- 4/5*a.
4*a*(a - 1)*(a + 1)**2/5
Let l(g) be the first derivative of 0*g**3 + 1/720*g**6 + 0*g**5 + 7/2*g**2 - 1/144*g**4 + 0*g - 27. Let f(m) be the second derivative of l(m). Factor f(u).
u*(u - 1)*(u + 1)/6
Suppose -5*s + 30 = 4*v - 91, -5*v = -5*s - 185. Factor 15*y + v*y + 19*y + 280*y**3 + 32*y**4 - 12 - 232*y**3 - 120*y**2.
4*(y + 3)*(2*y - 1)**3
Let w(t) be the first derivative of -3*t**5/40 - 27*t**4/32 + 11*t**3/8 + 27*t**2/16 - 15*t/4 + 6402. Suppose w(v) = 0. What is v?
-10, -1, 1
Let s be (2793/524 + -1)*(-1368)/(-3705). Let w = s - -2/1703. Suppose 12/5*m**2 + 2/5*m**4 - 8/5*m + 2/5 - w*m**3 = 0. What is m?
1
Let d(z) be the first derivative of -5*z**4/16 + 191*z**3/12 - 5*z**2/2 - 171*z - 7039. Determine c so that d(c) = 0.
-9/5, 2, 38
Factor -1/6*g**3 - 9800/3 - 35/2*g + 9*g**2.
-(g - 35)**2*(g + 16)/6
Suppose j - 2*v + 2 = -3*j, 5*j - 15 = -v. Suppose 6*c - 10 = j. Factor c*m**5 + 2*m + 89*m**2 - 4*m**5 - 93*m**2 + 4*m**4.
-2*m*(m - 1)**3*(m + 1)
Let m(u) be the second derivative of u**4/48 - 415*u**3/24 + 4*u + 575. Factor m(k).
k*(k - 415)/4
Let n(k) be the first derivative of -4*k**5/5 - 55*k**4 + 1172*k**3/3 - 834*k**2 + 720*k - 1370. Find a, given that n(a) = 0.
-60, 1, 3
Let w = -95 - -119. Find u such that 27*u**3 - 11*u**3 - w*u**2 - 13*u**3 = 0.
0, 8
Let d(l) be the first derivative of l**4/9 + 13472*l**3/9 + 22686848*l**2/3 + 152818608128*l/9 - 6868. Find m such that d(m) = 0.
-3368
Let w(f) = 9*f**5 + 585*f**4 - 5973*f**3 + 5403*f**2 + 24. Let p(o) = -4*o**5 - 234*o**4 + 2389*o**3 - 2161*o**2 - 10. Let c(y) = 12*p(y) + 5*w(y). Factor c(i).
-3*i**2*(i - 19)**2*(i - 1)
Let t(d) be the third derivative of d**5/15 - 29*d**4/24 + 5*d**3 + 383*d**2. Let t(c) = 0. What is c?
5/4, 6
Let q(b) be the second derivative of b**4/9 - 52*b**3/3 + 1014*b**2 + 18*b + 79. Factor q(w).
4*(w - 39)**2/3
Let a(o) = -6*o**2 + 286*o - 8. Let q(g) = -10*g**2 + 571*g - 14. Let r(b) = 7*a(b) - 4*q(b). Factor r(k).
-2*k*(k + 141)
Let n(v) = 189*v - 2889. Let z(h) = -h**2 + 377*h - 5780. Let t(a) = -5*n(a) + 3*z(a). Let b(q) = -1. Let d(c) = 12*b(c) - t(c). Suppose d(w) = 0. What is w?
31
Let c be (-1302)/765*(3 - (3 - 3)). Let w = -80/17 - c. Solve 0 + 1/5*j**4 + 2/5*j - w*j**3 - 1/5*j**2 = 0 for j.
-1, 0, 1, 2
Suppose -343*b**3 - 20853*b + 340*b**3 + 18939*b - 963*b**2 = 0. Calculate b.
-319, -2, 0
Let z(j) be the second derivative of 0*j**2 - 33/140*j**5 + 5/98*j**7 + 105*j - 1/10*j**6 + 1/4*j**4 + 3/7*j**3 + 0. Solve z(v) = 0.
-1, -3/5, 0, 1, 2
Suppose -3*b - b + 4*t + 1008 = 0, 5*t - 532 = -2*b. Factor b*g**2 + 0 - 64*g - 260*g**2 + 0.
-4*g*(g + 16)
Let l(y) be the third derivative of -y**6/210 - 2*y**5/15 - 25*y**4/42 - 8*y**3/7 - 3*y**2 + 176. Factor l(h).
