j**5/60 + j**4/4 + 89*j**3/6 - 41*j**2. Let p(f) be the first derivative of s(f). Factor p(i).
2*(i - 3)*(i - 1)*(i + 1)
Let q(x) be the third derivative of -x**5/120 + 71*x**4/6 - 20164*x**3/3 - 663*x**2. Determine b, given that q(b) = 0.
284
Suppose -5*d = -5*o + 65, 21*o - 26*o + 62 = -4*d. Let z be o/8 + 1 - 58/29. Factor 0*n - z*n**4 + 3/4*n**3 - 1/2*n**2 + 0.
-n**2*(n - 2)*(n - 1)/4
Let d(b) be the second derivative of -b**5/90 + b**4/2 + 10*b**3/3 + 2263*b. Factor d(s).
-2*s*(s - 30)*(s + 3)/9
Let m(y) be the second derivative of -y**6/900 - 31*y**5/300 - y**4/2 - 23*y**3 - y - 12. Let v(a) be the second derivative of m(a). Factor v(n).
-2*(n + 1)*(n + 30)/5
Let h(z) be the third derivative of z**6/30 + z**5/5 - 2*z**4/3 - 1208*z**2. Find q, given that h(q) = 0.
-4, 0, 1
Let w(k) = k**2 + 266*k - 1316. Let s be w(5). Factor -507/2 + s*r - 3/2*r**2.
-3*(r - 13)**2/2
Let x(y) be the third derivative of y**6/900 + 17*y**5/450 + 11*y**4/36 + 13*y**3/15 + 16*y**2 - 11. Factor x(k).
2*(k + 1)*(k + 3)*(k + 13)/15
Let x(j) be the first derivative of j**4/6 - 254*j**3/9 + 4331*j**2/3 - 37210*j/3 + 2049. Suppose x(w) = 0. What is w?
5, 61
Suppose 0 = -5*d + 15*d - 60. Let q = -2 + d. Factor -31*h**3 + 21*h**3 + 15*h**q - 35*h**3 + 5*h**5 + 25*h**2.
5*h**2*(h - 1)**2*(h + 5)
Let a(l) be the third derivative of -25*l**8/168 - 2*l**7/3 + 31*l**6/60 + 26*l**5/15 + l**4 + 22*l**2 + 4. Find k, given that a(k) = 0.
-3, -2/5, 0, 1
Suppose -42*k + 48 = -38*k. Let b(q) = 5*q**3 + 13*q**2 - 4. Let u(d) = d**3 + 2*d**2 - 1. Let m(a) = k*u(a) - 3*b(a). Let m(p) = 0. Calculate p.
-5, 0
Let b(m) be the first derivative of m**5/10 + 89*m**4/8 + 337*m**3 + 440*m**2 - 1936*m - 1605. Determine d so that b(d) = 0.
-44, -2, 1
Suppose 11*r - 24*r = 0. Let 20*f - 37*f + r*f**3 + 12*f**3 + f - 4*f**4 = 0. What is f?
-1, 0, 2
Suppose 0 = -92*c - 53*c - c + 438. Suppose -2/9*q**c + 2/3*q**2 - 2/3*q**4 + 4/9*q + 0 - 2/9*q**5 = 0. What is q?
-2, -1, 0, 1
Suppose -2641*s = -2560*s - 162. Let j(i) be the second derivative of 5/2*i**3 + 5/12*i**4 + 0 - 10*i**s - 21*i. Factor j(b).
5*(b - 1)*(b + 4)
What is f in -2*f**5 - 780*f**4 - 87*f**3 - 13*f**3 + 1555*f**4 + 54*f - 799*f**4 - 144*f**2 + 216 = 0?
-4, -3, 1
Solve -596/9*t - 2/9*t**2 - 1184/9 = 0.
-296, -2
Let o(i) = i**3 + i - 2105*i**2 + 2103*i**2 - 6*i + 2*i + 8. Let d be o(2). Solve 0*s - 1/3*s**d + 0 = 0.
0
Let s(q) be the third derivative of -5*q**8/336 + 8*q**7/21 + 7*q**6/8 - 16*q**5/3 - 85*q**4/6 + 3239*q**2. Solve s(a) = 0.
-2, -1, 0, 2, 17
Factor -1564*a + 3808*a**3 - 6348 + 172*a**2 - 7627*a**3 + 3815*a**3.
-4*(a - 23)**2*(a + 3)
Suppose -5*s + 3*j + 54 = 0, 2*s - 2*j = -6*j + 6. Suppose -s*k + 4*k = k. Suppose 3/2*o**4 + 3/8*o + 0*o**3 - 9/8*o**2 + k = 0. Calculate o.
