- -4237. Let l(y) = q*h(y) + s*g(y). Let l(x) = 0. What is x?
-11
Suppose 0 = -0*r - 36*r + 180. Suppose r*n + 8 = -x - 14, 3*x - 4*n = 29. Solve v + 1/2 - v**x + 0*v**2 - 1/2*v**4 = 0 for v.
-1, 1
Let f(l) be the second derivative of -3*l**5/80 - 57*l**4/16 - 72*l**3 - 1215*l**2/2 + 2884*l. Factor f(j).
-3*(j + 6)**2*(j + 45)/4
Let x(n) be the third derivative of -n**8/252 + 58*n**7/945 + 28*n**6/45 + 40*n**5/27 - 8*n**4/9 - 224*n**3/27 - 4*n**2 - 133*n. Solve x(o) = 0 for o.
-2, -1, 2/3, 14
Let p be 4/(-30) - ((-11876)/(-30) - 0). Let a = -394 - p. Factor -2/7*n**a + 20/7 - 18/7*n.
-2*(n - 1)*(n + 10)/7
Let o(x) be the third derivative of -x**6/30 + 134*x**5/15 - 770*x**4 + 5808*x**3 + 814*x**2. Factor o(l).
-4*(l - 66)**2*(l - 2)
Let j be 38/14 - 14/(-49). Suppose 0 = j*y + 2*s - 34, -4*y - 2*s + 51 = -5*s. Factor -y*k - 83*k**2 + 0*k**3 + 5*k**3 - k**3 + 75*k**2.
4*k*(k - 3)*(k + 1)
Let j(g) = -5*g**2 + g + 2. Let c(i) = -95*i**2 + 95*i - 1040. Let n(z) = -c(z) + 20*j(z). What is t in n(t) = 0?
-24, 9
Let m be 17*(-2)/(-18) + -21 + (-13 - -33). Factor 4/3*g + 0 + m*g**2 + 1/9*g**3.
g*(g + 2)*(g + 6)/9
Let s be (-5)/(-3) + (-8)/3 + 21/14. Factor -s*z**3 + 0 - 5/2*z - 3*z**2.
-z*(z + 1)*(z + 5)/2
Let b(i) be the first derivative of -i**4/16 + 1727*i**3/12 - 746495*i**2/8 + 744769*i/4 - 1491. Factor b(n).
-(n - 863)**2*(n - 1)/4
Let x(i) be the first derivative of -5*i**4/4 + 10*i**3 + 280*i**2 + 8156. Solve x(n) = 0.
-8, 0, 14
Let j = 25396 + -25390. Let n(z) be the first derivative of -1/42*z**j - 3/28*z**4 + 1/21*z**3 + 0*z + 0*z**2 + 3/35*z**5 - 19. Factor n(o).
-o**2*(o - 1)**3/7
Let m(z) be the first derivative of 0*z - 65 + 2/57*z**3 - 6/19*z**2 + 1/38*z**4. Factor m(q).
2*q*(q - 2)*(q + 3)/19
Let i be ((-2)/4)/(-7 - (-1010)/180). Let s(z) be the first derivative of -9/20*z**4 - i*z**5 + 8 - 1/10*z**6 + 0*z + 0*z**2 - 1/5*z**3. Factor s(u).
-3*u**2*(u + 1)**3/5
Let b(c) be the first derivative of -3*c**4/4 + 19*c**3 + 300*c**2 + 1296*c + 3382. Determine i so that b(i) = 0.
-4, 27
Let k(b) be the first derivative of -b**3/15 + 236*b**2 - 278480*b + 4353. Factor k(m).
-(m - 1180)**2/5
Let a(q) = q**2 - 14*q + 10. Let p(t) = -t**2 + 13*t - 10. Let b(n) = 6*a(n) + 7*p(n). Let w be b(4). Factor -o**3 - 4*o**3 - 32*o**2 + 32*o**w.
-5*o**3
Let s = 2965 + -8891/3. Let a(f) be the first derivative of -4/5*f**5 + 0*f + 4/3*f**3 + s*f**6 + 2*f**2 - 3*f**4 + 6. Suppose a(y) = 0. Calculate y.
-1, -1/2, 0, 1
Let i(c) be the first derivative of 9*c**5/100 + 7*c**4/20 - 4*c**3/5 - 6*c**2 - 10*c - 175. Let k(n) be the first derivative of i(n). What is d in k(d) = 0?
-2, 5/3
Let t be (-84)/(-182) + (-1)/((-390)/1640). Factor 1/9*o**3 + 2744/9 + 196/3*o + t*o**2.
(o + 14)**3/9
Let l(t) be the second derivative of -17/45*t**3 + 1/9*t**4 + 8/15*t**2 + 80*t - 1/150*t**5 + 0. Solve l(q) = 0 for q.
