t s be o(5). Factor -3 + 1/2*r + g*r**s.
(r - 2)*(r + 3)/2
Let l(d) be the first derivative of 2*d**3/11 - 273*d**2/11 - 552*d/11 - 793. Determine p, given that l(p) = 0.
-1, 92
Determine i, given that -83/4 - 753/4*i**2 + 9/4*i**3 + 499/4*i = 0.
1/3, 83
Let p(v) = -28*v**2 - 103*v - 13. Let c(b) = -72*b**2 - 308*b - 37. Let a(i) = 4*c(i) - 11*p(i). Find n such that a(n) = 0.
-1/20, 5
Factor 2*g**4 + 80*g**3 + 3317*g + 13*g**4 - 2*g**5 - 832*g**2 - 1013*g - 9*g**4 + 6*g**4 - 2048.
-2*(g - 4)**3*(g - 2)*(g + 8)
Let o be (887 - 862) + -1 + 1 + -22. Factor 4/7*h**o + 0*h**4 - 2/7*h**5 - 2/7*h + 0*h**2 + 0.
-2*h*(h - 1)**2*(h + 1)**2/7
Let a(s) be the first derivative of -2*s**3/3 + 57*s**2 + 116*s + 2513. Let a(c) = 0. What is c?
-1, 58
Let g(n) be the first derivative of -4*n**3/3 - 508*n**2 - 64516*n - 1008. Determine i so that g(i) = 0.
-127
Let b be 28/(-1*4) + 49651/6055. Let -4/5*i - 2/5*i**3 + 0 + b*i**2 = 0. What is i?
0, 1, 2
Let f be -1 - (-1 + (6/6 - 721)). Let a = 723 - f. Find i such that 6/7*i**2 - 3/7*i + 3/7*i**5 + 0 - 6/7*i**4 + 0*i**a = 0.
-1, 0, 1
Factor 225/2*g**2 + 222*g - 6.
3*(g + 2)*(75*g - 2)/2
Let j be 3 + (-235)/75 - 3/((-9135)/2146). Determine m so that -2/7 - j*m - 2/7*m**2 = 0.
-1
Factor 2/11*h**2 + 3553778/11 - 5332/11*h.
2*(h - 1333)**2/11
Let h(n) be the second derivative of n**5/200 + 5*n**4/12 - 26*n**3/15 - 517*n. Factor h(t).
t*(t - 2)*(t + 52)/10
Let t(p) be the first derivative of p**4 + 112*p**3/3 + 490*p**2 + 2744*p - 772. Factor t(w).
4*(w + 7)**2*(w + 14)
Let a(z) be the second derivative of -z**6/240 - z**5/24 - z**4/12 - 129*z**2/2 + 88*z. Let u(s) be the first derivative of a(s). Factor u(i).
-i*(i + 1)*(i + 4)/2
Let f = -1377574 - -1377576. Determine r, given that 30 + 8/3*r - 2/3*r**f = 0.
-5, 9
Find r, given that -17/3*r**3 + 35/6*r - 1/6*r**5 - 11/3 + 7/3*r**4 + 4/3*r**2 = 0.
-1, 1, 2, 11
Determine s so that -152/5*s**3 - 140 - 384/5*s**2 + 248*s - 4/5*s**4 = 0.
-35, -5, 1
Factor -1/4*z**3 + 5/2*z**2 - 35/2 - 11/4*z.
-(z - 7)*(z - 5)*(z + 2)/4
Let s(q) be the first derivative of 2/3*q**3 + 0*q + 40 + 51*q**2. Solve s(a) = 0.
-51, 0
Let v(j) be the second derivative of 3*j**5/20 + 39*j**4/2 - 522*j**3 + 4860*j**2 - 51*j - 24. Factor v(p).
3*(p - 6)**2*(p + 90)
Find n such that -12399/2*n + 8259/2*n**2 + 2067 + 3*n**3 = 0.
-1378, 1/2, 1
Let v(g) be the second derivative of g**6/180 + g**5/30 - 2*g**4/3 - 62*g**3/3 + 15*g + 1. Let p(k) be the second derivative of v(k). Factor p(b).
2*(b - 2)*(b + 4)
Let a(b) = -b**2 + 12*b + 7. Suppose 4*i - 24 = -2*j, 0*i = -j + 4*i + 12. Let q be a(j). Factor -98*c**4 + 94*c**4 - 4*c**2 + c**3 - q*c**3 - c**5 - c.
-c*(c + 1)**4
Let d = 527 - 525. Let u be (-345)/(-200) + 32/(-20). Factor -1/8*b**3 + 1/2*b**d + u*b - 1/2.
