i. Let f(o) be the second derivative of g(o). Factor f(n).
-n**3/3
Let a(m) be the first derivative of m**6/9 + 34*m**5/5 - 26*m**4/3 - 1539. Factor a(x).
2*x**3*(x - 1)*(x + 52)/3
Let m = 30835 - 30813. Let -m*z**3 - 70/9*z**4 - 194/9*z**2 - 64/9*z - 2/9*z**5 + 0 = 0. Calculate z.
-32, -1, 0
Let h(a) be the first derivative of -25*a**6/63 + 12*a**5/7 + 83*a**4/14 - 428*a**3/63 - 236*a**2/7 - 240*a/7 - 1308. Determine t, given that h(t) = 0.
-6/5, -1, 2, 5
Let k(q) = 6*q**4 - 10*q**3 - 42*q**2 + 2*q + 6. Let d(g) = 7*g**4 - 9*g**3 - 43*g**2 + 3*g + 9. Let n(m) = -2*d(m) + 3*k(m). Find c, given that n(c) = 0.
-2, 0, 5
Let w(n) = 10*n - 97. Let d be w(10). Suppose 0 = -d*j + 67 - 61. Factor 3/2 + 1/2*k**2 + j*k.
(k + 1)*(k + 3)/2
Let d(m) be the first derivative of m**4/2 - 238*m**3/3 + 234*m**2 - 1941. Determine y so that d(y) = 0.
0, 2, 117
Factor -1/7*s**4 - 690/7*s**3 - 118333/7*s**2 + 238740/7*s - 119716/7.
-(s - 1)**2*(s + 346)**2/7
Let o(b) be the second derivative of 0 - 1/45*b**6 + 20/9*b**3 - 125*b - 4/3*b**4 + 0*b**2 + 3/10*b**5. Factor o(d).
-2*d*(d - 5)*(d - 2)**2/3
Let u = -57 - -59. Factor 40*z - 46*z**u + 28*z**2 + 13*z**2.
-5*z*(z - 8)
Suppose -2*c + 4*g = 544, -4*g - 1136 = -27*c + 31*c. Let h be -2 - (c/21)/5. Factor 0*n + h*n**2 + 0.
2*n**2/3
Factor -493014*l + 1290371*l**3 - 72200 + 203454*l - 1290379*l**3 - 3042*l**2.
-2*(l + 190)**2*(4*l + 1)
Let v = 10/110531 + 1326242/1436903. Solve 2/13*y**2 + v*y + 16/13 = 0.
-4, -2
Factor -143*r**3 - 5*r**2 - 134*r**3 - 6*r**2 - 9*r**2 + 282*r**3 - 25*r.
5*r*(r - 5)*(r + 1)
Let y(l) be the second derivative of 2 + 7/15*l**6 - 23/10*l**5 - 3*l + 10*l**2 - 19/2*l**4 - 17/3*l**3. Let y(t) = 0. Calculate t.
-1, 2/7, 5
Suppose -7232/7*i + 6537728/7 + 2/7*i**2 = 0. Calculate i.
1808
Let r(a) be the third derivative of -a**5/30 - 158*a**4/3 - 99856*a**3/3 - 184*a**2. Determine p, given that r(p) = 0.
-316
Let a be (-1)/(-6) + 8*203/1008. Let a*j**3 + 16/9*j**2 - 4/3*j**4 + 0*j + 0 = 0. What is j?
-2/3, 0, 2
Let o = 93247/6 + -15507. Let r = -92/3 + o. Factor -1/2*n**5 + r*n**4 - 8 - 8*n**3 + 4*n**2 + 8*n.
-(n - 2)**4*(n + 1)/2
Let x = -173 - -175. Solve -7 - 4*p + 8 - 1 + 2*p**x = 0 for p.
0, 2
Let f(h) be the second derivative of -21*h**5/20 - h**4/6 - 658*h - 3. Factor f(o).
-o**2*(21*o + 2)
Factor 6*m**4 + 4*m**4 - 798309*m**2 - 832509*m**2 + 3612*m**3 - 12*m**4.
-2*m**2*(m - 903)**2
Let c(i) = -2*i**5 + 35*i**4 - 125*i**3 + 286*i**2 - 250*i + 77. Let j(l) = -l**4 - l**3 - 2*l**2 + 1. Let w(q) = -2*c(q) - 14*j(q). Find h such that w(h) = 0.
1, 2, 3, 7
Let h(g) be the first derivative of -2028*g**5/5 + 21177*g**4/4 + 4079*g**3 + 1116*g**2 + 132*g + 1798. Find r, given that h(r) = 0.
