 the third derivative of d**6/1260 + 23*d**5/210 + 15*d**4/28 + 101*d**3/3 + 4*d**2 + 3. Let k(v) be the first derivative of r(v). Factor k(z).
2*(z + 1)*(z + 45)/7
Let m(x) be the second derivative of 2*x**6/45 - 12*x**5/5 + 358*x**4/9 - 136*x**3 + 578*x**2/3 - 5*x - 53. Determine q, given that m(q) = 0.
1, 17
Solve 5*b**2 - 5*b**3 + 16*b**2 + 74*b + 11*b + 75 - 16*b**2 = 0.
-3, -1, 5
Let w be (-13)/(572/24) + 1552/264. Solve 8/3*y + w - 20/3*y**2 + 2*y**3 = 0.
-2/3, 2
Let w = -385 + 587. Suppose -4*i - w = -4*c + i, -5*i - 154 = -3*c. Let -211*q**3 - 112*q**2 - c*q**4 - 92*q**4 - 16*q - 10*q**3 - 15*q**3 = 0. What is q?
-1, -2/5, -2/7, 0
Let d = 7 + -5. Let r = 2884 + -2789. Factor 53*h**2 - r*h**d + 45*h**2.
3*h**2
Let z(d) be the second derivative of -5/6*d**4 + 9/4*d**5 + 0*d**3 - 2*d**6 + 25/42*d**7 + 32*d + 0*d**2 + 0. Suppose z(g) = 0. What is g?
0, 2/5, 1
Suppose 0 = -3*l + 2*l + 16. Factor 192 - 11*s + l*s + 54*s - 11*s + 3*s**2.
3*(s + 8)**2
Let t(y) be the third derivative of y**5/15 + 35*y**4/3 - 1274*y**3 - y**2 - 195*y - 3. Suppose t(l) = 0. Calculate l.
-91, 21
Let n be (26/(-39)*(-10)/(-9))/((-33)/99). Find s, given that -2*s**2 - 2/9 + n*s = 0.
1/9, 1
Let m be ((-7052)/287)/43*(-7)/6. Factor -2/3*j + 4/3*j**3 - 2/3 - m*j**5 - 2/3*j**4 + 4/3*j**2.
-2*(j - 1)**2*(j + 1)**3/3
Let s = -99581 - -99586. Determine o so that -o**s + 0*o - 5/4*o**4 + 0 + 0*o**2 - 1/4*o**3 = 0.
-1, -1/4, 0
Let f(b) be the second derivative of -b**6/180 - b**5/24 + 13*b**4/72 - 7*b**3/36 + 10*b + 6. Find q, given that f(q) = 0.
-7, 0, 1
Factor 1314/5*j**2 - 3036/5*j + 132/5*j**3 + 3/5*j**4 + 1587/5.
3*(j - 1)**2*(j + 23)**2/5
Let q(h) be the first derivative of 0*h**2 + 0*h + 5/3*h**3 + 5/2*h**4 + h**5 - 22. Find p, given that q(p) = 0.
-1, 0
Let w = 18131/2 + -9065. Let s(t) be the first derivative of 3/4*t**3 - 1/20*t**5 + 17 + 0*t**4 - w*t**2 - 3*t. Solve s(g) = 0 for g.
-3, -1, 2
Suppose 72*n - 436 + 4 = -4*n - 140*n. Factor 3/7*s**n + 78/7*s + 0.
3*s*(s + 26)/7
Let z(r) be the third derivative of -27*r**6/10 + 1284*r**5 + 4283*r**4/6 + 476*r**3/3 + 2*r**2 + 28*r + 7. Determine k, given that z(k) = 0.
-1/9, 238
Let f(a) be the third derivative of -a**5/15 - a**4 + 14*a**3/3 - 467*a**2. Factor f(n).
-4*(n - 1)*(n + 7)
Let b(v) be the third derivative of -1/100*v**5 - 4/5*v**3 - 3/20*v**4 + 7*v + 3*v**2 + 0. Solve b(f) = 0 for f.
-4, -2
Solve 0 + 5/4*x**2 + 195/4*x = 0.
-39, 0
Let k(n) be the second derivative of -n**4/24 + 85*n**3/12 - 273*n**2/2 - 3*n + 127. Factor k(o).
-(o - 78)*(o - 7)/2
Factor 1515/2*v + 3/2*v**2 - 759.
3*(v - 1)*(v + 506)/2
Let v(h) be the third derivative of h**6/20 + 607*h**5/20 + 303*h**4/8 + 383*h**2. Let v(t) = 0. What is t?
