r 3*f + p*f**2 + 139*f**3 + 0*f**2 - 2*f - 143*f**3.
-f*(f - 1)*(4*f + 1)
Let z be ((-30)/(-40))/(1/4). Let f(n) be the first derivative of -7/5*n**5 + 0*n + 1/2*n**4 - 2 + 7/3*n**z - n**2. Factor f(t).
-t*(t - 1)*(t + 1)*(7*t - 2)
Let t be (9/6 + -1)/((-14)/(-28)). Let g be 60/75*((-10)/(-4))/t. Factor 3*x**g + 12/5*x - 3/5.
3*(x + 1)*(5*x - 1)/5
Let p(s) be the third derivative of s**7/16380 + 3*s**4/8 - 2*s**2. Let v(a) be the second derivative of p(a). Solve v(b) = 0 for b.
0
Let h(n) be the second derivative of n**7/21 + 6*n**6/5 + 109*n**5/10 + 42*n**4 + 196*n**3/3 - 51*n. Factor h(w).
2*w*(w + 2)**2*(w + 7)**2
Let z(k) be the third derivative of k**7/105 + 34*k**6/15 + 1156*k**5/5 + 39304*k**4/3 + 1336336*k**3/3 - k**2 - 45*k. Let z(q) = 0. What is q?
-34
Suppose 50*l - 3*x = 48*l + 15, 0 = -3*l + 3*x + 15. Factor 1/6*z**3 - 1/6*z**5 + 0 + 1/6*z**4 + l*z - 1/6*z**2.
-z**2*(z - 1)**2*(z + 1)/6
Let a(c) be the third derivative of 0*c**4 + 0*c + 0 + 0*c**3 + 1/60*c**5 - 9*c**2. Factor a(q).
q**2
Let -10*h**4 - h**5 + 63*h**2 - 23*h**2 - 28*h + 48*h - 4*h**5 + 15*h**3 = 0. What is h?
-2, -1, 0, 2
Let r(q) be the third derivative of q**5/15 - 2*q**3/3 + 17*q**2. Let r(y) = 0. Calculate y.
-1, 1
Let t be 3*((-57)/(-9) - 6). Let o be t - 3/(-78)*-22. Let 6/13*b**2 + o*b + 6/13*b**3 + 2/13*b**4 + 0 = 0. What is b?
-1, 0
Let c = 113 + -109. Let l be c/((-42)/(-8)*(-8)/(-12)). Factor -l*x**2 - 18/7*x - 4/7.
-2*(x + 2)*(4*x + 1)/7
Let l be (-6)/(-1) - 6/3. Let d = 4 + -2. Factor 2/3 + 1/6*o**l - d*o - o**3 + 13/6*o**2.
(o - 2)**2*(o - 1)**2/6
Let w(t) be the first derivative of 10*t**3/21 + 92*t**2/7 + 72*t/7 + 88. Factor w(r).
2*(r + 18)*(5*r + 2)/7
Let l(w) be the third derivative of w**7/420 - w**6/48 + w**5/15 - w**4/12 + 22*w**2 + 3. Find a such that l(a) = 0.
0, 1, 2
Let b be (8/(-10))/(((-8)/(-20))/(-1)). Factor 8/3*x**b - 2/3*x + 0.
2*x*(4*x - 1)/3
Find b such that -24 + 49*b**3 - 7*b**3 - 865*b**2 + 880*b**2 - 24*b + 9*b**4 - 18*b = 0.
-4, -1, -2/3, 1
Let o(m) be the third derivative of 0 - 1/350*m**7 + 0*m - 97/100*m**5 - 32/5*m**3 - 10*m**2 - 18/5*m**4 - 9/100*m**6. Solve o(k) = 0.
-8, -1
Let h(q) be the second derivative of 18*q - 1/50*q**5 + 0 + 16/5*q**2 + 3/10*q**4 - 8/5*q**3. Solve h(g) = 0.
1, 4
Suppose -2*z + 2*r + 100 - 14 = 0, -z - 5*r = -37. Suppose 0 = -15*f - 12 + z. Factor -q + 3/2 - 1/2*q**f.
-(q - 1)*(q + 3)/2
Suppose 0*s - 27 = -3*s. Solve -s*f - 5*f**2 + 29*f - 7 - 13 = 0 for f.
2
Let g(u) be the first derivative of -u**5/50 + 8*u - 29. Let t(m) be the first derivative of g(m). Find q, given that t(q) = 0.
0
Let k = -602053/17 - -35415. Solve 2/17*y**2 - 12/17 + k*y = 0 for y.
-3, 2
Suppose 36*j - 9*j - 81 = 0. Let s(c) be the first derivative of -11 + 9/2*c**2 + 3/4*c**4 - 3*c**j - 3*c. Let s(d) = 0. Calculate d.