1, 8
Let g(u) be the second derivative of -4*u**6/75 + 25*u**5/2 - 4082*u**4/5 + 2028*u**3/5 - 3017*u. Factor g(l).
-2*l*(l - 78)**2*(4*l - 1)/5
Suppose -15022 = -6197*p + 97*p + 3278. Solve 4 - 11/3*m**4 + 7*m**5 - 23*m**3 + 40/3*m - p*m**2 = 0.
-1, -1/3, 6/7, 2
Solve 1657*f - 6*f**3 + 24*f**3 + 1065 - 5*f**3 - 10*f**3 + 231*f**2 - 364*f = 0.
-71, -5, -1
Let g be 4/30 + -5 + (-1788)/(-90). Let j(u) be the first derivative of 2/3*u**3 - g + u**2 - 12*u. Determine o so that j(o) = 0.
-3, 2
Suppose -505 = 18*j - 5113. Solve -r - 6 - j*r**2 + 127*r**2 + 10*r + 126*r**2 = 0 for r.
1, 2
Let z(d) = d**2 + 9*d - 16. Let o be z(-11). Let h be 1/((-1)/o*-2). Solve 5*y**4 - 6*y**h + 3*y**2 - 5*y**4 - 2*y**4 - y**2 + 6*y**5 = 0.
-1, 0, 1/3, 1
Let k(a) be the first derivative of 33635*a**4/4 + 38750*a**3/3 + 13995*a**2/2 + 1620*a + 977. Solve k(m) = 0.
-4/7, -9/31
Factor -1/7*j**3 - 3364/7 - 3480/7*j - 117/7*j**2.
-(j + 1)*(j + 58)**2/7
Let l = -1159 + 1627. Let n = -1403/3 + l. Find f such that n*f**2 - 2/9*f - 1/9 = 0.
-1/3, 1
Let m(l) = -l**3 + 123*l**2 + 479*l + 3726. Let o be m(127). Find n, given that 735/2*n + 343 - 1/2*n**5 - o*n**3 - 28*n**2 + 9*n**4 = 0.
-2, -1, 7
Solve 108*v**3 + 191*v - 1002*v - 32*v**3 + 350*v**3 - 93*v + 18*v**4 + 368 + 236*v**2 = 0 for v.
-23, -2, 2/3
Let o(j) = 15*j**5 + 20*j**4 - 56*j**3 - 60*j**2 + 91*j - 13. Let z(p) = p**5 + 4*p**4 - 2*p**3 - p - 1. Let h(t) = o(t) + 3*z(t). Solve h(w) = 0 for w.
-2, 2/9, 1
Factor -2*d**2 - 119 + 211 - 298 - 694 - 110*d.
-2*(d + 10)*(d + 45)
Let x(d) be the third derivative of -d**6/1080 + 19*d**5/540 - d**4/18 - 2*d**3 - 943*d**2. Suppose x(q) = 0. What is q?
-2, 3, 18
Suppose -122*i - 5*i = -254. Factor 4/5*m + 3/5 + 1/5*m**i.
(m + 1)*(m + 3)/5
Let f(j) be the second derivative of j**6/30 + 67*j**5/120 + 125*j**4/72 + 73*j**3/36 + 3*j**2/4 + 3*j + 32. Factor f(r).
(r + 1)**2*(r + 9)*(6*r + 1)/6
Let j = -5/19939 - -59857/159512. Find k, given that 9 - 15/4*k + j*k**2 = 0.
4, 6
Let r be (-6)/9*3*-1. Factor -9*i**r + 10*i + 11*i - 26*i + 4*i**2.
-5*i*(i + 1)
Find f such that -12*f**5 + 112 + 6553701*f**2 + 374 - 345*f**3 + 123*f - 111*f**4 + 174*f - 6554016*f**2 = 0.
-3, -9/4, -2, 1
Suppose -4*h + 22 = 16*r - 18*r, 3*h + 16 = -5*r. Let v(i) be the second derivative of 5/12*i**4 + 3*i + 0 - 5/6*i**h + 1/4*i**5 - 5/2*i**2. Factor v(k).
5*(k - 1)*(k + 1)**2
Let l(j) = -18119*j - 251354. Let i be l(-14). Find g such that i - 1/2*g**3 - 2244*g - 135/2*g**2 = 0.
-68, 1
Let t(u) be the first derivative of u**3/6 + 657*u**2/4 + 7486. Factor t(q).
q*(q + 657)/2
Let h be (18/(-14) - -1) + 635/(-889). Let a be ((-4)/(-8))/(3*h/(-2)). Factor -2/3*u - 1/3 - a*u**2.
