/102*x**4 - 7*x + 0 + p*x**3 + 1/17*x**2. Factor h(d).
2*(d + 1)**2/17
Let w(z) be the second derivative of 5*z + 1/24*z**4 + 9/4*z**2 + 1 - 5/6*z**3. Factor w(o).
(o - 9)*(o - 1)/2
Let v(l) be the second derivative of l**6/30 - 4*l**5/5 - 79*l**4/12 - 13*l**3/3 + 60*l**2 + 1987*l. Determine k so that v(k) = 0.
-3, -2, 1, 20
Let h be 1/(45/(-12) + 4). Let o(m) = m**3 - 4*m**2 - 2*m + 10. Let d be o(h). Factor -6*q + 0*q**2 + 2 + d*q**2 - 5 - 5.
2*(q - 4)*(q + 1)
Factor 28/5*b**2 + 128/5*b + 192/5 + 2/5*b**3.
2*(b + 4)**2*(b + 6)/5
Let g(i) = -i**3 + 25*i**2 + 359*i + 93. Let v be g(-10). Find j such that 6/13*j**v - 6/13*j**2 - 14/13*j + 2/13*j**4 + 12/13 = 0.
-3, -2, 1
Let c be ((-8)/((-208)/39))/(-21 + 22). Factor -c*a - 3/2 + 3/2*a**3 + 3/2*a**2.
3*(a - 1)*(a + 1)**2/2
Suppose -606*d = -4*r - 602*d + 76, 76 = -3*r - 4*d. Let j = 5 - 0. Factor 3/2*s**3 + 1/2*s**j - 3/2*s**4 + r*s - 1/2*s**2 + 0.
s**2*(s - 1)**3/2
Let y be (12/(-22 + 274))/(4/72). Factor 0*o**3 - y*o**2 - 4/7*o + 2/7*o**4 + 0.
2*o*(o - 2)*(o + 1)**2/7
Let u be (8/6)/((-3140)/(-1413)). Factor -3/5*v**3 + u*v**2 + 3/5*v + 0 - 3/5*v**4.
-3*v*(v - 1)*(v + 1)**2/5
Let g = -447 - -441. Let o be (g - -4)*(-4 + (-9)/(-3)). Factor 2/5*h - 8/15 + 2/15*h**o.
2*(h - 1)*(h + 4)/15
Let a be (-3)/(-9) + ((-7761)/1800)/13. Let v(i) be the third derivative of 0*i - 1/24*i**4 + 19*i**2 - 5/12*i**3 - a*i**5 + 0. Suppose v(z) = 0. What is z?
-5
Factor 4/7*l**4 - 2/7*l**5 - 8/7*l + 0 - 8/7*l**2 + 6/7*l**3.
-2*l*(l - 2)**2*(l + 1)**2/7
Let r(o) = o**3 + 3*o**2 + 3. Let z(g) = -g**3 - 501*g**2 + 490*g - 9. Let d(u) = 3*r(u) + z(u). Factor d(m).
2*m*(m - 245)*(m - 1)
Let l(o) be the first derivative of 0*o - o**5 + 0*o**2 - 5*o**3 - 5/6*o**6 - 51 + 25/4*o**4. Factor l(w).
-5*w**2*(w - 1)**2*(w + 3)
Let u be 3 - ((-5)/20 - (-5)/20). Let m(k) be the first derivative of -1/2*k**4 + 0*k + 1/5*k**5 + 0*k**2 + 0*k**u - 15. Factor m(t).
t**3*(t - 2)
Suppose 7*w = -93 + 114. Suppose -w*h - 6 = 3*t - 6*h, -5*t + 20 = h. What is m in m**t + 0*m + 1/3*m**2 + 1/3*m**5 + 0 + m**4 = 0?
-1, 0
Let p(z) = -58*z - 46. Let y be p(-1). Let q be (-84)/(12 - 5) + y. Factor 2/5*d**3 + q*d**4 - 1/5*d + 0*d**2 + 0 - 1/5*d**5.
-d*(d - 1)**2*(d + 1)**2/5
Suppose 0 = -3*y - 3, -4*b - 5*y = -31 + 16. Factor -b*m**3 + m**4 - 5*m**2 + 6*m**2 + 2*m**4 - 7*m**3 + 8*m**2.
3*m**2*(m - 3)*(m - 1)
Let -39 - 99/2*l**2 + 279/2*l + 9/2*l**4 - 111/2*l**3 = 0. What is l?
-2, 1/3, 1, 13
Let b(u) be the first derivative of -u**6/600 + 27*u**5/200 + 7*u**4/10 + 63*u**3 + 164. Let c(n) be the third derivative of b(n). Find s, given that c(s) = 0.