-4*(h + 1)**2*(h + 12)/7
Let y(m) be the second derivative of -11*m - 1/6*m**6 + 2*m**5 + 4 + 0*m**3 + 0*m**2 - 35/12*m**4. Determine x so that y(x) = 0.
0, 1, 7
Let c(a) be the third derivative of a**6/4 + 37*a**5/12 - 15*a**4/2 - 35*a**3/6 + a**2 + 1527. Solve c(m) = 0 for m.
-7, -1/6, 1
Let b(x) be the second derivative of 3*x**5/20 + 27*x**4/4 + 1395*x. Find k, given that b(k) = 0.
-27, 0
Let f(j) = 9*j + 34. Let i be f(-2). Factor 24*z**4 + z + i*z**2 + 41*z**2 + 3*z + 75*z**3 + 2*z.
3*z*(z + 1)*(z + 2)*(8*z + 1)
Solve -100*g**3 + 100*g - 405/4 - 5/4*g**4 + 205/2*g**2 = 0.
-81, -1, 1
Let f = -297 - -291. Let n be ((-260)/(-312))/((-10)/f). Suppose 0 - n*x**2 - 1/2*x = 0. Calculate x.
-1, 0
Suppose -3*j = 2*a + 3395, -4*a + j - 4770 = 2027. Let k = 3405/2 + a. Factor 3 - 3/2*i**2 + k*i.
-(i - 3)*(3*i + 2)/2
Factor -12 - 2/7*o**2 - 46/7*o.
-2*(o + 2)*(o + 21)/7
Let a(z) = -13*z**2 + 2*z + 4. Let j be a(0). Suppose -46*v + 66*v - 41 + v**j + 2*v**2 - 5*v**3 + 17 = 0. What is v?
-2, 2, 3
Let y(n) be the second derivative of 5/6*n**4 + 0*n**2 + 3*n + 7/20*n**5 + 1/30*n**6 + 0*n**3 + 5. Factor y(k).
k**2*(k + 2)*(k + 5)
Let p(s) be the second derivative of -s**5/70 + 15*s**4/7 + 13*s**3/3 - 18*s + 2. Determine n so that p(n) = 0.
-1, 0, 91
Suppose 0 = -25*p - 3*p + 280. Factor 16*n - 12*n**3 - 30*n**5 + 54*n**5 - 5*n**2 + p*n**4 - 26*n**5 - 3*n**2.
-2*n*(n - 2)**3*(n + 1)
Suppose -17*k + 116 = 12*k. Let j(z) be the second derivative of 0*z**2 - 5/12*z**3 + 1/24*z**k + 0 + 36*z. Determine m, given that j(m) = 0.
0, 5
Let v(s) = s**3 - 10*s**2 - 13*s + 25. Suppose -8*g = 12*g - 220. Let z be v(g). Determine c so that -c + 1/3*c**z - 2/3*c**2 + 0 = 0.
-1, 0, 3
Factor -512/3*q - 170 - 2/3*q**2.
-2*(q + 1)*(q + 255)/3
Solve -169/2 + 86/3*y - 1/6*y**2 = 0.
3, 169
Let t = -143924878 + 568503274029/3950. Let n = t - 2/1975. Suppose 0 - n*j + 3/2*j**2 = 0. What is j?
0, 1
Let -8*p - 11*p**2 - 120 + p**3 - 32*p + 72 + 0*p**3 - 2*p**3 = 0. Calculate p.
-4, -3
Determine k so that -78*k**3 + 5*k**4 + 6459 - 1437*k**2 + 3440*k + 6*k**4 + 4*k**4 - 1659 - 16*k**4 = 0.
-40, -1, 3
Let m = -3770569/4 + 942643. Find y, given that 21/4*y + 9/4 - 9/2*y**3 - m*y**5 + 3/2*y**2 - 15/4*y**4 = 0.
-3, -1, 1
Let r(b) be the first derivative of 28*b + 205*b**3 - 415*b**3 + 16*b**2 + 4*b**2 + 209*b**3 + 2. Factor r(u).
-(u - 14)*(3*u + 2)
Let o(i) = 6*i**2 - 1033*i - 1039. Let c(l) = l**2 - 172*l - 173. Let m(r) = -34*c(r) + 6*o(r). Determine f so that m(f) = 0.
-1, 176
Let z be (8448/(-10560))/(-1 + 4/5). Find g, given that -4/3*g**5 - 4*g**3 - 68/3*g**2 + 20/3*g**z + 112/3*g - 16 = 0.
-2, 1, 2, 3
Let o(r) = -4*r**2 - 389*r - 10000. Suppose -38*f - 375 = 461. Let y(q) = -q**2 - 97*q - 2500. Let p(m) = f*y(m) + 6*o(m). Factor p(w).
