1/3, 0
Let l(j) be the first derivative of -j**3/24 - 31*j**2/4 - 123*j/8 - 1246. Determine n, given that l(n) = 0.
-123, -1
Let m(t) = t**3 - t**2 + 3. Let s(c) = -3*c**3 - 14*c**2 - 39*c + 154. Let h(r) = -4*m(r) - s(r). Let b(j) be the first derivative of h(j). Factor b(x).
-3*(x - 13)*(x + 1)
Let z(w) be the first derivative of -151/2*w**2 - 19*w - 4 + 4*w**4 - 296/3*w**3. Solve z(a) = 0.
-1/4, 19
Let a(f) be the second derivative of 8*f**7/21 - 112*f**6/15 + 57*f**5 - 207*f**4 + 324*f**3 - 5203*f. Determine k, given that a(k) = 0.
0, 2, 3, 9/2
Suppose 4/7*r**3 + 0 + 408/7*r + 148/7*r**2 = 0. What is r?
-34, -3, 0
Solve 177/4*u**2 + 345/4*u + 3/4*u**3 + 171/4 = 0.
-57, -1
Let b(l) be the second derivative of l**5/60 - l**4/9 - l**3/18 + 2*l**2/3 + 579*l. What is y in b(y) = 0?
-1, 1, 4
Let t(y) be the first derivative of y**7/420 + 19*y**6/300 + 6*y**5/25 + y**4/3 - 115*y**3/3 - 190. Let r(v) be the third derivative of t(v). Factor r(x).
2*(x + 1)*(x + 10)*(5*x + 2)/5
Let q(c) = c**2 - 1. Let i(a) be the first derivative of a**5 + 5*a**4/4 - 14*a**3/3 - 10*a**2 - 6*a - 50. Let k(m) = -i(m) + 6*q(m). Factor k(p).
-5*p*(p - 2)*(p + 1)*(p + 2)
Let y(p) be the second derivative of p**7/105 + p**6/30 - p**5/10 + 86*p**2 - 110*p. Let m(a) be the first derivative of y(a). Determine t so that m(t) = 0.
-3, 0, 1
Factor 3/4*s**2 - 195/4*s - 207.
3*(s - 69)*(s + 4)/4
Let s(o) = 2109*o - 71704. Let p be s(34). Factor 2/9*d**p + 72 + 8*d.
2*(d + 18)**2/9
Let s(h) be the second derivative of 1/42*h**4 + 16/7*h**2 + 0 + 8/21*h**3 + 71*h. Suppose s(j) = 0. What is j?
-4
Let j(v) be the first derivative of 0*v - 52 - 1/14*v**2 + 1/21*v**3. Factor j(d).
d*(d - 1)/7
Suppose -10 = 5*b + 2*t, -3*b + 4*t = -65 + 19. Factor -4050/7 + 180/7*s - 2/7*s**b.
-2*(s - 45)**2/7
Let g(t) be the third derivative of 1/4*t**4 + 2/3*t**3 + 0*t**7 + 0*t - 1/15*t**6 + 4*t**2 - 1/15*t**5 + 1 + 1/168*t**8. Factor g(p).
2*(p - 2)*(p - 1)*(p + 1)**3
Let b(v) = 5*v**4 + v**3 - 15*v**2 + 75*v - 54. Let l(g) = 14*g**4 + 2*g**3 - 47*g**2 + 225*g - 161. Let k(s) = -11*b(s) + 4*l(s). Find r, given that k(r) = 0.
-5, 1, 2, 5
Suppose 500748 + u**2 + 13288*u + 2582518 + 8045052 + 3*u**2 - 92634 = 0. What is u?
-1661
Suppose 7*m + 105 + 77 = 0. Let f = -22 - m. Solve -28/5*p - 4/5 - 14*p**3 - 69/5*p**2 - 5*p**f = 0 for p.
-1, -2/5
Factor -1139 - 1304*t + 12*t**2 - 1085 + 1788.
