he third derivative of d**8/2016 + d**7/252 + d**6/240 - d**5/72 - d**4/36 + 855*d**2. Factor q(r).
r*(r - 1)*(r + 1)**2*(r + 4)/6
Find a such that 954*a + 18*a**3 - 1/6*a**4 - 1511/3*a**2 - 2809/6 = 0.
1, 53
Suppose 308*t - 4*n = 304*t + 4, 15 = 5*n. Let l(j) be the first derivative of 0*j**2 + 0*j + 1/3*j**6 + 6/5*j**5 - 14 - 8/3*j**3 + 0*j**t. Factor l(o).
2*o**2*(o - 1)*(o + 2)**2
Factor -702/7*t**2 - 706/7 - 1410/7*t + 2/7*t**3.
2*(t - 353)*(t + 1)**2/7
Let v(q) = -7*q**2 - q + 1. Let b(a) = -60*a**2 + 2804*a - 2800. Let g(c) = -b(c) + 8*v(c). Factor g(l).
4*(l - 702)*(l - 1)
Let p be (-5)/(4 - 2 - 161/28). Solve -10/3*y**2 - 2/3*y**3 + 16/3 - p*y = 0 for y.
-4, -2, 1
Let q be 70/(-28) - 30/(-4). Suppose x + 2*i = -3, 3*x - q*x = -5*i - 21. What is l in 4/5*l**x + 8*l**2 + 0 + 20*l = 0?
-5, 0
Let x be (9/18)/(2/24 + 22/132). Let b(q) be the first derivative of 0*q + 14 - q**x + 1/3*q**3. Factor b(m).
m*(m - 2)
Factor -41/2*s**2 + 3/2*s**3 - 32*s + 30.
(s - 15)*(s + 2)*(3*s - 2)/2
Let i = 124458 - 1369022/11. Factor i*f + 2/11*f**2 + 14/11.
2*(f + 1)*(f + 7)/11
Suppose 2*n + 2334 = -5*a, -101*n - 938 = 2*a - 98*n. Let r = a - -471. Solve -4/9*f**2 + 2/9 + 2/9*f**4 - 2/9*f + 4/9*f**3 - 2/9*f**r = 0 for f.
-1, 1
Let n(h) = -8*h**2 + 405*h - 5000. Let b(s) = -44*s**2 + 2228*s - 27500. Let v(y) = -5*b(y) + 28*n(y). Factor v(a).
-4*(a - 25)**2
Let k = 164311 + -164306. Factor -22/3*h**2 - 8*h - 2/3*h**3 + 2*h**4 - 8/3 + 2/3*h**k.
2*(h - 2)*(h + 1)**3*(h + 2)/3
Let k(h) be the second derivative of -h**7/147 - 17*h**6/21 - 922*h**5/35 - 712*h**4/21 + 352*h**3 + 1008*h**2 + 1263*h. Suppose k(v) = 0. Calculate v.
-42, -2, -1, 2
Let p(k) = 11*k**2 - 55*k + 12. Let b be p(5). Let s(o) = -4*o**2 + 304*o - 5776. Let a(g) = -10*g**2 + 760*g - 14440. Let m(t) = b*s(t) - 5*a(t). Factor m(u).
2*(u - 38)**2
Let u(j) be the first derivative of -j**3/3 - 6*j**2 - 32*j + 250. What is s in u(s) = 0?
-8, -4
Suppose -3*b = 2*d + 2, 195*b - d = 190*b + 1. Let v(a) be the third derivative of 1/12*a**4 + 0 + b*a**3 + 7*a**2 + 0*a + 1/30*a**5. Let v(q) = 0. Calculate q.
-1, 0
Let f(p) = -105*p**3 - 49*p**2 + 39*p - 11. Let y(n) = -210*n**3 - 97*n**2 + 77*n - 23. Let c(i) = 13*f(i) - 6*y(i). Solve c(w) = 0.
-1, 1/7, 1/3
Factor -268/3*n - 1/3*n**4 + 7/3*n**3 + 18*n**2 + 280/3.
-(n - 10)*(n - 2)**2*(n + 7)/3
Let d(l) = -393*l**3 - 9639*l**2 - 16704*l + 2499. Let r(c) = 49*c**3 + 1205*c**2 + 2088*c - 312. Let o(f) = -4*d(f) - 33*r(f). Determine n so that o(n) = 0.
-25, -2, 2/15
Suppose -13*k - 9*k + 134 = 24. Let s(u) be the first derivative of 3/14*u**4 + 3/35*u**k - 1/7*u**3 + 0*u - 19 - 3/7*u**2. What is o in s(o) = 0?
