n that j(g) = 0.
-1, 1, 32
Factor -102 + 276*g + g**5 + 264*g**3 - 56*g**4 + 83*g - 198*g**2 - 268*g**2.
(g - 51)*(g - 2)*(g - 1)**3
Let a = 513 - 538. Let h = a - -29. Factor 1/5*y**2 - 1/5*y**h - 1/5*y**3 + 1/5*y + 0.
-y*(y - 1)*(y + 1)**2/5
Let s = -84985 + 84985. Determine n, given that -1/3*n**4 + 0*n + 1/3*n**2 + 0 + s*n**3 = 0.
-1, 0, 1
Let h(q) be the second derivative of q**7/504 - q**6/6 + 6*q**5 + 29*q**4/12 + 4*q + 11. Let b(p) be the third derivative of h(p). Factor b(k).
5*(k - 12)**2
Let h = -2922 + 2926. Let b(u) be the second derivative of 0*u**2 - 17*u + 0*u**3 + 0 + 1/36*u**h. Factor b(d).
d**2/3
Suppose -17*b = -181 - 23. Solve 16*d**3 + 33*d**4 + 43*d**2 + b*d**5 + 8*d**3 - 107*d**4 + 5*d**2 - 32*d + 30*d**4 = 0.
-1, 0, 2/3, 2
Let z be 120/105 - (-3 + 2717/693). What is l in 0 + 18*l - 4*l**2 + z*l**3 = 0?
0, 9
Suppose -22508 - 21578 = -67*r. Let f = -653 + r. Factor -1/3 + 2/3*s**2 - 1/3*s**4 - 1/3*s**f - 1/3*s + 2/3*s**3.
-(s - 1)**2*(s + 1)**3/3
Let d(v) = v**2 - 2*v - 7. Let q be d(3). Let w(t) = -6*t**2 + 27*t - 30. Let n(m) = 7*m**2 - 25*m + 30. Let p(r) = q*w(r) - 3*n(r). Factor p(y).
3*(y - 10)*(y - 1)
Solve y**2 - 7/8 - 1/8*y**4 + 3/4*y**3 - 3/4*y = 0 for y.
-1, 1, 7
Let h(a) be the second derivative of a**4/66 + 58*a**3/33 - 133*a**2 + 432*a. Factor h(y).
2*(y - 19)*(y + 77)/11
Let b(t) = -9*t**4 + 42*t**3 - 318*t**2 + 474*t - 213. Let i(m) = 25*m**4 - 128*m**3 + 955*m**2 - 1422*m + 638. Let h(y) = 17*b(y) + 6*i(y). Factor h(s).
-3*(s - 3)*(s - 1)**2*(s + 23)
Suppose 11*y - 2*c - 1 = 4*y, -3*y - 2*c + 9 = 0. Let j be y/2 + (6 - (-748)/(-120)). Factor -2/5*a**3 - j*a**2 - 2/15*a**4 + 0*a + 0.
-2*a**2*(a + 1)*(a + 2)/15
Factor -77/4*z**2 + 77/4 - 1/8*z**3 + 1/8*z.
-(z - 1)*(z + 1)*(z + 154)/8
Let o(f) = -2*f**2 + 51*f + 141. Let q be o(28). Let a(b) be the first derivative of -2*b - 1/3*b**2 + 1/6*b**4 + 2/3*b**3 - q. Factor a(h).
2*(h - 1)*(h + 1)*(h + 3)/3
Factor 1/3*m**3 - 92/3*m + 20/3*m**2 + 32.
(m - 2)**2*(m + 24)/3
Find l, given that 3641573376/5*l - 611784327168/5 - 8128512/5*l**2 - 3/5*l**4 + 8064/5*l**3 = 0.
672
Let b(j) = 23 - 37*j + 111 + 127. Let q be b(7). Factor -10/3*o + 0 - 2/3*o**q.
-2*o*(o + 5)/3
Determine d, given that 381 + 324 + 450 - 90*d - 27683*d**2 + 27678*d**2 + 245 = 0.
-28, 10
Let c(t) = t**3 - 30*t**2 + 56*t - 2. Let b be c(28). Let r be (b - (-9)/(-6)) + (-40)/(-10). Find o such that 1/4*o - 1/2 + r*o**2 - 1/4*o**3 = 0.
-1, 1, 2
Let c(m) = 4*m - 23. Let t be c(11). Let w be 5 + 6*(-7)/t. Solve 25/2*y - 45/4*y**2 - 5*y**w + 15/4 = 0.
-3, -1/4, 1
Let z(b) be the first derivative of -b**4/8 + 297*b**3 - 264627*b**2 + 104792292*b - 3677. Factor z(d).