-1/4, -2/13, 11
Let d(q) be the first derivative of 8*q**6/5 - 264*q**5/25 + 267*q**4/20 + 23*q**3 - 207*q**2/10 + 27*q/5 - 889. Suppose d(v) = 0. Calculate v.
-1, 1/4, 3
Factor c**4 + 9*c**4 + 12*c**3 + 190*c**2 + 67*c**3 + c**4 + 24 + 164*c.
(c + 2)**2*(c + 3)*(11*c + 2)
Let s(v) = -120*v**2 - 14*v - 3. Let n(t) = -147*t**2 - 16*t - 4. Let b(y) = 3*n(y) - 4*s(y). Factor b(m).
m*(39*m + 8)
Determine i, given that -6/11 + 6/11*i**2 - 16/11*i = 0.
-1/3, 3
Let c(s) be the second derivative of -1/6*s**6 + 10*s**3 + 0 + 20*s**2 - 180*s - 3/4*s**5 + 5/6*s**4. Factor c(t).
-5*(t - 2)*(t + 1)*(t + 2)**2
Suppose 0 = 4*o + c + 24925 - 24955, 0 = -o - 3*c + 68. Determine j so that 5/3*j**o + 3375 + 150*j = 0.
-45
Let a = 1405196/1639379 - 2/234197. Determine p, given that -2/21*p**5 - 6/7*p - 2/21*p**4 + 20/21*p**3 + 20/21*p**2 - a = 0.
-3, -1, 1, 3
Let m(f) = -f**3 - 1. Let y(a) = -4*a**4 - 12*a**2 - 4*a + 12. Let v = -5 - -5. Let c be 0*(-1)/(-3) + v - -1. Let t(n) = c*y(n) + 12*m(n). Factor t(l).
-4*l*(l + 1)**3
Let d be (2736/(-8265) - 2/29)/(42/(-300)). Factor -2*x - d - 2/7*x**2.
-2*(x + 2)*(x + 5)/7
Let c(v) be the first derivative of -2*v**5/5 + 53*v**4/2 + 220*v**3/3 - 1945. Let c(b) = 0. What is b?
-2, 0, 55
What is p in -1/4*p**2 + 2413/4*p + 0 = 0?
0, 2413
Let m(l) be the first derivative of -l**5/150 - 19*l**4/60 - 34*l**3/15 + 16*l**2 - 160. Let k(g) be the second derivative of m(g). Factor k(r).
-2*(r + 2)*(r + 17)/5
Let o(n) be the third derivative of n**8/28 + 2*n**7/21 - 31*n**6/15 - 178*n**5/15 - 23*n**4/2 + 30*n**3 + 366*n**2. What is v in o(v) = 0?
-3, -1, 1/3, 5
Let i be (-584 + 591)/((-35)/(-12)). Let i*q**2 - 6/5*q**4 + 16/5*q**3 - 16/5*q - 6/5 = 0. What is q?
-1, -1/3, 1, 3
Let y(p) be the second derivative of 1/90*p**5 + 25 + 7/18*p**4 + 0*p**3 - 3*p + 0*p**2. Find x, given that y(x) = 0.
-21, 0
Factor 59*u**2 - 23*u**2 - 13*u**2 - 17*u**2 - 11*u**2 - 1790*u.
-5*u*(u + 358)
Let c = -321 - -361. Suppose 2*j = 10, 3*j - j = -5*m + c. Factor -18*h - 39/2*h**2 - m - 9*h**3 - 3/2*h**4.
-3*(h + 1)**2*(h + 2)**2/2
Let v = -5/25749 + 489266/180243. Factor 1/7*g**2 - v*g + 18/7.
(g - 18)*(g - 1)/7
Let h be -6*(-3)/(-48)*2816/(-144). Factor 0 + 70/3*o**2 - 50/3*o + 2/3*o**4 - h*o**3.
2*o*(o - 5)**2*(o - 1)/3
Factor -42*m**2 + 12*m - 30*m**4 + 74*m**3 + 4 - 30*m**3 - 159*m**4 - 3 + 174*m**4.
-(m - 1)**3*(15*m + 1)
Find j such that -40/19*j - 198/19 - 2/19*j**2 = 0.
-11, -9
Let b(k) = k**3 + k - 1. Suppose -18*q - 9*q - 27 = 0. Let l(z) = -4*z**3 - 14*z**2 - 6*z + 19. Let u(x) = q*l(x) - 5*b(x). Find h such that u(h) = 0.
-1, 1, 14
Let z(v) = -v**2 + 7*v + 7. Let b be z(6). Let t = 16 - b. Suppose t*d**4 - 12*d**3 - 7 - 16*d - 4*d**2 + 3 + 28*d + 5*d**4 = 0. What is d?
