f g**7/2520 - g**6/60 - 13*g**5/120 + 5*g**4/4 - g**3/3 - 293*g. Let c(l) be the third derivative of n(l). Factor c(k).
(k - 13)*(k + 1)
Let y(s) = -116*s**3 - 648*s**2 - 932*s - 416. Let g(c) = c**4 - c**2 - 2*c + 2. Let a(j) = -4*g(j) - y(j). Find n such that a(n) = 0.
-3, -1, 34
Let v be ((-85)/153)/(-1) + 1/3. Factor -v*f**4 - 7/3*f**3 - 2*f**2 + 0*f - 1/9*f**5 + 0.
-f**2*(f + 2)*(f + 3)**2/9
Let z be (31955/(-715) - -45) + 49/52. Factor -45/4*i**2 + 25 - z*i**3 + 15*i.
-5*(i - 2)*(i + 1)*(i + 10)/4
Let r(w) = -3*w**2 - 1880*w - 299568. Let d(v) = 12*v**2 + 7512*v + 1198272. Let q(k) = 2*d(k) + 9*r(k). Factor q(u).
-3*(u + 316)**2
Let x(i) be the second derivative of 3*i**5/20 + 1103*i**4/4 - 2209*i**3/2 + 3315*i**2/2 + 9423*i. Factor x(z).
3*(z - 1)**2*(z + 1105)
Let o be -1*2/5 + -37*30/(-2220). Let s(j) be the first derivative of 0*j - o*j**4 + 8 + 2/5*j**2 + 2/15*j**3. Factor s(a).
-2*a*(a - 2)*(a + 1)/5
Suppose -2*y - 1 = -9. Suppose 4*k + k - 20 = 0. Factor -2*n**3 - 39*n**4 + n + n**5 + 2 + 80*n**4 - y*n**2 - 39*n**k.
(n - 1)**2*(n + 1)**2*(n + 2)
Let g(s) = s**2 + 98*s - 1075. Let d be g(10). Let i(n) be the third derivative of 1/12*n**5 + 0*n + d*n**2 - 3 + 0*n**3 - 5/6*n**4. Factor i(k).
5*k*(k - 4)
Let r be 50/125 + (-2)/(-10)*2*9. Let k(a) be the first derivative of 0*a + 8/27*a**3 - 1/18*a**r - 3 - 1/3*a**2. Determine l, given that k(l) = 0.
0, 1, 3
Let b(q) = -3*q**3 + 119*q**2 + 1327*q + 4219. Let v(c) = 2*c**3 - 60*c**2 - 666*c - 2110. Let u(d) = -3*b(d) - 5*v(d). Factor u(y).
-(y + 7)**2*(y + 43)
Let y = 621 - 619. Let z(n) be the first derivative of 10*n**y - 2/3*n**3 - 50*n - 6. Factor z(q).
-2*(q - 5)**2
Factor -1/7*t**2 - 984064/7 - 1984/7*t.
-(t + 992)**2/7
Let m(y) be the second derivative of -25*y**7/231 - 16*y**6/33 + 601*y**5/110 - 218*y**4/33 + 28*y**3/11 + 3090*y. What is j in m(j) = 0?
-7, 0, 2/5, 3
Let s(u) be the first derivative of 3*u**4/4 + 2*u**3 - 21*u**2/2 + 12*u + 1557. Factor s(q).
3*(q - 1)**2*(q + 4)
Let f(w) be the first derivative of -7*w**6/360 - w**5/120 + w**4/4 + w**3/3 - 11. Let o(j) be the third derivative of f(j). Factor o(x).
-(x + 1)*(7*x - 6)
Let w be ((-1)/(-2))/(51/34). Let q(s) = 3*s**3 - 351*s**2 - 352*s - 232. Let p be q(118). Factor r**p + 4/3*r + 0 - 8/3*r**2 + w*r**3.
r*(r - 1)*(r + 2)*(3*r - 2)/3
Let n = 1111/2 - 543. Let y be (-17)/2 + (-1364)/(-124). Suppose y*u**2 + n - 15*u = 0. Calculate u.
1, 5
Let w(r) be the second derivative of 11449*r**5/40 - 107*r**4/4 + 3*r**3/4 - 1306*r. Factor w(h).
h*(107*h - 3)**2/2
Let r be ((-120)/48)/(1*(-3)/6). Factor -17/4*x - 3/2 + x**4 - 7/2*x**2 + 0*x**3 + 1/4*x**r.
(x - 2)*(x + 1)**3*(x + 3)/4
Let s(j) = -7*j**3 - 266*j**2 - 4*j - 150. Let d be s(-38). Factor 0 + 0*h + 8/9*h**d + 14/9*h**3 - 4/9*h**4.