-1, 0, 1/2
Let q be 6 + -3 + -4 + (-82324)/(-16). Solve 3249/4*h + 3/4*h**3 + 171/4*h**2 + q = 0 for h.
-19
Suppose -7587 = 7*f + 7463. Let l = f + 19352/9. Solve l*o**2 + 14/9*o + 4/3 = 0.
-6, -1
Let s be 20/(-90)*9*-2. Let m(q) be the third derivative of 0*q + 1/60*q**5 - 1/90*q**6 + 7*q**2 + 1/72*q**s + 0*q**3 + 0. Factor m(c).
-c*(c - 1)*(4*c + 1)/3
Let u(i) = 65*i - 646. Let d be u(10). Let t be -1 + 2 + -5 + (3 - -1). Factor -2/9*q**d + t + 0*q + 0*q**2 + 2/3*q**3.
-2*q**3*(q - 3)/9
Let o(v) be the first derivative of v**4/2 + 82*v**3/3 - 185*v**2 - 450*v - 1988. Find q, given that o(q) = 0.
-45, -1, 5
Let k(i) be the first derivative of 6*i**3 + 46*i**2 + 10*i + 747. Find a such that k(a) = 0.
-5, -1/9
Suppose -r = 2*n + 2*n - 4, -5*r - 30 = -5*n. Let f(t) be the third derivative of -8*t**n - 1/48*t**4 + 1/600*t**5 + 0 + 0*t - 1/10*t**3. Solve f(o) = 0 for o.
-1, 6
Let b be (5490/21777)/(5/7). Suppose b*m**5 + 36/17*m**2 + 0*m - 32/17*m**4 + 0 + 30/17*m**3 = 0. Calculate m.
-2/3, 0, 3
Let w be ((-98)/(-56))/((-28)/(-40)). Let l(j) be the third derivative of -1/42*j**7 - 1/6*j**6 + 5/6*j**4 + 0*j + 0 + 5*j**2 - 1/6*j**5 + w*j**3. Factor l(y).
-5*(y - 1)*(y + 1)**2*(y + 3)
Let u(z) be the first derivative of z**4/38 + 68*z**3/19 + 3276*z**2/19 + 63504*z/19 - 3693. Find a, given that u(a) = 0.
-42, -18
Determine h so that -h**5 + 363*h**2 + 1230*h**4 - 1991*h**4 - 2*h**5 + 1118*h**4 + 723*h**3 = 0.
-1, 0, 121
Let v = 36 - 34. Suppose -v*h - 20 = -28. Find u such that 2*u**5 + 27*u**4 - 2*u**3 - 55*u**4 + 28*u**h = 0.
-1, 0, 1
Let o(t) = 15*t**2 - 2. Let b(r) = -2*r**2 + 9*r - 3. Let d(f) = -3*f**2 + 7*f - 2. Let v(w) = 4*b(w) - 5*d(w). Let g(u) = 6*o(u) - 13*v(u). Factor g(n).
-(n - 1)*(n + 14)
Suppose 0 + 4/3*n**2 - 4/3*n**3 + 8/3*n = 0. What is n?
-1, 0, 2
Find q, given that -4208/3*q**2 - 8/3*q**4 - 21504*q + 16384/3 + 150*q**3 = 0.
-8, 1/4, 32
Let 152*b + 15659*b**2 - 7819*b**2 - 8554*b**2 - 3 - 5 + 283*b**4 + 439*b**4 - 152*b**3 = 0. What is b?
-1, 2/19, 1
Let h = -22 - -26. Factor 5*w**2 + 4 - h - 71*w + 26*w.
5*w*(w - 9)
Solve -869*d**4 - 33436*d - 2298*d**2 + 4*d**5 - 3430*d**2 - 843*d**4 - 28392 + 504*d**3 + 1816*d**4 + 1088*d**2 = 0 for d.
-13, -6, -1, 7
Suppose -5642 = -4*i - 13*j + 18*j, -j = -i + 1410. Let o = i - 1406. Suppose 136/5*k**3 + 0 + 32/5*k + 6*k**4 - 18/5*k**5 + 24*k**o = 0. Calculate k.
-1, -2/3, 0, 4
Let m be -2 + 192/(34 + -2). Suppose -1/6*r**2 + 1/4 + 1/3*r**3 - 1/3*r - 1/12*r**m = 0. What is r?
-1, 1, 3
Let v(a) be the third derivative of -a**8/504 + 32*a**7/315 - 53*a**6/45 - 433*a**5/45 + 221*a**4/4 + 578*a**3 - 3*a**2 + 2897*a. Let v(m) = 0. What is m?
-3, -2, 3, 17
Let d(n) = -2*n**3 - 66*n**2 - 2142*n + 13230. Let b(z) = 6*z**3 + 168*z**2 + 6426*z - 39690. Let m(i) = -6*b(i) - 17*d(i). Determine c so that m(c) = 0.
