4 - 1 - 4*r**2. Find i, given that q(i) = 0.
1, 2
Suppose 5*p = -18 + 28. Factor -614*f**2 + 0*f**4 + f**4 + 613*f**p.
f**2*(f - 1)*(f + 1)
Suppose -3*v = 2*r + 9, 2*v = -0*r - 2*r - 6. Let u = 1/5 - 4/45. Factor -u*y + r - 1/9*y**2.
-y*(y + 1)/9
Let l(y) be the second derivative of y**7/4725 - y**6/450 + y**5/100 + 7*y**4/6 - 5*y. Let z(n) be the third derivative of l(n). Factor z(a).
2*(2*a - 3)**2/15
Let u(p) be the first derivative of p**5/12 - 5*p**4/4 + 25*p**3/6 + 7*p**2 - 18. Let m(r) be the second derivative of u(r). Factor m(w).
5*(w - 5)*(w - 1)
Let g = 23 - 20. Let r be 1 - (32/(-14) + g). Find k such that -1/7*k**2 + r*k + 0 = 0.
0, 2
Suppose 13*y - 123 + 123 = 0. Determine l, given that -1/6*l**3 + 0 - 1/6*l**2 + y*l = 0.
-1, 0
Let 48*m + 77*m**2 + 34*m**3 + 42*m**4 - 74*m**3 - 9*m**5 + 32 - 125*m**2 = 0. Calculate m.
-2/3, 2
Let p be -4 + (8 - 2 - 0). Let f = -1/104 + 835/312. Factor -4/3*g - f*g**p + 0 - 4/3*g**3.
-4*g*(g + 1)**2/3
Let q(d) be the second derivative of 0 + 2*d**2 + 1/3*d**4 + 14*d - 4/3*d**3. Factor q(a).
4*(a - 1)**2
Let j(k) be the first derivative of -k**3/18 + 8*k/3 + 143. What is a in j(a) = 0?
-4, 4
Let u(g) be the third derivative of g**5/180 - 5*g**4/36 + 25*g**3/18 + 68*g**2. Factor u(l).
(l - 5)**2/3
Let g be (1*(-6)/14)/(-1). Let x = -356 + 2507/7. Factor x*k + g*k**3 + 12/7*k**2 + 6/7.
3*(k + 1)**2*(k + 2)/7
Let j = -7/3197 - -6429/15985. Find r, given that 0 + 16/5*r - j*r**4 + 12/5*r**3 - 24/5*r**2 = 0.
0, 2
Let r(v) = 23*v - 13. Let i be r(-4). Let u be (-70)/i + (-5)/12. Factor -1/2*c**2 + 0 + 0*c + 1/4*c**3 + u*c**4.
c**2*(c - 1)*(c + 2)/4
Let n(f) be the third derivative of f**6/120 - f**5/15 + f**4/12 - 4*f**2. Let s be n(4). What is w in -8*w**3 - 5*w - w**3 + s*w**2 + 3*w**3 + 3*w = 0?
0, 1/3, 1
Let k be 0*((-3)/6)/((-24)/16). Let l(a) be the first derivative of 3*a**2 + 8 + 0*a - 3/5*a**5 + k*a**4 + 3*a**3. Suppose l(n) = 0. What is n?
-1, 0, 2
Let r be (-9705)/40 + -4 + 1. Let o = 246 + r. Factor 9/8*g - 9/8*g**2 - o + 3/8*g**3.
3*(g - 1)**3/8
Let l(b) be the second derivative of b**5/15 - 7*b**4/9 + 237*b. Suppose l(d) = 0. What is d?
0, 7
Solve 3042/11*j + 2/11*j**3 + 0 + 156/11*j**2 = 0 for j.
-39, 0
Let t(h) be the second derivative of -h**6/150 + 29*h**5/50 - 781*h**4/60 - 58*h**3 - 90*h**2 - 547*h. Factor t(x).
-(x - 30)**2*(x + 1)**2/5
Suppose -2*s - 288 = -4*j + 3*s, j - 3*s = 72. Let m be 2 + (j/(-64))/((-3)/(-4)). Find w such that 7/4*w - 1/2*w**2 - 7/4*w**3 + m = 0.
-1, -2/7, 1
Let i(x) be the second derivative of x**7/84 - x**6/10 + x**5/10 + x**4/4 - 5*x**3/12 + 312*x - 1. Factor i(m).
m*(m - 5)*(m - 1)**2*(m + 1)/2
Suppose -3*j = -4*j - 11. Let h(u) = -u - 8. Let q be h(j). Factor 3*s**3 + s**2 - 4*s**2 - 1 - q*s + 4.