-2, -1, 0, 1
Let l be (-2 - (-9)/6)/(-1). Let w be ((-2)/12 + 2/(-36))/(188/(-282)). Solve l*z**2 + 0 - 1/6*z**3 - 1/2*z**4 + w*z - 1/6*z**5 = 0 for z.
-2, -1, 0, 1
Let l(b) be the second derivative of -8/3*b**3 + 1/360*b**6 + 0 - 1/60*b**5 - 1/8*b**4 - 6*b + 0*b**2. Let x(c) be the second derivative of l(c). Factor x(n).
(n - 3)*(n + 1)
Let s = -6 - 39. Let o = -43 - s. Factor 67 - 50*q - 17 + 5*q**o + 75.
5*(q - 5)**2
Suppose -1/3*g**2 - 756*g - 428652 = 0. What is g?
-1134
Factor -78*w - 50*w + 43 + 61*w - 36*w - 70*w + 4*w**2.
(w - 43)*(4*w - 1)
Let u(i) be the first derivative of -3*i**5/20 - 9*i**4/4 - 15*i**3/2 - 21*i**2/2 - 66*i + 47. Let d(y) be the first derivative of u(y). Factor d(g).
-3*(g + 1)**2*(g + 7)
Let z be 39/(-9)*26 + (4 - 1). Let m = z - -111. Find l such that -10/3*l**3 - m*l + 0 - 14/3*l**2 = 0.
-1, -2/5, 0
Let u(v) = 19 - 22*v**2 + 15*v - 20*v**3 + 7*v**2 - 4 + 10*v**2. Let i(n) = n**4 + 20*n**3 + 6*n**2 - 16*n - 15. Let y(p) = -5*i(p) - 4*u(p). Factor y(s).
-5*(s - 1)*(s + 1)**2*(s + 3)
Let y be 1*5/(-4*10/(-40)). Factor -3/7*r**4 + 0*r + 0 - 9/7*r**2 + 3/7*r**y - 15/7*r**3.
3*r**2*(r - 3)*(r + 1)**2/7
Let w(m) be the first derivative of -4*m**3/3 + 29*m**2 + 30*m + 529. Solve w(x) = 0.
-1/2, 15
Let q = 1119 + -1116. Suppose -w + h = 3*w - q, w - 4*h - 12 = 0. Find b, given that 9/2*b**3 + 3*b**2 + 0 + 3/2*b**4 + w*b = 0.
-2, -1, 0
Let m be 15 - ((-100232)/102)/(-67). Find p, given that 13/3 + m*p**2 - 14/3*p = 0.
1, 13
Let s(f) be the second derivative of -3087*f**5/10 - 2352*f**4 - 7168*f**3 - 32768*f**2/3 + 9929*f. Factor s(h).
-2*(21*h + 32)**3/3
Let a(p) be the third derivative of -11/180*p**5 + 0*p - 63*p**2 + 1/720*p**6 + 0 + 0*p**3 + 7/48*p**4. Suppose a(c) = 0. What is c?
0, 1, 21
Suppose -1890 + 948*p - 3/2*p**2 = 0. What is p?
2, 630
Let s(t) be the second derivative of -5*t**4/4 - 100*t**3/3 - 385*t**2/2 + 8005*t. Factor s(v).
-5*(v + 11)*(3*v + 7)
Let t = -1767 + 1886. Let f be 918/t*(-2)/(-6). Find u, given that 0*u - f + 2/7*u**2 = 0.
-3, 3
Factor -2390/7*c**3 - 2/7*c**5 + 110/7*c**4 + 25610/7*c**2 - 135200/7*c + 281216/7.
-2*(c - 13)**3*(c - 8)**2/7
Let x(o) = -2*o**2 + 286*o + 1222. Let n(f) = -3*f**2 + 264*f + 1223. Let m(k) = -3*n(k) + 2*x(k). Factor m(u).
5*(u - 49)*(u + 5)
Let n(x) = 3*x**3 + 24*x**2 + 57*x - 94. Let l(h) = 3*h - 4. Let v(r) = -10*l(r) + n(r). Solve v(d) = 0.
-6, -3, 1
Suppose -23 + 40 = 313*q + 17. Factor q + 4/7*y**3 + 8/7*y - 2*y**2 + 2/7*y**4.
2*y*(y - 1)**2*(y + 4)/7
Determine k, given that 34 - 140*k**5 - 160*k**2 + 168*k**3 - 156*k - 10 + 136*k**4 + 128*k = 0.
-1, -3/7, 2/5, 1
Let m be 1/(149281/(-14927) - -10). Let o = m + 1359. Find w, given that 44/9*w + 242/9 + 2/9*w**o = 0.
-11
Let g(o) = -8*o**2 + 57*o - 8. Let p be g(7). Let z be (-1 - p) + 2/1. Solve -1/2*i**z - 1/2*i + 1 = 0.