-(d - 594)**3/2
Let m(u) be the first derivative of -u**7/273 + 3*u**6/65 - 129*u - 8. Let i(o) be the first derivative of m(o). What is x in i(x) = 0?
0, 9
Let p = 79849 - 239543/3. Factor -p + 0*z + 4/3*z**2.
4*(z - 1)*(z + 1)/3
Let m(b) be the second derivative of -25*b**7/42 - 2*b**6/3 + 321*b**5/20 - 10*b**4/3 - 94*b**3/3 - 24*b**2 - 269*b + 4. Let m(q) = 0. What is q?
-4, -2/5, 1, 3
Let q(t) = -9*t**2 - 6422*t - 5177300. Let w(g) = -4*g**2 - 3212*g - 2588683. Let o(x) = 3*q(x) - 7*w(x). Determine n so that o(n) = 0.
-1609
Let p = -3512 + 17561/5. Let -1/5*o**2 + p*o + 1/5 - 1/5*o**3 = 0. Calculate o.
-1, 1
Let r(g) be the second derivative of g**5/240 + 3*g**4/16 + 17*g**3/24 - 45*g**2 + 85*g. Let w(u) be the first derivative of r(u). Factor w(c).
(c + 1)*(c + 17)/4
Let a(w) be the first derivative of -5*w**4 - 85*w**3 + 1865*w**2/2 - 450*w - 2478. Factor a(p).
-5*(p - 5)*(p + 18)*(4*p - 1)
Let u(z) be the second derivative of -z**5/110 - 479*z**4/66 - 19040*z**3/11 + 57600*z**2/11 - 847*z. Factor u(r).
-2*(r - 1)*(r + 240)**2/11
Let o(b) be the third derivative of -b**7/1365 - 2*b**6/195 - 3*b**5/130 + 3*b**4/26 - 6*b**2 + 200*b. Solve o(a) = 0 for a.
-6, -3, 0, 1
Let o(m) be the second derivative of m**5/10 - 11*m**4/6 - 4*m**3 + 188*m + 3. Factor o(y).
2*y*(y - 12)*(y + 1)
Let b(u) = -2*u**3 - 77*u**2 + 39*u + 45. Let f be b(-39). Let w be (6/(-4))/(f/(-18)). Find s, given that 1/5*s**4 + s**3 + 0 + w*s + 7/5*s**2 = 0.
-3, -1, 0
Let j(m) = 3*m - 29. Let h be j(11). Let z be -20*(h + (-51)/12). Factor -28*n + 9*n**4 + 12*n**z + 28*n - 8*n**2 - 4*n**3 + 7*n**4.
4*n**2*(n + 1)**2*(3*n - 2)
Let t = -114841 - -114841. Factor 7/2*p**3 + 0*p - 2*p**2 - 7/4*p**4 + 1/4*p**5 + t.
p**2*(p - 4)*(p - 2)*(p - 1)/4
Let l(c) = 13*c**2 + c - 1. Let v be l(1). Suppose v*t = 11*t + 4. Factor 2*g - 14 - 2*g - 6*g + 3*g**t - 10.
3*(g - 4)*(g + 2)
Suppose 4*x + 5*u = 7*x - 25, x + 7*u = -35. Factor -28/3*f + 4/3*f**2 - 4/3*f**4 + 28/3*f**3 + x.
-4*f*(f - 7)*(f - 1)*(f + 1)/3
Let t = 21486916144/102465 + -11534537/55. Let x = 1/1863 - t. Solve 28/5 - 14/5*h**2 + x*h = 0 for h.
-2/7, 7
Let g(z) be the first derivative of 2*z**5/5 - 47*z**4/3 + 1120*z**3/9 - 736*z**2/3 - 512*z + 8916. What is x in g(x) = 0?
-2/3, 4, 24
Let s(f) be the second derivative of -f**7/189 + 73*f**6/135 - 7*f**5/9 - 8*f**4/3 + 2*f + 3075. Let s(p) = 0. Calculate p.
-1, 0, 2, 72
Let g(d) = d**3 + 31*d**2 + 172*d - 202. Let n(f) = 6*f**3 + 156*f**2 + 858*f - 1009. Let u(a) = 33*g(a) - 6*n(a). Factor u(b).
-3*(b - 34)*(b - 1)*(b + 6)
Let y be 1/3 + (-68)/(-3). Suppose -y = -5*s + 32. Solve 2 - 8 - 21*f**3 - 27*f**4 + s*f**2 + 22*f**2 + 21*f = 0 for f.
-1, 2/9, 1
Let w = 8707/42 - -277/21. Let -21*u + w + 1/2*u**2 = 0. Calculate u.
21
Suppose -894 + 2781*j - 1379*j - 3*j**4 - 153*j**2 + 5229 - 291*j**2 + 2576*j - 90*j**3 = 0. What is j?