3*(s - 1)**2*(s + 1)
Let n = -36 - -38. Let q(g) be the third derivative of -2/3*g**3 - 2/15*g**5 + 1/60*g**6 + 5/12*g**4 - 2*g**n + 0 + 0*g. Let q(r) = 0. Calculate r.
1, 2
Let d(b) be the first derivative of -b**6/6 + b**5 + 3*b**4/4 - 13*b**3/3 - 5*b**2 - 504. Solve d(u) = 0 for u.
-1, 0, 2, 5
Let c(f) be the third derivative of 9/8*f**4 + 0*f - f**3 + 6*f**2 - 7/20*f**5 + 0. Let c(y) = 0. Calculate y.
2/7, 1
Let o(s) = -10*s**2 - 11*s + 2. Let k(r) = 7*r**2 + 7*r - 1. Let h(p) = -7*k(p) - 5*o(p). Let u(a) = a**2 + a. Let v(q) = h(q) - 2*u(q). Factor v(j).
-(j - 3)*(j - 1)
Let i(x) be the first derivative of -3*x**4/2 + 3*x**3 - 3*x + 90. Let i(j) = 0. What is j?
-1/2, 1
Factor 3/8*w**3 - 15/8*w**2 + 0 + 0*w.
3*w**2*(w - 5)/8
Let o = -11407 + 11407. Solve 8/9 - 2/9*w**2 + o*w = 0 for w.
-2, 2
Determine f, given that 10*f - 51*f**2 + 5*f**4 + 98*f**2 - 52*f**2 - f**3 - 9*f**3 = 0.
-1, 0, 1, 2
Let s(a) be the first derivative of 2*a**5/65 - 7*a**4/26 - 8*a**3/13 + 176*a**2/13 - 640*a/13 - 23. Factor s(p).
2*(p - 4)**3*(p + 5)/13
Let w(j) = 2*j**2 - 2*j - 1. Let f(h) = -2 + 3 + 1 - 5*h**2 + 4*h. Let b(y) = 3*f(y) + 7*w(y). Factor b(z).
-(z + 1)**2
Let m(f) be the second derivative of f**5/5 + 14*f**4/3 + 38*f**3 + 144*f**2 + 2*f. Suppose m(n) = 0. What is n?
-8, -3
Suppose p = 928 - 924. Let z(m) be the first derivative of 15/2*m**p - 5 - 3*m - 10*m**3 + 1/2*m**6 + 15/2*m**2 - 3*m**5. Let z(w) = 0. Calculate w.
1
Let z(t) = 2*t**5 + 4*t**4 - 5*t**2 + 5*t - 3. Let s(n) = 0 + n**4 + 3 - 6 + n**5 + 2 + n - n**3. Let c(v) = -3*s(v) + z(v). Factor c(j).
-j*(j - 1)**3*(j + 2)
Let s(g) be the first derivative of -g**4/30 + 8*g**3/15 - 29*g**2/15 + 12*g/5 + 639. Factor s(j).
-2*(j - 9)*(j - 2)*(j - 1)/15
Let v(u) be the third derivative of 1/24*u**6 + 5/6*u**3 + 0 + 0*u + 5/8*u**4 + 1/4*u**5 + 5*u**2. Factor v(w).
5*(w + 1)**3
Let w(p) be the first derivative of -p**4 + 32*p**3 - 42*p**2 - 184*p + 179. Suppose w(d) = 0. Calculate d.
-1, 2, 23
Let r(z) be the first derivative of 13*z**4/10 + 76*z**3/15 + 37*z**2/5 + 24*z/5 + 811. Find w such that r(w) = 0.
-1, -12/13
Let q(a) be the third derivative of -a**7/1008 + a**6/720 + a**5/360 + 5*a**3/2 - 5*a**2. Let m(o) be the first derivative of q(o). Solve m(k) = 0 for k.
-2/5, 0, 1
Let 16/5 - 12/5*q + 2/5*q**2 = 0. Calculate q.
2, 4
Suppose 3*l - 4*j = -7 + 4, -3*j + 21 = 4*l. Factor -7318 + 108*g**l + 8748*g - 3*g**4 + 6191 - 1458*g**2 - 18556.
-3*(g - 9)**4
Let h(s) be the first derivative of s**5/20 - 3*s**4/16 + s**3/12 + 3*s**2/8 - s/2 - 51. Factor h(u).
(u - 2)*(u - 1)**2*(u + 1)/4
Let c(p) be the second derivative of -20*p**3 + 0 + 75/4*p**4 - 35*p + 10*p**2 - 25/4*p**5. Factor c(g).
-5*(g - 1)*(5*g - 2)**2
Factor 131426*k**2 - 131430*k**2 + 8 - 1 + 6*k**3 - 6*k - k**4 - 2.
