o) = -7*o**5 - 11*o**4 - 20*o**3 + 36*o**2 + 92*o + 44. Let f(m) = m**5 - m**4 + 2*m**3 + 3*m**2 + m + 1. Let h(s) = 4*f(s) + k(s). Factor h(y).
-3*(y - 2)*(y + 1)*(y + 2)**3
Let c be (-4 + 156/40)*3212 - -2. Let g = -318 - c. Factor -2/5*t**2 + g*t - 4/5.
-2*(t - 2)*(t - 1)/5
Let q be 23 - ((-69069)/92)/(-33). Factor 3/4*f - q*f**2 + 0.
-f*(f - 3)/4
Let z(u) = -