-303, -1/2, 0
Let n(r) = -3*r**2 + 15836*r - 12561127. Let p(i) = 23*i**2 - 126681*i + 100489017. Let d(w) = 17*n(w) + 2*p(w). Suppose d(l) = 0. What is l?
1585
Suppose -3111*d + 3086*d = -50. Factor -2 + 2/3*o + 2*o**d - 2/3*o**3.
-2*(o - 3)*(o - 1)*(o + 1)/3
Find d such that 220/17*d + 2/17*d**2 + 218/17 = 0.
-109, -1
Let m(v) be the second derivative of -v**5/10 + 73*v**4/3 - 6097*v**3/3 + 53868*v**2 - 4310*v. Suppose m(f) = 0. Calculate f.
12, 67
Let u(s) = 8*s - 54. Let j be u(7). Factor -18 - 2048*k**4 + 508*k**2 - 348*k - 41*k**2 - 1765*k**j + 3712*k**3.
-2*(k - 1)**2*(32*k + 3)**2
Factor -1106/5 + 146/5*a**2 + 2/5*a**3 - 962/5*a.
2*(a - 7)*(a + 1)*(a + 79)/5
Let w be 0/(-13)*(-2)/(-4) - -4. Let h(z) be the first derivative of -z**w + 0*z + 0*z**2 + 4/3*z**3 - 2. Factor h(c).
-4*c**2*(c - 1)
Let y(o) be the second derivative of 0*o**3 - 1/90*o**5 + 1/72*o**4 + 1/360*o**6 + 0 + 1/2*o**2 - 8*o. Let h(a) be the first derivative of y(a). Factor h(u).
u*(u - 1)**2/3
Let m = 730/873 - 4237/6111. Factor 1/7*w + 0 + 2/7*w**2 + m*w**3.
w*(w + 1)**2/7
Let b(j) be the first derivative of 2*j**3 - 123 - 54*j**2 + 21*j + 11*j - 2*j**2 + 7*j**2. Solve b(n) = 0.
1/3, 16
Let l(v) be the third derivative of -v**6/120 - 19*v**5/60 + 145*v**4/24 - 125*v**3/6 - 1422*v**2. Determine q, given that l(q) = 0.
-25, 1, 5
Suppose 39*m + 39*m - 4*m = 222. Let p(l) be the first derivative of -l**2 + 8*l - 1/3*l**m - 11. Factor p(k).
-(k - 2)*(k + 4)
Let j(t) be the first derivative of -4*t**4 - 64/3*t**3 + 4*t**5 + 64*t**2 - 64*t - 12 - 2/3*t**6. Factor j(x).
-4*(x - 2)**3*(x - 1)*(x + 2)
Let g(s) be the second derivative of 1/90*s**6 + 49/36*s**4 + 122*s + 0 + 1/4*s**5 + 19/6*s**3 + 11/3*s**2. What is u in g(u) = 0?
-11, -2, -1
Suppose -11*y + 44*y + 100*y + 55*y = 5*y. Determine i so that 2/5*i**2 - 8/5*i**4 - 6/5*i**3 + y + 0*i = 0.
-1, 0, 1/4
Let w be (-42904)/(-5190) - (14 - -2)*3/6. Let m(p) be the first derivative of 27 + 16/9*p**3 + 0*p**2 - 1/9*p**6 + 2/3*p**4 + 0*p - w*p**5. Factor m(i).
-2*i**2*(i - 2)*(i + 2)**2/3
Solve 9/5*w**2 - 36/5 - 32*w = 0 for w.
-2/9, 18
Let l(s) be the third derivative of -s**5/15 - 215*s**4/3 - 1094*s**2. Find y, given that l(y) = 0.
-430, 0
Let c(u) = -15*u**3 - 2*u**2 - 14*u - 11. Let p be c(-1). Suppose 10 = 5*i - 10. What is s in 3*s**4 - 2*s**4 - 5*s**i + 12*s**3 - p*s = 0?
-1, 0, 2
Let h(d) be the second derivative of -7/12*d**3 + 7/40*d**5 + 1/4*d**2 - 41*d - 1/24*d**4 + 0. Find c such that h(c) = 0.
-1, 1/7, 1
Let q(b) be the first derivative of 0*b + 59 - 4/3*b**3 + 26*b**2. Factor q(n).
-4*n*(n - 13)
Suppose 53*y - 12832 = -12726. Suppose 1/2*q**3 - 9 + 2*q**y - 3/2*q = 0. Calculate q.
-3, 2
Let v(b) be the first derivative of -2*b**3/9 - 436*b**2 - 5758. Suppose v(t) = 0. Calculate t.
-1308, 0
Let s(n) be the second derivative of 3/4*n**3 + 1/20*n**6 + 0 + 0*n**2 + 42*n - 1/8*n**4 - 9/40*n**5. Factor s(b).