-17, -1, 5
Suppose -279*k + 80*k**2 + 76*k**2 + 934092 + 86*k**2 - 3069*k - 239*k**2 = 0. Calculate k.
558
Solve -60/17 + 2/17*a**2 - 2/17*a = 0.
-5, 6
Let m(a) = -2*a**3 - 4*a**2 - 8*a - 12. Let z be m(-2). Let 36*g**5 - 321 + 94*g**3 - 64*g**z - 2048*g + 1512*g**2 + 833 - 42*g**5 = 0. Calculate g.
-8, 1/3, 1, 4
Let p(w) be the second derivative of w**4/36 - 4*w**3 + 66*w**2 + 4390*w + 2. Determine k so that p(k) = 0.
6, 66
Let a(f) be the second derivative of 5*f**7/42 - 8*f**6/3 + 81*f**5/4 - 455*f**4/6 + 470*f**3/3 - 180*f**2 + 1602*f. Find g, given that a(g) = 0.
1, 2, 9
Let b be ((-16)/(-40) - 1)/(1/80*-4) - 9. Find j such that 10/7*j**2 - 10/7 + 2/7*j - 2/7*j**b = 0.
-1, 1, 5
Let m(o) be the first derivative of -15/8*o**2 + 1/12*o**3 + 57 - 4*o. Suppose m(i) = 0. What is i?
-1, 16
Let h(d) be the second derivative of 20*d - 1/20*d**5 + 1/6*d**3 + d**2 + 0 - 1/6*d**4. Factor h(t).
-(t - 1)*(t + 1)*(t + 2)
Factor 6/7*c**3 + 240/7 + 344/7*c + 111/7*c**2 - 1/7*c**4.
-(c - 15)*(c + 1)*(c + 4)**2/7
Suppose m - 5*v = -16, -5*m - 5*v + 20 = -10*m. Let p be (-1 - m)/(-1*2/2). Find a such that 1/10*a**5 + 0 + p*a**2 + 8/5*a - 4/5*a**3 + 0*a**4 = 0.
-2, 0, 2
Determine r so that 346/9*r**3 - 29584/3 + 30269/9*r**2 + 58136/9*r + 1/9*r**4 = 0.
-172, -3, 1
Suppose 4/3*c**5 - 116/3*c**2 + 0 + 36*c**3 - 112/3*c + 116/3*c**4 = 0. What is c?
-28, -1, 0, 1
Let v(y) be the third derivative of -y**6/240 - 23*y**5/24 - 7*y**4/3 + 19*y**3 + 1835*y**2. Let v(o) = 0. What is o?
-114, -2, 1
Let o = -595 - -597. Suppose b - 4 = -c + 2*b, 32 = 6*c - o*b. Factor 4*d - c - 2/3*d**2.
-2*(d - 3)**2/3
Let m(u) be the first derivative of -u**4/4 - u**3 - 155*u + 109. Let s(g) be the first derivative of m(g). Let s(v) = 0. What is v?
-2, 0
Let i be (-22 + 2 + 8)*4/(-48)*4. Factor 8/7*n**3 + 0*n**2 + 0 + 0*n - 4/7*n**i.
-4*n**3*(n - 2)/7
Solve 80/7*l - 17/7*l**2 - 100/7 + 1/7*l**3 = 0 for l.
2, 5, 10
Suppose -4*p**5 + 84 + 2*p**3 + 20*p**4 + 17 - 180*p**2 + 302 + 18*p**3 + 29 = 0. What is p?
-2, 3
Let y(g) be the second derivative of 0 + 1/24*g**4 + 0*g**2 - 1/4*g**3 - 110*g. Solve y(u) = 0.
0, 3
Let a(b) be the first derivative of -2/3*b**5 - 14/3*b**4 + 32/3*b - 32/3*b**3 - 16/3*b**2 - 79. Solve a(q) = 0.
-2, 2/5
Find t such that -6084*t**2 + 3514*t**3 - 57024*t - 4*t**4 - 7280*t**3 + 3502*t**3 - 186624 = 0.
-24, -9
Let d = -38 - -42. Suppose -d*v + 5 = -3. Factor -25*w + 100*w + 17*w**2 + 24 + w**3 + 101 - v*w**2.
(w + 5)**3
Factor -125/3*a - 15625/6 - 1/6*a**2.
-(a + 125)**2/6
Let y = -57131/12 - -4761. Let b(f) be the first derivative of f**2 - 20 - 2/5*f**5 - 1/8*f**4 - 4*f + 5/3*f**3 - y*f**6. Factor b(g).
-(g - 1)**2*(g + 2)**3/2
Let b(t) be the third derivative of t**5/