-2*(w + 50)**2
Let h(v) be the second derivative of 2*v**7/49 - 13*v**6/105 + v**5/35 + 2*v**4/7 - 8*v**3/21 + v**2/7 + 1884*v. Find c such that h(c) = 0.
-1, 1/6, 1
Let d = -15705 + 125643/8. Let j(x) be the first derivative of 3/2*x**3 - 10 + 9/4*x**2 + 3/2*x + d*x**4. Solve j(s) = 0.
-1
Suppose -5*f + 3*n - 29 = 0, -5*n + 23 = 6*f - 8*f. Let a be f*(8/(-24))/((-24)/(-27)). Let 3/2*p - a*p**2 - 1/2 + 1/2*p**3 = 0. What is p?
1
Let y be 0/(((-289)/(-51))/(-17) - 5/3). Let r(q) be the third derivative of 2/9*q**4 + 1/135*q**5 - 27*q**2 + 8/3*q**3 + 0 + y*q. Factor r(c).
4*(c + 6)**2/9
Let k be (-1173)/(-69) + (-34)/2. Let y(x) be the third derivative of 0 + 1/18*x**3 + 5*x**2 - 1/360*x**5 + 1/144*x**4 + k*x. Factor y(c).
-(c - 2)*(c + 1)/6
Suppose 13*n = -3*o + 8*n - 24, -20 = 5*o + 5*n. Solve -1/7*w**o - 11/7 - 12/7*w = 0 for w.
-11, -1
Factor -21*b + 214012*b**2 - 372*b**3 - 215563*b**2 + 3*b**4 + 993*b + 948*b.
3*b*(b - 128)*(b - 1)*(b + 5)
Let s(c) = 27 + 3*c - 2*c - 3*c + 7*c. Let x be s(-5). Suppose -23*t**2 + 49*t**2 + 8*t**5 + 10*t**3 - 28*t**x - 16*t**4 = 0. Calculate t.
0, 1/2, 1
Let h be (-47)/(-117) + -1*5*(-32)/1040. Let p(j) be the first derivative of 20 - h*j**3 + 10*j - 5/6*j**2. Factor p(l).
-5*(l - 2)*(l + 3)/3
Let j(d) = -5*d**4 - 29*d**3 + 100*d**2 - 4*d - 20. Let b(o) = 14*o**4 + 87*o**3 - 299*o**2 + 11*o + 55. Let x(c) = -4*b(c) - 11*j(c). Factor x(t).
-t**2*(t - 3)*(t + 32)
Let p(h) be the second derivative of 0*h**4 + 1/110*h**5 - 8*h + 0 + 0*h**2 - 1/231*h**7 + 0*h**6 + 0*h**3. Factor p(t).
-2*t**3*(t - 1)*(t + 1)/11
Suppose 0 = 12*x - 6 - 30. Let f(m) = m**3 + m + 1. Let h(j) = 9*j**3 - 156*j**2 - 168*j - 45. Let u(c) = x*f(c) + h(c). Solve u(v) = 0 for v.
-1/2, 14
Let h = 1797/1238 + 30/619. Let t(o) be the first derivative of 39/10*o**5 + h*o**2 - 9*o**4 + 0*o - 17 + 9/2*o**3. Factor t(x).
3*x*(x - 1)**2*(13*x + 2)/2
Let x(c) = c**2 + 3*c + 1. Let a(p) = -2*p**3 + 109*p**2 + 33*p + 11. Let h(n) = a(n) - 11*x(n). Factor h(q).
-2*q**2*(q - 49)
Let l(p) = -74*p + 3194. Let s be l(43). Let q(c) be the second derivative of 1/3*c**4 + 10/3*c**3 + 0 - s*c**2 - 21*c. Factor q(x).
4*(x - 1)*(x + 6)
Let c(k) = -64*k**4 - 183*k**3 - 9406*k**2 - 18240*k - 9025. Let j(a) = -7*a**4 + a**3. Let y(n) = c(n) - 9*j(n). Factor y(b).
-(b + 1)**2*(b + 95)**2
Let g = -5280 + 5282. Let l(o) be the second derivative of 0*o**4 + 3/8*o**3 + 3*o - 3/80*o**5 + 3/4*o**g + 0. Factor l(v).
-3*(v - 2)*(v + 1)**2/4
Let c be 32/28*(-98)/(-49). Let m(u) be the first derivative of -1/7*u**4 - 21 + c*u**3 + 256/7*u - 96/7*u**2. Factor m(z).
-4*(z - 4)**3/7
Let q(t) be the third derivative of 119*t - t**2 + 0 + 5/84*t**4 - 1/210*t**5 - 2/7*t**3. Solve q(u) = 0 for u.
2, 3
Let r(m) = -3*m**4 + 