3*b*(b - 3)*(b - 1)*(b + 1)/2
Let u be (-12)/30 - ((-111)/15 + 2). Factor -13983*h - 13039*h - 3465*h + 3550*h - 732*h**2 - 10658 - u*h**3.
-(h + 73)**2*(5*h + 2)
Factor -216/7 - 150/7*i**2 + 316/7*i + 3*i**3 + 1/7*i**4.
(i - 2)**3*(i + 27)/7
Factor 0*p**2 - 6*p**3 - 1/6*p**5 + 13/6*p**4 + 0 + 0*p.
-p**3*(p - 9)*(p - 4)/6
Let m(v) = -v**3 + 20*v**2 - 27*v + 154. Let f be m(19). Let g(o) be the first derivative of 6*o**f + 0*o + 8/3*o**3 + 7 - o**4. Factor g(i).
-4*i*(i - 3)*(i + 1)
Let c be (-2412)/(-21440) + 3/16. Let r(o) be the first derivative of 24 + c*o**2 + 0*o + 3/20*o**4 + 2/5*o**3. Factor r(y).
3*y*(y + 1)**2/5
Suppose 314928 - 1296*y + 4/3*y**2 = 0. What is y?
486
Let n(a) be the first derivative of -2*a**3/11 + 210*a**2/11 - 1206*a/11 + 5251. Find i such that n(i) = 0.
3, 67
Factor -1198*a - 128 + 5 - 59 + a**2 + 1109*a.
(a - 91)*(a + 2)
Let k(l) = 2*l**3 + 21*l**2 + 9*l - 9. Let w be k(-10). Let t be (w/4)/(220/528). Solve 0 + 6/5*h**2 + 3/5*h**3 + t*h = 0 for h.
-1, 0
Let y(f) be the second derivative of -f**4/48 - 145*f**3/24 + 4194*f. Factor y(i).
-i*(i + 145)/4
Let t(c) be the first derivative of -54 - 961/2*c - 1/6*c**3 - 31/2*c**2. Factor t(m).
-(m + 31)**2/2
Factor -317394/5*n + 154551/5*n**2 + 2748/5*n**3 + 12/5*n**4 + 160083/5.
3*(n - 1)**2*(2*n + 231)**2/5
Let j(s) = 6*s**3 + 268*s**2 + 166*s - 90. Let n(g) = -6*g**3 - 266*g**2 - 166*g + 89. Let l(q) = -5*j(q) - 6*n(q). Solve l(m) = 0.
-42, -1, 1/3
Let q(r) = -31*r**2 + 107 + 11*r + 2*r**3 - 13*r**3 - 88. Let v(m) = 23*m**3 + 63*m**2 - 23*m - 37. Let w(k) = -13*q(k) - 6*v(k). Factor w(d).
5*(d - 1)*(d + 1)*(d + 5)
Let p be -17 + 17 - 2/(-8). Let o = -211/4 + 53. Solve -o*a**2 + p*a + 0 = 0 for a.
0, 1
Suppose 4*m - 4 = 0, -3*m + 8 + 10 = 5*a. Factor 0*d**5 - 80*d - 125*d**2 + 8*d**5 - 6 - 14 - 35*d**4 - 13*d**5 - 95*d**a.
-5*(d + 1)**3*(d + 2)**2
Let p = 33077/21 - 1575. Let w(h) be the second derivative of 0*h**2 - p*h**3 + 0 - 1/21*h**4 + 27*h. Factor w(j).
-4*j*(j + 1)/7
Find n, given that 47916 + 2178*n + 33*n**2 + 1/6*n**3 = 0.
-66
Let w(c) be the third derivative of c**7/42 - 3*c**6 + 851*c**5/6 - 3045*c**4 + 206045*c**3/6 - 5181*c**2. Factor w(x).
5*(x - 29)**2*(x - 7)**2
Let c(f) be the first derivative of 96/7*f**2 - 25/21*f**6 + 36 + 38/7*f**4 - 18/7*f**5 + 352/21*f**3 + 32/7*f. Let c(h) = 0. What is h?
-2, -1, -2/5, 2
Let w = -6742/45 - -1352/9. Let d(c) be the first derivative of w*c**3 + 0*c + 0*c**2 - 1/10*c**4 - 11. Factor d(i).
-2*i**2*(i - 3)/5
Suppose -2*m - 5*a + 19 = 0, m = -4*m - a + 36. Suppose 3*u - 8*u = m*u. Factor 0*k + 0*k**2 + 2/9*k**3 + u.
2*k**3/9
Let x(o) be the th