-2, 1
Let y(b) = 12*b**5 - 56*b**4 + 12*b**3 + 272*b**2 + 160*b. Let z(x) = 4*x**5 - 19*x**4 + 4*x**3 + 91*x**2 + 54*x. Let u(f) = 5*y(f) - 16*z(f). Factor u(o).
-4*o*(o - 4)**2*(o + 1)**2
Solve -208/7*l + 4/7*l**2 - 432/7 = 0 for l.
-2, 54
Let i be 34/(-391) + (-94)/(-23). Suppose k - i = -2*n, 3*k - 1 = -5*n + 10. Determine h, given that -2*h**4 + 4*h + k*h**2 - 1/4*h**5 - 15/4*h**3 + 0 = 0.
-4, -1, 0, 1
Let q(w) be the first derivative of 0*w - 13/3*w**4 - 2/9*w**6 + 106 - 12/5*w**5 + 100/3*w**2 + 20*w**3. What is j in q(j) = 0?
-5, -1, 0, 2
Determine q so that 0 - 14/5*q + 2/5*q**3 - 12/5*q**2 = 0.
-1, 0, 7
Let a(u) be the first derivative of -u**5/20 - 27*u**4/8 - 51*u**3/4 + 108. Solve a(d) = 0 for d.
-51, -3, 0
Let z(y) = -6*y - 1. Let p(c) = -5*c**2 + 10430*c - 5376835. Let m(v) = -p(v) - 10*z(v). Find t such that m(t) = 0.
1037
Factor -5*b**3 + 33098 + 33103 + 15*b**2 - 66216 + 5*b.
-5*(b - 3)*(b - 1)*(b + 1)
Let l(y) be the first derivative of y**7/42 + y**6/15 - 29*y**5/30 - y**4 + 4*y**3/3 + 5*y**2/2 + 202. Let m(w) be the third derivative of l(w). Factor m(g).
4*(g - 2)*(g + 3)*(5*g + 1)
Let x be 10222/2152*(-6)/(-3). Determine z so that 21 + x*z - 1/2*z**2 = 0.
-2, 21
Factor -105*k**2 - 600 - 8*k**3 + k**3 - 490*k - 5*k**3 + 7*k**3.
-5*(k + 2)*(k + 4)*(k + 15)
Let b(q) = 218*q + 3272. Let y be b(-15). Let f(t) be the third derivative of 1/270*t**5 + 14*t**y + 121/27*t**3 + 11/54*t**4 + 0 + 0*t. What is i in f(i) = 0?
-11
Let n(i) be the first derivative of i**3 + 1503*i**2/2 + 335. Determine g, given that n(g) = 0.
-501, 0
Suppose -j - 18 = -5*x, 2*x + 13 = 4*j - x. Let -3*k**2 - 42*k + 5*k**3 + 10*k + j*k**3 + 48 - 65*k**2 = 0. What is k?
-1, 2/3, 6
Let h(v) be the first derivative of 1/10*v**5 + 6*v - 1/3*v**4 - 1/3*v**3 + 20 + 2*v**2. Let p(d) be the first derivative of h(d). Suppose p(w) = 0. What is w?
-1, 1, 2
Suppose 153*s**2 + 90*s - 151*s**2 - 3*s**3 + 82 - 10*s + 14 = 0. What is s?
-4, -4/3, 6
Let p be 24/(-4) + 5 + 4. Let h(d) = d**2 - 3*d - 25. Let r(l) = 2*l - 1. Let j(m) = p*r(m) + h(m). Solve j(q) = 0 for q.
-7, 4
Solve -3/8*a**5 + 0 + 243/8*a**2 - 135/8*a**3 + 33/8*a**4 - 81/4*a = 0.
0, 2, 3
Let a(h) = h**3 + h**2 - h + 2. Let u(x) = -3*x**4 - 533*x**3 - 23225*x**2 + 24833*x + 47522. Let r(m) = -2*a(m) - u(m). What is s in r(s) = 0?
-89, -1, 2
Let b(t) be the second derivative of -1/4*t**2 - 121*t + 1/24*t**4 - 1/12*t**3 + 1/40*t**5 + 0. Determine l, given that b(l) = 0.
-1, 1
Let d(f) = f**2 - f. Let y(p) = -p**3 + 3*p**2 + 2*p - 7. Let r be y(3). Let w(j) = -8*j**2 - 12*j - 28. Let h(q) = r*w(q) - 12*d(q). Factor h(t).
-4*(t - 7)*(t + 1)
Let w(y) be the third derivative of y**5/360 - y**4/3 + 47*y**3/36 + 8308*y**2 - 2*y. Find r such that w(r) = 0.
1, 47
Let -2568/7