1
Let t(x) be the third derivative of -x**7/315 + 7*x**6/540 - x**4/27 - 5*x**2 - 17*x. What is s in t(s) = 0?
-2/3, 0, 1, 2
Factor 6/5*w - 4/5 + 3/5*w**4 - 1/10*w**5 - 11/10*w**3 + 1/5*w**2.
-(w - 2)**3*(w - 1)*(w + 1)/10
Suppose -h = h - 8. Suppose -2*u + 0 = -h. Factor -6*m**4 - m**5 + 6*m**2 - 9*m**3 + 8*m + 6*m**u + 4*m + 4*m**5.
3*m*(m - 2)**2*(m + 1)**2
Suppose 0 = 2*r - 4*t - 30, -r - 2*t - 35 = -26. Factor -16/3*q + r*q**2 - 4/3.
(q - 2)*(9*q + 2)/3
Suppose 2*g = 11 - 3. Factor -19*v**4 + 9*v**3 - 102*v**g + 52*v**4 - 27*v**5 + 117*v**5.
3*v**3*(5*v - 3)*(6*v - 1)
Suppose 18*z + 13*z = 6*z. Let y(g) be the third derivative of 1/4*g**4 + 1/20*g**5 + 6*g**2 + z + 1/2*g**3 + 0*g. Determine h, given that y(h) = 0.
-1
Let y be ((-3575)/273 - -13) + (-50)/(-35). Factor y*g - 1 - 1/3*g**2.
-(g - 3)*(g - 1)/3
Let b be (-97 - -101) + (0 + -5)*-1. Let k be 2 - ((-63)/48)/(b/(-12)). Solve 1/4*j**5 + 1/4*j - 1/4*j**4 + 1/2*j**2 - 1/2*j**3 - k = 0.
-1, 1
Let d(l) be the second derivative of l**6/105 + 2*l**5/35 + l**4/14 - 4*l**3/21 - 4*l**2/7 + 24*l. Factor d(b).
2*(b - 1)*(b + 1)*(b + 2)**2/7
Let k be (0 - -4) + 105/(-54)*2. Let i(x) be the third derivative of 0 + 1/60*x**5 - k*x**3 - 4*x**2 + 0*x + 1/72*x**4. Factor i(a).
(a + 1)*(3*a - 2)/3
Let m(c) be the first derivative of c**5 - 5*c**4 - 10*c**3 + 10*c**2 + 25*c + 75. Let m(i) = 0. Calculate i.
-1, 1, 5
Let o(m) be the second derivative of m**6/345 - m**5/46 - 14*m**4/69 + 32*m**3/69 - 2*m + 13. Factor o(x).
2*x*(x - 8)*(x - 1)*(x + 4)/23
Let f(q) = q**2 - 4*q**3 + 4*q + 13*q**2 - 6 - 2*q**2 - 6. Let v(h) = -4*h**3 + 12*h**2 + 4*h - 12. Let b(t) = -5*f(t) + 6*v(t). Find d, given that b(d) = 0.
-1, 1, 3
Factor -60 + 16/3*j**3 + 79/3*j**2 + 28*j + 1/3*j**4.
(j - 1)*(j + 5)*(j + 6)**2/3
Suppose -59*i = -41*i - 36. Determine j so that 2/5 - 1/5*j + 1/5*j**3 - 2/5*j**i = 0.
-1, 1, 2
Let w be (-5 + (13277/154)/17)*4. Suppose 0*c - 2/7*c**4 + 0 - w*c**2 + 4/7*c**3 = 0. What is c?
0, 1
Let l be (-166)/(-8)*(-8 - 96/(-8)). Suppose -5*b**2 - 39 + l + 10*b - 29 = 0. Calculate b.
-1, 3
What is h in 5*h + 5/3*h**3 + 50/3 - 10*h**2 = 0?
-1, 2, 5
Let j(h) be the third derivative of -h**5/100 - 13*h**4/40 + 3*h**3 + 3*h**2 - 26. Find l, given that j(l) = 0.
-15, 2
Let s(n) be the second derivative of n**6/15 + n**5/5 - 7*n**4/6 - 20*n**3/3 - 12*n**2 - n + 32. Factor s(o).
2*(o - 3)*(o + 1)*(o + 2)**2
Let j(r) be the second derivative of -7*r + 1/4*r**4 + 0 + 1/3*r**3 + 0*r**2. Let u(g) = 7*g**2 + 4*g. Let c(b) = -9*j(b) + 4*u(b). Factor c(y).
y*(y - 2)
Let q(b) be the third derivative of 1/420*b**7 + 1/672*b**8 - 1/3*b**3 + 1/6*b**4 + 2*b - 1/48*b**6 - 1/120*b**5 + 0 + 4*b**2. Factor q(x).