-1, 28
Let p(f) be the third derivative of -19*f**5/240 + 27*f**4/32 - 3*f**3 - 9*f**2 - 283*f. Solve p(z) = 0 for z.
24/19, 3
Let k(c) be the second derivative of 9*c**7/70 - 681*c**6/50 + 42177*c**5/100 - 44139*c**4/20 + 2484*c**3 - 5832*c**2/5 - 706*c. Let k(w) = 0. What is w?
1/3, 3, 36
Let d(l) be the first derivative of l**6/1080 + l**5/120 + l**4/36 - 8*l**3/3 + l**2/2 + 52. Let z(h) be the third derivative of d(h). Let z(b) = 0. What is b?
-2, -1
Let w(j) be the first derivative of -25*j**6/2 + 191*j**5 - 2245*j**4/4 - 2025*j**3 + 2590*j**2 - 980*j - 944. Determine u, given that w(u) = 0.
-2, 1/3, 2/5, 7
Suppose -4*t - 242 = v, 1036 = -4*v - 0*t + t. Let n = 261 + v. Factor 0*i**2 - 1/6*i**n + 1/6*i + 0.
-i*(i - 1)*(i + 1)/6
Let z(r) be the second derivative of r**4/12 - 11*r**3/2 - 164*r**2 + 101*r + 15. Find n, given that z(n) = 0.
-8, 41
Let b = -177 + 182. Factor -15*x**3 + 10*x + 9*x**4 - 4*x**4 - 40*x**2 + 35*x**2 + b*x**5.
5*x*(x - 1)**2*(x + 1)*(x + 2)
Let x(j) be the third derivative of j**7/11340 - 13*j**6/3240 + j**5/18 - 53*j**4/12 + 44*j**2. Let k(m) be the second derivative of x(m). Solve k(c) = 0 for c.
3, 10
Suppose 6 = -2*p - 3*o, -4*p + 0*p = 3*o. Factor -7123*f - 5*f**2 - 10*f**p + 7123*f - 5*f**4.
-5*f**2*(f + 1)**2
Let z = -190229/30 + 6341. Let o(a) be the second derivative of -3/10*a**2 + 10*a - z*a**3 + 1/20*a**4 + 1/100*a**5 + 0. Factor o(v).
(v - 1)*(v + 1)*(v + 3)/5
Let m(s) be the second derivative of -s**5/10 + 31*s**4/24 - 89*s**3/24 + 15*s**2/4 - 373*s. Factor m(f).
-(f - 6)*(2*f - 1)*(4*f - 5)/4
Let z(b) be the second derivative of 11*b - 1/7*b**7 + 0*b**2 + 0*b**3 - 1/3*b**4 - 2/15*b**6 + 7/10*b**5 + 0. Solve z(a) = 0.
-2, 0, 1/3, 1
Let s(y) be the first derivative of -y**6/18 - 41*y**5/15 - 31*y**4/2 + 814*y**3/9 - 901*y**2/6 + 105*y - 6010. Find w, given that s(w) = 0.
-35, -9, 1
Let c(v) be the second derivative of -v**6/1140 + 7*v**5/285 - 219*v**2/2 - 3*v - 50. Let u(l) be the first derivative of c(l). Solve u(b) = 0.
0, 14
Let h(t) be the third derivative of 0 + 1/10*t**4 - 12/5*t**3 - 1/600*t**5 + 2*t**2 + 15*t. Find r such that h(r) = 0.
12
Let i(x) be the first derivative of x**4/60 + 8*x**3/5 + 47*x**2/10 + 84*x - 314. Let n(l) be the first derivative of i(l). Suppose n(s) = 0. Calculate s.
-47, -1
Let b(w) be the second derivative of -w**6/30 + 147*w**5/10 - 21313*w**4/12 - 7252*w**3 - 10952*w**2 - 169*w. Factor b(x).
-(x - 148)**2*(x + 1)**2
Let a(f) be the third derivative of -f**7/42 - 43*f**6/15 + 379*f**5/10 - 159*f**4 + 225*f**3/2 + 2*f**2 - 7*f + 66. Factor a(n).
-(n - 3)**2*(n + 75)*(5*n - 1)
Let g(s) be the first derivative of -1/3*s**4 + 0*s**2 - 2/15*s**6 - 2/5*s**5 + 0*s**3 - 4 + 12*s. Let x(l) be the first derivative of g(l). Factor x(f).
-4*f**2*(f + 1)**2
Let t be 20 - (13 + -3) - 10. Let z(w) be the first derivative of -1/26*w**4 + 0*w + 28 + 2/65*w**5 + 0*w**3 + t*w**2. Factor z(v).