4*(t - 109)*(3*t + 1)
Solve 251/5*i - 6*i**2 + 1/5*i**3 - 78 = 0 for i.
2, 13, 15
Let p(s) = -2*s**3 - 762*s**2 - 1542*s - 770. Let r(c) = 4*c**3 + 2288*c**2 + 4628*c + 2312. Let t(w) = 8*p(w) + 3*r(w). Factor t(o).
-4*(o - 194)*(o + 1)**2
Let a(l) be the second derivative of 1 + 5*l**4 - 28/3*l**3 - 9/10*l**5 + 8*l**2 + 2*l. Factor a(y).
-2*(y - 2)*(3*y - 2)**2
Let k(m) = -9*m**3 + 309*m**2 - 5769*m - 6000. Let a(i) = -i**3 + 31*i**2 - 577*i - 600. Let u(b) = 58*a(b) - 6*k(b). Let u(o) = 0. What is o?
-25, -1, 12
Let c(t) be the first derivative of 2*t**5/15 + 7*t**4/3 + 38*t**3/3 + 76*t**2/3 + 64*t/3 + 3531. Let c(k) = 0. Calculate k.
-8, -4, -1
Suppose 322 + 261 = 522*k - 237 - 224. Suppose -8/11*f + 2/11*f**k + 6/11 = 0. Calculate f.
1, 3
Suppose -4*v + 14 = -3*a, -8001*a + 8004*a - 21 = -3*v. Solve -2/11*t**a - 32/11 + 16/11*t = 0.
4
Let z = 29 - 19. Let k be 7 + 2*z/5. Factor 4 - n + n**2 - k*n + 2*n**2 + 6*n**2.
(3*n - 2)**2
Let y(q) = 545*q**2 + 80*q - 237. Let w(x) = -363*x**2 - 81*x + 238. Let l(b) = 3*w(b) + 2*y(b). Factor l(s).
(s - 80)*(s - 3)
Let j(a) be the first derivative of 2*a**4/17 - 6*a**3/17 - 138*a**2/17 + 70*a/17 + 147. Solve j(w) = 0 for w.
-5, 1/4, 7
Let 176/3*t - 1/3*t**2 + 179 = 0. Calculate t.
-3, 179
Suppose -145/7*s - 16/7*s**2 + 50/7 + 3/7*s**3 = 0. What is s?
-5, 1/3, 10
Let h(m) = m. Let j(n) = 5*n - 34. Let p(f) = 4*h(f) - j(f). Let d be p(-5). Suppose -1587*u**3 + 1671*u**3 - 66*u**2 + 15*u**2 + 6*u - d*u**4 = 0. Calculate u.
0, 2/13, 1
Let z = -21531 + 172249/8. Let u(j) be the third derivative of -z*j**3 + 42*j**2 + 0*j + 1/48*j**4 - 1/720*j**5 + 0. Determine c so that u(c) = 0.
3
Suppose -282/5*n + 0 + n**5 + 169*n**2 + 2541/5*n**3 + 1419/5*n**4 = 0. Calculate n.
-282, -1, 0, 1/5
Let q = 3866 - 3863. Let r(z) be the second derivative of 14*z + 0*z**2 + 7/10*z**5 + 0 + 0*z**q + 1/3*z**4. Suppose r(l) = 0. What is l?
-2/7, 0
Let b(m) be the second derivative of m**6/18 - 2*m**5/3 - 955*m**4/36 - 95*m**3 + 4210*m. Determine h so that b(h) = 0.
-9, -2, 0, 19
Let b(t) = -3*t**2 - 3*t + 1. Let n(h) = -2*h**3 + 119*h**2 + 705*h + 5. Let f(o) = -10*b(o) + 2*n(o). Determine p so that f(p) = 0.
-5, 0, 72
Let g(p) = -2*p - 21. Let c be g(-21). Suppose 0 = -c*j + 23*j - 32. What is n in -2*n - j - 22*n + 12*n + 4*n**2 = 0?
-1, 4
Let d**2 + 47 + 2176*d - 47 + 578*d = 0. Calculate d.