(x - 1)**3*(x + 2)**2/2
Let k(a) be the third derivative of a**6/24 - 5*a**5/12 - 5*a**4/4 - 177*a**2. Determine s, given that k(s) = 0.
-1, 0, 6
Let y(s) be the third derivative of 0*s + 0 + 2/3*s**3 - 42*s**2 - 1/120*s**6 + 1/12*s**5 - 1/3*s**4. Suppose y(r) = 0. What is r?
1, 2
Let g = 1 - 2. Let k be ((-6)/(-12))/(g/(-4)). Factor -6*h**3 + 2 + h**5 + 3*h - k*h**2 + 2*h**4 + 2*h**3 - 2*h**4.
(h - 2)*(h - 1)*(h + 1)**3
Suppose -2*i + 5*m - 21 = -0*m, -3*m = -15. Let q be -1*((-3)/i - -1). Factor 0*z**2 + 0*z**3 + 0*z + 0 + 1/2*z**5 - q*z**4.
z**4*(z - 1)/2
Let i(n) be the third derivative of -n**5/100 + 2*n**3/5 - 814*n**2. Determine k so that i(k) = 0.
-2, 2
Let z(w) = 9*w**3 + 21*w**2. Let m(r) = -15*r**2 - 8*r**3 + 4*r**2 - 9*r**2. Let v(y) = -6*m(y) - 5*z(y). Factor v(u).
3*u**2*(u + 5)
Let j(x) be the first derivative of x**4/30 - x**3/15 - 4*x + 10. Let s(b) be the first derivative of j(b). Factor s(z).
2*z*(z - 1)/5
Let y = 390536551/399 + -978787. Let z = y + -2/133. Find g, given that 2/3*g**4 + 8/3*g**3 + z*g + 10/3*g**2 + 0 = 0.
-2, -1, 0
Let g(h) be the third derivative of -5*h**2 - 1/30*h**6 + 5 + 0*h**7 + 1/168*h**8 + 0*h + 0*h**3 + 0*h**5 + 1/12*h**4. Determine p, given that g(p) = 0.
-1, 0, 1
Let w(l) = 9*l**2 - 6*l - 6. Let k(d) = -d**4 + d**3 + 27*d**2 - 17*d - 18. Let u(a) = -3*k(a) + 8*w(a). Determine v so that u(v) = 0.
-1, 1, 2
Suppose -3*y - 3 = 0, y - 9 = -3*r - 2*r. Let d(j) = -j**3 + 8*j**2 + 10*j - 8. Let w be d(9). Factor 3*f + 2*f**r + 5*f + 7 - w + 0*f.
2*(f + 1)*(f + 3)
Let j = -594 - -596. Let l(i) be the first derivative of 0*i - 8 - j*i**3 + 3/2*i**2 + 3/4*i**4. Factor l(y).
3*y*(y - 1)**2
Let y(l) be the third derivative of l**5/300 + 17*l**4/60 + 289*l**3/30 + 37*l**2. Factor y(g).
(g + 17)**2/5
Let a(c) be the first derivative of c**6/30 + 2*c**5/5 + 2*c**4 + 16*c**3/3 + 3*c**2 + 12. Let o(f) be the second derivative of a(f). Find q such that o(q) = 0.
-2
Let o(f) = -11*f**3 + 2*f**2 + 69*f - 84. Let b(a) = -2*a**3 + 3*a**2 + 1. Let i(w) = -6*b(w) + o(w). Suppose i(q) = 0. Calculate q.
3, 10
Factor -68/23*k - 2/23*k**2 - 578/23.
-2*(k + 17)**2/23
Suppose 0 = 140*v - 138*v - 10. Let x(r) be the third derivative of 0*r**4 + 0*r**7 - v*r**2 - 1/1176*r**8 + 0 + 0*r + 0*r**6 + 0*r**5 + 0*r**3. Factor x(a).
-2*a**5/7
Let f be (27/(-18))/(2/(-4)). Let c be 0 + 1*f/1 - 1. What is s in 1/3*s**c + s + 2/3 = 0?
-2, -1
Factor 9*k**3 + 11*k**2 + 15*k**2 + 70*k - 7*k**3 - 98 + 0*k**2.
2*(k - 1)*(k + 7)**2
Let p(s) = -13*s**2 + 10*s - 69. Let d(k) = -15*k**2 + 8*k - 71. Let f(z) = 6*d(z) - 7*p(z). Find u such that f(u) = 0.
3, 19
Let f = -45 + 17. Let u be (f/(-35))/(2/5). Factor -1 + c + 2*c - 5*c - c**u.
-(c + 1)**2
Let d(p) = -4*p**4 - 32*p**3 + 41*p**2 +