-(b - 4)*(b - 1)*(b + 1)/8
Let p(n) be the first derivative of 2*n**6 + 40*n**5 + 799*n**4/4 - 289*n**3/3 + 744. Determine r, given that p(r) = 0.
-17/2, 0, 1/3
Suppose -4*s = -3*l + 17, -l = 1546*s - 1548*s - 7. Let -18/7 - 39/7*t - 24/7*t**2 - 3/7*t**l = 0. What is t?
-6, -1
Let v(i) be the third derivative of -i**7/420 + i**6/40 - 13*i**5/120 + i**4/4 - i**3/3 - 2*i**2 - 20*i. Solve v(y) = 0.
1, 2
Let m(t) be the first derivative of t**4/4 - 3*t**3 - 9*t**2/2 - 8*t + 8. Let y be m(10). Factor -3*u + 8*u**4 - 5*u + 3*u - 10*u**y - u + 6*u**3 + 2.
2*(u - 1)*(u + 1)**2*(4*u - 1)
Let s(j) be the first derivative of 13/12*j**4 - 100 + 11/6*j**2 - 11/3*j**3 + 5/3*j + 4/15*j**5. Let s(d) = 0. What is d?
-5, -1/4, 1
Factor 1098*z - 3*z**2 + 523*z + 796*z + 1656 - z**2 - 765*z.
-4*(z - 414)*(z + 1)
Let l(i) be the third derivative of -19/540*i**6 - 7/15*i**5 - 1/945*i**7 + 39 - 8*i**3 + 0*i - 3*i**4 - i**2. Factor l(j).
-2*(j + 1)*(j + 6)**3/9
Let z be (216/4536)/(12/112). Let s = -13 - -15. Let 2/9*g - z + 2/9*g**s = 0. What is g?
-2, 1
Let o be 3*2*(-8 - 102/(-12)). Let m(w) be the second derivative of 0*w**2 + 0*w**5 + 1/18*w**4 + 0 + 0*w**o - 15*w - 1/45*w**6. Let m(p) = 0. What is p?
-1, 0, 1
Let d be 156/(-832)*(4 - 448/42). Factor -5/2 + 23/4*k + d*k**2.
(k + 5)*(5*k - 2)/4
Let z = 898 - 1996. Let i = 1103 + z. Factor -3/4 + 9/4*j**i + 33/2*j**3 - 39/4*j**4 - 27/2*j**2 + 21/4*j.
3*(j - 1)**4*(3*j - 1)/4
Let g(t) be the first derivative of 0*t**4 + 2 + 0*t - 1/4*t**5 + 0*t**3 + 19/2*t**2 - 1/24*t**6. Let w(l) be the second derivative of g(l). Factor w(n).
-5*n**2*(n + 3)
Let g be 21*-4*(-6)/(-846). Let f = -37/141 - g. Find h, given that -f*h**4 + 14/3*h + 4*h**2 + 2/3*h**3 + 5/3 = 0.
-1, 5
Let p(g) = -50*g**3 - 299*g**2 + 2916*g + 157483. Let q(f) = 16*f**3 + 102*f**2 - 972*f - 52494. Let l(d) = -6*p(d) - 19*q(d). Let l(w) = 0. Calculate w.
-27, 18
Let t = 12 + -16. Let k(j) be the second derivative of -j**4/6 + 4*j**3/3 + j + 19. Let n(x) = x. Let q(o) = t*n(o) - k(o). Factor q(d).
2*d*(d - 6)
Let c(b) be the third derivative of -1/14*b**3 - 34*b**2 + 0*b**4 + 0*b + 1/140*b**5 + 0. Determine x so that c(x) = 0.
-1, 1
Let g(b) be the second derivative of 532257*b**5/20 + 14732*b**4 - 994*b**3 + 24*b**2 + 4827*b. Find u such that g(u) = 0.
-4/11, 2/127
Factor -264 + 125*o**3 + 1255*o - 72*o**3 - 58*o**3 - 620*o**2 - 366.
-5*(o - 1)**2*(o + 126)
Let p be (-3)/88*-28*15/(360/132). Factor 3/2 + 1/4*r + p*r**3 - 16*r**2.
(r - 3)*(3*r - 1)*(7*r + 2)/4
Determine l, given that -285/4*l - 573/8 + 3/8*l**2 = 0.
-1, 191
Let h(w) be the third derivative of -w**7/9240 - 13*w**6/3960 - 83*w**3/6 - 14*w**2. Let o(p) be the first derivative of h(p). Factor o(z).
-z**2*(z + 13)/11
Factor -3200608*p**3 - 2*p + 6*p - 24 + 3200612*p**3 + 16*p**2.