15, 21
Suppose -101*u + 708 = 135*u. Let i(f) be the first derivative of 0*f**2 - 2/21*f + 1 + 2/63*f**u. Factor i(r).
2*(r - 1)*(r + 1)/21
Let p(x) be the second derivative of x**4/6 + 26*x**3 + 1521*x**2 - 5706*x. Factor p(q).
2*(q + 39)**2
Factor -1134/5 + 84/5*w**2 + 3/5*w**3 + 387/5*w.
3*(w - 2)*(w + 9)*(w + 21)/5
Let u = 15575506/1769945 - -2/353989. Solve u*p - 484/5 - 1/5*p**2 = 0.
22
Let 717/2*z + 3/4*z**3 + 723/4*z**2 + 0 = 0. Calculate z.
-239, -2, 0
Let o be 2/(-2) + 18 + -14. Factor 10*y - 5*y**4 - 1419*y**3 + 1419*y**o + 15*y**2.
-5*y*(y - 2)*(y + 1)**2
Let z(q) be the first derivative of 14 + 1/24*q**4 + 1/12*q**2 + 0*q - 1/9*q**3. Factor z(x).
x*(x - 1)**2/6
Let r(p) be the first derivative of -5/34*p**4 + 4/51*p**3 + 130 + 0*p - 1/51*p**6 + 8/85*p**5 + 0*p**2. Factor r(t).
-2*t**2*(t - 2)*(t - 1)**2/17
Let u = 254813/178374 + 1/25482. Suppose 2/7*z**4 + 6/7*z**2 - u*z - 8/7 + 10/7*z**3 = 0. What is z?
-4, -1, 1
Let s(b) be the third derivative of b**5/90 - b**4/3 + 11*b**3/9 - 2*b**2. Solve s(o) = 0 for o.
1, 11
Let f(w) = -11*w**3 + 2339*w**2 - 1815852*w + 470910957. Let g(o) = -2*o**3 + o**2 + 1. Let j(m) = -f(m) + 5*g(m). What is x in j(x) = 0?
778
Let d = -43613/71489 - -41/67. Let j = d - -1059/4268. Factor 0 - j*u**2 + 0*u.
-u**2/4
Determine d so that 6*d**2 - 5122*d - 5787*d + 3609*d - d**2 = 0.
0, 1460
Let k(b) be the first derivative of -5*b**4/4 + 255*b**3 - 28875*b**2/2 - 29645*b + 1023. Factor k(u).
-5*(u - 77)**2*(u + 1)
Let o = 440 - 425. Let h be o/(-9) + 138/54. Solve 2/9*n**4 + h + 26/9*n**2 - 8/3*n - 4/3*n**3 = 0 for n.
1, 2
Let a(s) be the third derivative of -5*s**8/336 - 13*s**7/42 - 43*s**6/24 - 5*s**5/4 + 15*s**4 - 2693*s**2. Suppose a(j) = 0. Calculate j.
-8, -3, 0, 1
Suppose 43*h - 22 = 32*h. Solve -9*d**3 + h*d**4 + 4*d**4 - 9*d**2 + 5*d**2 + 7*d**2 = 0.
0, 1/2, 1
Let -75/7*k**5 + 18/7 + 208/7*k**3 - 40/7*k**4 + 278/7*k**2 + 123/7*k = 0. What is k?
-1, -3/5, -1/3, 2
Let o(w) be the first derivative of 4*w**6/15 - 7*w**5/25 - 9*w**4/20 + 7*w**3/15 + w**2/10 - 1259. Let o(i) = 0. What is i?
-1, -1/8, 0, 1
Let w(i) = 21*i**4 + 682*i**3 + 2084*i**2 + 1716*i + 271. Let k(a) = -a**4 + 2*a**2 - 2*a - 1. Let n(l) = 22*k(l) + 2*w(l). Solve n(d) = 0 for d.
-65, -2, -1, -1/5
Factor 88*s + 33*s**2 - 18 - 10*s**3 - 22 + 21*s**2 + 19*s**2 - 39*s**2.
-2*(s - 5)*(s + 2)*(5*s - 2)
Factor 2*k**3 + 69*k**2 + 70*k**2 - 205*k**2 - 2 + 0*k**3 + 68*k**2 - 2*k.
2*(k - 1)*(k + 1)**2
Let 22*j**2 - 69696 + 1056*j + 21*j**2 - 47*j**2 = 0. What is j?
132
Factor 72*z - 6492953 + 4*z**2 + 6493081 + 0*z**2.
4*(z + 2)*(z + 16)
Let b(v) = -v**3 - 3*v**2 - 2*v - 9. Let m be b(-4). Supp