-(k - 5)*(k - 1)**2*(k + 1)
Let i(x) = -86*x - 1290. Let m be i(-15). Factor -3/7*k + 6/7*k**2 + 9/7*k**3 + m.
3*k*(k + 1)*(3*k - 1)/7
Let k be -1*(9/(-6))/(2/52). Let m = k + -37. Factor -14/5*a**m + 24/5*a + 8/5.
-2*(a - 2)*(7*a + 2)/5
Let p be 33 - ((-2)/(-3))/(4/(-18)). Let s be (-11)/(-5)*45/p. Factor 7/4*d + 1/2 - s*d**2 - 7/4*d**3 + 9/4*d**4.
(d - 1)**2*(d + 1)*(9*d + 2)/4
Suppose -w = -2*w + 5*g - 21, 4*g - 16 = w. Solve -146*n**w - 2*n**3 - 12*n**5 - 7*n**3 + n**3 - 8 + 30*n**2 + 112*n**4 + 8*n = 0.
-2, -1, 1/2, 2/3
Find a such that -453*a**2 - 60*a - 36 + 140 + 457*a**2 = 0.
2, 13
Let i(a) be the second derivative of -a**5/30 + 25*a**4/18 - 50*a**3/3 + 26*a - 8. What is x in i(x) = 0?
0, 10, 15
Suppose -r + 39*k - 2 = 37*k, -r + 5*k - 8 = 0. Solve 1/2 - 6*s + 18*s**r = 0.
1/6
Let q(k) be the second derivative of -k**8/3360 + k**7/180 - 11*k**6/360 + k**5/12 - 17*k**4/6 - 3*k + 1. Let c(u) be the third derivative of q(u). Factor c(m).
-2*(m - 5)*(m - 1)**2
Let z(l) be the second derivative of l**5/100 - l**4/20 + l**3/10 - 10*l**2 - 11*l. Let g(t) be the first derivative of z(t). Factor g(o).
3*(o - 1)**2/5
Solve -102*s**4 + 99*s**4 - 192 + 7*s**2 + 29*s**2 - 96*s + 12*s**3 = 0.
-2, 4
Let a(m) = m**2 - 3*m - 1. Let c(j) = -12*j**2 + 4*j - 8. Let q(h) = 8*a(h) + c(h). Factor q(x).
-4*(x + 1)*(x + 4)
Let p(s) be the second derivative of -3*s**5/100 + s**4/12 + 2*s**3/15 - 2*s**2/5 - 6*s - 8. Factor p(y).
-(y - 2)*(y + 1)*(3*y - 2)/5
Suppose 4*x = -x + 10. Suppose -5*r - 9 = 2*i + i, -1 = 4*i + 3*r. Suppose 0*d**3 - 3 - d**3 + 4 + 3*d**i - d - x*d = 0. What is d?
1
Let n(f) be the second derivative of f**5/60 - f**4/24 - f**3/3 - 9*f**2/2 - 23*f. Let g(p) be the first derivative of n(p). What is o in g(o) = 0?
-1, 2
Suppose 2*v = -2*j + 12, 4*j - 23 = v - 9. Suppose -5*p + j*p = -25. Suppose -30*d**2 - 4*d**3 - d**4 + 2*d + 8*d**3 + p*d**2 = 0. Calculate d.
0, 1, 2
Let p = -7663/16 - -479. Let l(r) be the third derivative of -1/20*r**6 - 1/56*r**7 + 0*r**3 - 3*r**2 + 0 + 0*r + p*r**4 - 1/80*r**5. Let l(b) = 0. What is b?
-1, 0, 2/5
Let j(z) be the first derivative of -5*z**4/4 + 10*z**3/3 - 40. Factor j(c).
-5*c**2*(c - 2)
Let c(g) be the second derivative of -5*g**7/42 + 3*g**5/4 - 5*g**4/6 - 18*g - 4. Factor c(l).
-5*l**2*(l - 1)**2*(l + 2)
Factor -128 + 20*b - 43*b + 4*b**3 - 7*b**4 + 24*b**2 - 41*b + 5*b**4 + 4*b**3.
-2*(b - 4)**2*(b + 2)**2
Let o be (277/8)/(63/(-66) + 1). Let w = o - 758. Let -3*j**3 + 0 + w*j**2 - 3/4*j = 0. What is j?
0, 1/4, 1
Let l = 104731/2 + -52364. Factor 0*p**3 + l*p**4 + 12*p - 9*p**2 - 9/2.
3*(p - 1)**3*(p + 3)/2
Find u such that 1/5*u**2 - 24/5*u - 5 = 0.
-1, 25
Factor -1076*m**2 - 1074*m**2 - 72 + 215