2*v**3*(v - 1)/13
Let u = -1375 - -1342. Let i be (18/(-168))/(u/440). Suppose 2/7*z**2 + i*z - 12/7 = 0. Calculate z.
-6, 1
Let l = 2224 + 3813. Factor -u + u**2 + l - 6037.
u*(u - 1)
Suppose 4*c - 29 = -x + 10, 53 = 2*x + 3*c. Suppose 0 = -16*m + x*m + 2*l - 1, -5*m = -2*l - 23. Factor 0*b + 0*b**m - 2/5*b**2 + 1/5 + 1/5*b**4.
(b - 1)**2*(b + 1)**2/5
Factor 2/19*c**5 - 14/19*c**4 - 8/19 + 2*c**3 - 50/19*c**2 + 32/19*c.
2*(c - 2)**2*(c - 1)**3/19
Let l = -190/3 - -2518/39. Suppose 2*u - w - 9 = 0, -5*u - 6*w + 3*w = 5. Solve 12/13*k - 2/13*k**u - l = 0.
2, 4
Let k(t) be the first derivative of t**6/42 - 5*t**4/14 + 20*t**3/21 - 15*t**2/14 + 4*t/7 + 1306. Suppose k(i) = 0. Calculate i.
-4, 1
Let j(i) be the first derivative of -2*i**2 - 74 + 4/3*i**3 - 24*i. Factor j(f).
4*(f - 3)*(f + 2)
Let r(d) be the second derivative of d**6/60 + 11*d**5/10 - d**4/24 - 11*d**3/3 - 3955*d. Let r(h) = 0. What is h?
-44, -1, 0, 1
Let k(x) be the first derivative of -x**5/35 - 3*x**4/28 + x**3/21 + 3*x**2/14 + 1582. Find s such that k(s) = 0.
-3, -1, 0, 1
Find s such that 25/2*s - 1/4*s**3 + 0 - 5/4*s**2 = 0.
-10, 0, 5
Let b(r) be the second derivative of 3/2*r**2 + 0 - 16*r - 1/3*r**3 - 1/12*r**4. Solve b(a) = 0.
-3, 1
Suppose 1/2*h**4 - 28/3*h**3 + 0 + 4/3*h**5 + 3*h + 9/2*h**2 = 0. Calculate h.
-3, -3/8, 0, 1, 2
Let q(b) be the first derivative of b**5/20 + 7*b**4/8 - 53*b**3/4 + 91*b**2/2 - 55*b + 3547. Suppose q(k) = 0. What is k?
-22, 1, 2, 5
Let w(i) = -i**3 - i**2 + 24*i + 34. Let n be w(-5). Let p be (-30)/210 - (-18)/n. Factor -p - 68/7*r - 60/7*r**2.
-4*(r + 1)*(15*r + 2)/7
Let m = -299/5 - -60. Let z(j) = -685*j + 18497. Let g be z(27). Solve -m*d + 1/5*d**g - 2/5 = 0.
-1, 2
Let m be 3*69/(14835/86). Find p such that -m - 1/5*p + 1/5*p**3 + 6/5*p**2 = 0.
-6, -1, 1
Suppose 0 = -161*i + 216 + 56 + 211. What is d in 17/3*d + d**i + 5*d**2 + 2 - 1/3*d**4 = 0?
-1, 6
Let q be (-15)/(-40)*116/2958. Let h(i) be the third derivative of 0 + 2/255*i**5 + 1/1020*i**6 + 0*i + q*i**4 + 0*i**3 - 36*i**2. Solve h(a) = 0.
-3, -1, 0
Let g = -80 + 80. Let s(o) = 4*o + 2. Let a be s(g). Factor -2*n**3 - 9*n**2 - 5*n**2 - 8*n - 2*n**a + 8*n**2.
-2*n*(n + 2)**2
Let o(s) = -132*s**2 - 230*s - 107. Let d(t) = -265*t**2 - 465*t - 215. Let h(u) = -3*d(u) + 5*o(u). Find z, given that h(z) = 0.
-1, -22/27
Let t(u) be the third derivative of 8*u**7/105 + u**6/10 - 7*u**5/15 - 765*u**2. Factor t(x).
4*x**2*(x - 1)*(4*x + 7)
Factor 152/5*u**2 + 22801/5 - 4681/2*u - 1/10*u**3.
-(u - 151)**2*(u - 2)/10
Suppose -10*a + 2*i + 324 = 0, 43*i - 177 = -5*a + 39*i. Let l(y) be the third derivative of 0 - 1/15*y**5 + a*y**2 - 2/9*y**4 + 0*y + 8/9*y**3. Factor l(g).
-4*(g + 2)*(3*g - 2)/3
Let i b