4*(p - 1)*(p + 2)*(p + 3)
Let x(q) be the first derivative of q**4/34 + 274*q**3/17 + 410*q**2/17 + 1216. Factor x(g).
2*g*(g + 1)*(g + 410)/17
Let c(h) be the third derivative of 0*h - 6 + 1/24*h**6 + 845/3*h**3 + 1105/24*h**4 + 7/3*h**5 - 17*h**2. Factor c(g).
5*(g + 2)*(g + 13)**2
Let 0*t + 16/5*t**2 - 22/15*t**4 + 2/15*t**5 - 28/15*t**3 + 0 = 0. What is t?
-2, 0, 1, 12
Suppose 57 = o + n, -295*o + 290*o - 4*n = -283. Solve -165/4*f**3 + 0 - 5/4*f**5 - 25/2*f**4 - 25*f - o*f**2 = 0 for f.
-5, -2, -1, 0
Let -96/13 - 2/13*b**4 + 42/13*b**2 - 12/13*b**3 + 68/13*b = 0. What is b?
-8, -2, 1, 3
Factor -10524*k**3 - 3*k**5 - 17684*k**3 + 576*k**4 - 7915*k**3 + 786432*k**2 - 4644*k**3 + 3903*k**3.
-3*k**2*(k - 64)**3
Let r(x) = -20 + 0 - 19*x - 10*x**2 + 11*x**3 + 10*x - 10*x**3. Let d be r(11). Factor -8/9*s**d + 0 - 2/3*s - 2/9*s**3.
-2*s*(s + 1)*(s + 3)/9
Let m = -5283/245 + 5577/245. Factor 2/5*v**4 - 48/5*v + 0 - 44/5*v**2 + m*v**3.
2*v*(v - 4)*(v + 1)*(v + 6)/5
Let s(b) be the first derivative of -5*b**4/4 + 95*b**3/3 - 155*b**2/2 - 255*b + 3410. Factor s(c).
-5*(c - 17)*(c - 3)*(c + 1)
Let k(n) be the third derivative of n**5/30 - 13*n**4/3 + 140*n**3 - 33*n**2 - 5. What is w in k(w) = 0?
10, 42
Suppose 7*n - 24 = -3*s, n - 56 = -4*s - 49. Let z(u) be the first derivative of -35/2*u**3 + 39/2*u**2 - 6*u + n - 147/16*u**4. Factor z(t).
-3*(t + 2)*(7*t - 2)**2/4
Let l(c) be the third derivative of -c**7/42 - 11*c**6/6 - 347*c**5/6 - 1925*c**4/2 - 18375*c**3/2 - 2465*c**2. Factor l(f).
-5*(f + 7)**2*(f + 15)**2
Let j(k) = k**3 + 7*k**2 - 9*k - 5. Let y be j(-8). Factor 13*b + b**4 + 48*b**2 - 59 - 19*b**3 + b + 5*b**y + 10.
(b - 7)**2*(b - 1)*(b + 1)
Let w = 220937/5 - 44187. Determine o, given that w*o**2 + 2/5*o**5 - 2/5*o**4 - 2/5*o**3 + 0 + 0*o = 0.
-1, 0, 1
Let s(x) be the second derivative of x**7/42 + 2*x**6/5 + x**5/20 - 17*x**4/2 + 44*x**3/3 - 3509*x. Solve s(m) = 0 for m.
-11, -4, 0, 1, 2
Factor 699 + 2796 + 41*f**2 - 38*f**2 + 529 - 480*f - 811.
3*(f - 153)*(f - 7)
Let n = -1363/2012 - -2227/503. Factor -n*k - 9/4*k**2 + 3/2.
-3*(k + 2)*(3*k - 1)/4
Suppose -4*u = 5*i - 0*i - 43, i - 17 = -5*u. Suppose -5*s + 4*g + i = 0, -5*s + 5 = -2*s - 2*g. Factor 3/5*v**s + 3/5*v**4 + 0 + 9/5*v - 3*v**2.
3*v*(v - 1)**2*(v + 3)/5
Solve -37/5*o**4 + 1/5*o**5 + 6864/5*o + 2737/5*o**2 + 4356/5 + 191/5*o**3 = 0.
-3, -1, 22
Let w(x) = x**2 + x + 1. Let h(y) = 5*y**2 + 2*y - 4. Let s = 6 - 11. Let i = 9 + s. Let o(k) = i*w(k) + h(k). Factor o(j).
3*j*(3*j + 2)
Let u(q) be the third derivative of q**9/45360 + q**8/7560 + 61*q**5/60 + 3*q**2. Let z(m) be the third derivative of u(m). Factor z(p).
4*p**2*(p + 2)/3
Let r(z) be the se