-(u + 1)**2/3
Let g be 24/(-8)*2*(-14 + (-10142)/(-726)). Solve 11250/11 + g*l**2 + 300/11*l = 0.
-75
Suppose 2*x - 49 = 23. Let j(m) be the third derivative of -m**3/6 - 24*m**2 + 2. Let c(z) = 2*z**2 - 10*z - 6. Let h(u) = x*j(u) - 2*c(u). Factor h(b).
-4*(b - 3)*(b - 2)
Let p(c) = c**3 + 15*c**2 - 15*c + 22. Let y be p(-16). Suppose -w - y + 9 = 0. Factor -w*n**4 + n**3 - 4*n**3 + 9*n**3 - 3*n**2.
-3*n**2*(n - 1)**2
Let m = -11978 - -11978. Let s(z) be the second derivative of 5/6*z**3 + 7/80*z**5 - z**2 - 3/8*z**4 - 1/120*z**6 + 33*z + m. What is y in s(y) = 0?
1, 2
Let j(n) = -n**2 - 2*n - 1. Let x be j(-6). Let k(r) = 65*r**2 + 120*r - 185. Let m(w) = 8*w**2 + 15*w - 23. Let t(o) = x*m(o) + 3*k(o). Factor t(i).
-5*(i - 1)*(i + 4)
Suppose -4*i = 5*a + 33, -49*a + 51*a + 4*i = -42. Factor -1089/2*s**2 - 33*s**a - 1/2*s**4 + 0*s + 0.
-s**2*(s + 33)**2/2
Solve -4*a**2 + 70*a**4 + 2*a**5 + 48*a**4 + 114*a - 190*a**4 + 58 + 18*a**4 - 116*a**3 = 0.
-1, 1, 29
Let l = 17633 + -123430/7. Suppose 1/7*d - l*d**2 + 0 = 0. What is d?
0, 1
Let d = -480 - -497. Suppose -d*z = -14*z. Factor 0 + 1/8*r**3 + 0*r + z*r**2.
r**3/8
Determine v so that -2*v**2 + 82*v + 4*v**2 - 20 - 107*v - 7*v**2 = 0.
-4, -1
Factor 2/5*n**3 - 34/5*n**2 - 1134 - 1098/5*n.
2*(n - 35)*(n + 9)**2/5
Let h = 90058 + -270166/3. Factor 2/3*b**4 - h*b**3 - 4/3*b + 10/3*b**2 + 0.
2*b*(b - 2)*(b - 1)**2/3
Suppose -609 = -x + r, 5*x = 2*r + 49 + 2984. Let g be -14*x/(-10) + -5. Factor 2*z + g - 27*z - 5*z**2 - 812.
-5*(z - 1)*(z + 6)
Let r(k) be the first derivative of k**6/120 - 23*k**5/20 + 529*k**4/8 + k**3/3 + k**2 + 49. Let l(c) be the third derivative of r(c). Factor l(s).
3*(s - 23)**2
Determine t so that -70 - 114*t**3 - 159 + 136*t + 252*t**2 - 22*t**3 - 27 + 4*t**4 = 0.
-1, 1, 2, 32
Suppose 0 = 8*a - 10*a + 4. What is y in a*y**2 - 60*y**2 + 140*y - 70*y**2 - 117*y**2 - 20 = 0?
2/7
Suppose -666*k = -676*k + 120. Let v(g) be the first derivative of k*g + 1/4*g**4 - 9 + 7/3*g**3 + 8*g**2. Factor v(q).
(q + 2)**2*(q + 3)
Let y(c) be the third derivative of -c**5/60 - 7*c**4/12 - 6*c**3 - c**2 - 104. Let b be y(-4). Determine t so that 0 + 0*t**2 - 1/6*t**b + 0*t + 2/3*t**3 = 0.
0, 4
Let r be (-4 - (39680/2300)/(-4))/(6/3855735). Suppose -159744/23*q**3 + 8192/23*q**4 - 3796416/23*q + 1168128/23*q**2 + r = 0. What is q?
39/8
Let b(m) be the second derivative of 7/6*m**3 - 22 + 1/60*m**5 + 1/3*m**4 - 2*m - 49/3*m**2. Factor b(n).
(n - 2)*(n + 7)**2/3
Let s(i) = i**3 + 3*i**2 - 98*i - 478. Let o be s(-6). Factor -1/2 + a**4 - 3/2*a - 1/2*a**o + 3/2*a**3.
(a - 1)*(a + 1)**2*(2*a + 1)/2
Let b(x) be the second derivative of x**5/4 + 95*x**4/6 + 545*x**3/2 + 2025*x**2 - 2253*x. Factor b(h).
5*(h + 5)