-2*h**2*(h - 4)*(2*h + 1)/9
Let w be -7 + -4 - ((-76518)/(-135))/(-26). Factor -9*j + j**3 + 1/5*j**4 - w - 3/5*j**2.
(j - 3)*(j + 2)*(j + 3)**2/5
Let p = -1724 - -1722. Let k(l) = 67*l**2 + 12*l. Let d(c) = -c**2 - 2*c + 2*c**2 + 3*c. Let y(w) = p*d(w) + k(w). Find b, given that y(b) = 0.
-2/13, 0
Let u(q) be the first derivative of -q**6/3 - q**5/10 + 8*q**4/15 - 4*q**3/15 - 137*q - 66. Let r(s) be the first derivative of u(s). Factor r(w).
-2*w*(w + 1)*(5*w - 2)**2/5
Let l(m) = 2*m**4 - 34*m**3 - 63*m**2 + 154*m + 283. Let r(x) = x**4 + x**3 + x**2 + 2*x + 1. Let n(z) = -l(z) + 3*r(z). Factor n(a).
(a - 2)*(a + 2)**2*(a + 35)
Let i be (-160)/45 - (5 - 9)*1. Let k be 28/12 + (-5)/15. Factor -i*r**k - 16/9 + 16/9*r.
-4*(r - 2)**2/9
Let l(y) be the first derivative of 22 + 0*y + 0*y**2 - 9/320*y**5 + 1/8*y**4 + 1/960*y**6 + 32/3*y**3. Let r(h) be the third derivative of l(h). Factor r(j).
3*(j - 8)*(j - 1)/8
Let y(c) be the third derivative of -c**6/30 + 7*c**5/15 - 24*c**3 - 1166*c**2. Suppose y(t) = 0. What is t?
-2, 3, 6
Suppose 0 = 4*v + 2*d - 16, -2*d = -d. Suppose z = -m + 8, -v*m + 5 = -5*z - 0. Factor 0 + 12*x**2 - 53*x - 4*x**z + 0*x**3 + 4 + 41*x.
-4*(x - 1)**3
Let y(m) = 6*m + 40. Let s be y(-5). Factor -14*d**4 + 45*d - 27*d**4 + d**5 + 4*d**5 - 60*d**2 + 61*d**4 - s*d**3.
5*d*(d - 1)**2*(d + 3)**2
Let l be (-2958)/187 - -11 - 1/(-2)*10. Factor 0 - l*x - 2/11*x**2.
-2*x*(x + 1)/11
Find h such that 507/2*h**2 + 182*h + 98/3 = 0.
-14/39
Let z(t) be the first derivative of 17/3*t**3 - 31/6*t**2 - 2/3*t - 21. Factor z(y).
(3*y - 2)*(17*y + 1)/3
Factor 10/9*o**2 + 14 - 104/9*o.
2*(o - 9)*(5*o - 7)/9
Let y(o) be the third derivative of -o**5/240 - 71*o**4/96 + 95*o**3/6 - 2159*o**2. Let y(p) = 0. Calculate p.
-76, 5
Suppose -49*i = 13*i + 4*i - 198. Factor -1/5*d**i + 2 + 19/5*d + 8/5*d**2.
-(d - 10)*(d + 1)**2/5
Suppose -m = -3*k - 3, 0 = -m + 5*k - 3*k + 3. Determine x so that 3*x**2 + 3705*x - 3*x**m + 1 - 3702*x - 4 = 0.
-1, 1
Let b(l) be the third derivative of -l**8/20160 - l**7/7560 + l**6/270 + l**5/30 + 28*l**4/3 + 261*l**2. Let n(a) be the second derivative of b(a). Factor n(k).
-(k - 3)*(k + 2)**2/3
Let z(o) = -19*o**3 - 11*o**3 - o**3 - 9*o**4 + 37*o**2 - 193*o + 8*o**3 + 489 + 589*o. Let k(y) = 2*y**4 + y**3 - 1. Let g(b) = 10*k(b) + 2*z(b). Factor g(d).
2*(d - 11)**2*(d + 2)**2
Let r(c) be the second derivative of -5*c**7/42 + 37*c**6/6 - 179*c**5/2 + 2155*c**4/6 - 3965*c**3/6 + 1265*c**2/2 - 2724*c. What is y in r(y) = 0?
1, 11, 23
Let v(h) = -13*h + 185. Let d be v(15). Let y be (d/100*5)/(6/(-8)). Determine g so that y*g**2 + 20/3*g + 50/3 = 0.
-5
Let k be (-9)/(-55)*74350/13383. Factor -k*j**3 - 324/11 - 184/11*j**2 - 882/11*j.