-1, 1/2, 1
Suppose 27466*c**3 - 48 + 0*c**2 - 12*c**4 + 60*c**2 - 27471*c**3 + c**5 + 4*c = 0. Calculate c.
-2, -1, 1, 2, 12
Let r(t) be the third derivative of -6 - 25/48*t**4 + t**2 + 1/240*t**6 + t**3 + 0*t - 1/420*t**7 + 13/120*t**5. Factor r(s).
-(s - 3)*(s - 1)**2*(s + 4)/2
Let h be -13 - (59 - 4)/(-6 + 2). Let x(t) be the first derivative of 21/8*t**4 - 11 + 3/8*t**6 - 3/2*t**3 - 3/8*t**2 - 33/20*t**5 + h*t. Factor x(r).
3*(r - 1)**4*(3*r + 1)/4
Let x(a) be the first derivative of 5*a**4/4 - 5*a**2/2 - 3381. What is r in x(r) = 0?
-1, 0, 1
Let h(a) be the second derivative of a**6/45 - 2101*a**5/30 + 245350*a**4/3 - 344470000*a**3/9 + 343000000*a**2/3 - a - 1985. Factor h(c).
2*(c - 700)**3*(c - 1)/3
Let i(v) be the second derivative of 3*v + 1/11*v**3 + 12 + 2/11*v**2 + 1/66*v**4. Factor i(q).
2*(q + 1)*(q + 2)/11
Let f(d) be the third derivative of d**5/90 - 53*d**4/36 + 34*d**3/3 - 32*d**2 + 3. Solve f(p) = 0.
2, 51
Let n be (40/(-160))/((-2 - -7)/(-120)). Suppose -33/4*c + 3/8*c**3 - n - 15/8*c**2 = 0. Calculate c.
-2, -1, 8
Let g(d) be the third derivative of -d**5/360 + 7*d**4/3 - 784*d**3 + 541*d**2. Suppose g(i) = 0. What is i?
168
Let m(c) be the first derivative of c**5/30 - 2*c**4/9 - 7*c**3/9 + 10*c**2/3 - 89*c + 114. Let n(b) be the first derivative of m(b). What is r in n(r) = 0?
-2, 1, 5
Let k = 1202 + -1196. Suppose 6*y - 17*y - k*y = 0. Factor -6*b - 3/5*b**3 + 21/5*b**2 + y.
-3*b*(b - 5)*(b - 2)/5
Suppose 4*i = 2*h + 4, -3*h + i = -8*h + 45. Suppose -5*n = -n - 8. Factor h*y**4 - 9*y**3 - 4*y**4 - y**4 + 8*y**n - 2*y**2.
3*y**2*(y - 2)*(y - 1)
Factor 276/5*l + 2/5*l**2 - 112.
2*(l - 2)*(l + 140)/5
Let j = 1198 - 4791/4. Let t(a) be the second derivative of 0 - 10*a - 5/24*a**3 + 1/20*a**5 - j*a**2 + 1/30*a**6 - 1/24*a**4 + 1/168*a**7. Factor t(m).
(m - 1)*(m + 1)**3*(m + 2)/4
Suppose -21 - 10*f + 32/3*f**2 - 2/3*f**3 - 1/3*f**4 = 0. Calculate f.
-7, -1, 3
Factor -2432/3*a**3 - 1848320*a**2 - 5618892800/3*a - 2/15*a**4 - 2135179264000/3.
-2*(a + 1520)**4/15
Let z(k) = -211*k + 104*k + 1 + 105*k + 0. Let n(p) = 35*p**2 - 175*p - 35. Let b(l) = -n(l) + 25*z(l). Factor b(w).
-5*(w - 4)*(7*w + 3)
Let f(x) be the second derivative of -x**6/300 + 4*x**5/75 - 7*x**4/60 + 58*x**2 + 120*x. Let h(v) be the first derivative of f(v). Factor h(c).
-2*c*(c - 7)*(c - 1)/5
Let w be ((3 + 3)/(-12))/((2/(-90))/((-284)/(-1278))). Let -8/5*j**4 + 2/5*j**w + 4/5 - 2*j + 8/5*j**3 + 4/5*j**2 = 0. What is j?
-1, 1, 2
Suppose 7*r - 181 + 118 = 0. Factor -248 - 39*j**3 - 109*j**2 + 254 - 32*j**3 - 41*j - r*j**4.
-(j + 1)**2*(j + 6)*(9*j - 1)
Let z(h) be the third derivative of 5*h**7/42 + h**6/4 - 4*h**5 + 145*h**4/12 - 35*h**3/2 + 16*h**2 + 10*h. Factor z(w).
5*(w - 1)**3*(5*w + 21)
Let t(b) be the first derivative of -b**6/10 - 3*b**5/20