-2*(j + 9)**2*(5*j + 2)/11
Let i(t) be the first derivative of -t**4/3 - 40*t**3/9 - 34*t**2/3 - 32*t/3 + 1332. Suppose i(b) = 0. What is b?
-8, -1
Let q(c) = -3*c**3 - 18*c**2 + 5*c + 20. Let n(d) = -3*d**3 + 19 + 28 + 6*d - 18*d**2 + 10 - 36. Let u(x) = -2*n(x) + 3*q(x). Factor u(o).
-3*(o - 1)*(o + 1)*(o + 6)
Let z(q) be the second derivative of q**8/3360 + q**7/105 - 13*q**6/360 - 7*q**4/4 + 2*q**2 - 24*q - 2. Let w(y) be the third derivative of z(y). Factor w(m).
2*m*(m - 1)*(m + 13)
Let w be -2*2/(-4)*5. Let s(c) = 9*c**3 + c**2 + c + 4. Let d be s(0). Factor -31*y**3 - w*y**4 + 20 + 6*y**3 + d*y**2 + 25*y - 19*y**2.
-5*(y - 1)*(y + 1)**2*(y + 4)
Let a be (-8)/6*(-351)/156. Let d(r) be the second derivative of -40*r**2 - 24*r - 5/12*r**4 - 20/3*r**a + 0. Find f such that d(f) = 0.
-4
Let j(w) = w + 2. Suppose 6*u = -4*a + u - 1, 4*a - 2*u = 6. Let k be j(a). Determine f, given that -f + 7 + 9*f**4 - 3*f - 16*f + 37*f**2 - 30*f**k - 3 = 0.
2/3, 1
Let u(h) be the first derivative of -h**4/22 + 86*h**3/33 - 160*h**2/11 + 312*h/11 + 7531. What is g in u(g) = 0?
2, 39
Let h = -236117/83 + 2845. Let l = 285/166 - h. Factor -3/4 + l*s - 3/4*s**2.
-3*(s - 1)**2/4
Suppose -q + 5*y - 2084 = 3*q, 2068 = -4*q + y. Let o be 8/(-44) - q/660. Factor 18/5*z - 27/5 - o*z**2.
-3*(z - 3)**2/5
Factor -41*i**4 - 10*i**4 + 17*i - 3*i**5 - 59*i + 77*i**3 - 129*i**2 - 212*i**3.
-3*i*(i + 1)**3*(i + 14)
Let a(w) be the second derivative of w**5/160 - 17*w**4/48 - 19*w**3/6 - 8*w + 54. Find u such that a(u) = 0.
-4, 0, 38
Solve 84*d**2 + 87*d**2 + 100467 + 95*d**2 - 342*d**2 + 79*d**2 - 1098*d = 0.
183
Let i(h) be the third derivative of h**6/180 - h**5/10 - 11*h**4/18 - 2*h**2 - 51*h. Factor i(w).
2*w*(w - 11)*(w + 2)/3
Let d(q) be the second derivative of q**6/15 + 17*q**5/10 + 49*q**4/3 + 220*q**3/3 + 168*q**2 + q - 411. Factor d(n).
2*(n + 2)**2*(n + 6)*(n + 7)
Let u(o) be the second derivative of -o**4/48 + 103*o**3/12 + 9504*o. Determine z so that u(z) = 0.
0, 206
Let p be (-319)/(-174) + -10*(-2)/24. Solve -p*m + 5/6*m**5 + 17/6*m**4 - 2/3 - 13/6*m**2 + 11/6*m**3 = 0 for m.
-2, -1, -2/5, 1
What is w in -642*w**2 + 24*w**3 + 1058 + 983*w**2 + 12788*w + 765*w**2 = 0?
-23, -1/12
Let k(i) = 8673*i - 52036. Let n be k(6). Solve 13/3*p**5 - 53/3*p**n + 2*p - 67/3*p**4 + 0 + 101/3*p**3 = 0.
0, 2/13, 1, 3
Let y(q) be the first derivative of -5*q**3/12 + 19*q**2/4 + 4*q + 1543. Factor y(w).
-(w - 8)*(5*w + 2)/4
Let k(y) = -136*y**2 - 5303*y + 39. Let w be k(-39). Find s, given that 3/2*s**2 + s - 1/2*s**4 + w + 0*s**3 = 0.
-1, 0, 2
Factor 5*g - 2*g**3 + 4*g**2 + 66*g**2 - 140*g - 81*g - 8*g**2.
-2*g*(g - 27)*(g - 4)
Let h(a) = 20*a**4 + 46*a**3 - 6*a**2 - 50*a - 40. Let x(z) = z**5 - z**4 + 14*z**2 + z. Let w(