-2754, 0
Let g(h) = -h**2 + 20*h + 116. Let o be g(28). Let u = -105 - o. Let -2/5 - 3/5*n**u + 3/5*n + 1/5*n**4 + 1/5*n**2 = 0. What is n?
-1, 1, 2
Suppose -3*p + 54 = 36. Determine r so that -p + 6*r + 49*r**2 + 6 - 3*r**3 - 46*r**2 = 0.
-1, 0, 2
Let x(a) = -a**3 - 2*a**2 - 59*a - 73. Let z(b) = -2*b**2 + 58*b + 70. Let t(s) = -2*x(s) - 3*z(s). Factor t(n).
2*(n - 4)*(n + 1)*(n + 8)
Let c = -7184443/15 - -478965. Factor 0 + 128/15*z - c*z**2 + 2/15*z**3.
2*z*(z - 8)**2/15
Let r(j) be the third derivative of -j**5/16 - 19*j**4/48 + 7*j**3/8 + 3676*j**2. Factor r(f).
-(f + 3)*(15*f - 7)/4
Find u, given that 12296/7*u**2 + 2*u**5 + 1952*u**3 - 33280/7*u - 886/7*u**4 + 8192/7 = 0.
-2, 2/7, 1, 32
Let l(y) be the first derivative of 2*y**5/5 - y**4 - 26*y**3/3 - 10*y**2 - 929. Solve l(b) = 0.
-2, -1, 0, 5
Let w(j) = -j**2 - 6*j - 1. Let x be w(-1). Let v(s) = -33*s**2 - 287*s + 217. Let i(g) = -16*g**2 - 144*g + 108. Let u(c) = x*v(c) - 9*i(c). Factor u(q).
4*(q + 13)*(3*q - 2)
Let z(q) be the second derivative of -q**8/8960 + q**7/840 + q**6/960 - q**5/40 + 133*q**4/12 + 10*q - 4. Let a(y) be the third derivative of z(y). Factor a(u).
-3*(u - 4)*(u - 1)*(u + 1)/4
Let h(i) = -i**3 + 33*i**2 - 12*i - 58. Let z be h(12). Solve 922 - 64*v**2 - 3106 - 2791 - z - 1312*v + 1073 = 0 for v.
-41/4
Suppose -3*z - 4*r = -393, z = -3*z - r + 511. Determine u, given that -3*u**4 - 4*u**2 - z*u**3 - 4*u**5 + 7*u**4 - 2*u + 131*u**3 + 2*u = 0.
-1, 0, 1
Let q(i) = i**3 - 27*i**2 + 24*i + 53. Let y be q(26). Let p be 15/60*(y - 0). Solve p*j - 1/2 + 1/4*j**2 = 0.
-2, 1
Let w(q) = -q**2 - 73*q + 262. Let c(y) = -3*y**2 + y - 2. Let d(z) = -2*c(z) + 2*w(z). Factor d(v).
4*(v - 33)*(v - 4)
Let g(t) be the third derivative of 0*t**3 - 1/80*t**5 - 1/64*t**4 - 1/320*t**6 + 0*t - 38*t**2 + 0. Suppose g(j) = 0. Calculate j.
-1, 0
Let p(c) = -19*c**2 + 393*c + 400. Let s(u) = 80*u**2 - 1572*u - 1601. Let w(z) = 17*p(z) + 4*s(z). Solve w(i) = 0.
-1, 132
Factor 30722 + 864*a + 4*a**3 - 31570 - 114*a**2 - 114*a**2.
4*(a - 53)*(a - 2)**2
Factor 340*c - 350*c - 8*c**2 - 14*c**2 - 12*c**3 - 7*c**2.
-c*(c + 2)*(12*c + 5)
Let 228326 + 1708*a + 4988*a - 174*a**2 + 222*a**2 + 5197 = 0. What is a?
-279/4
Let h be (14 - -14)*(-2)/4. Let b(f) = 12*f**2 + 70*f - 202. Let p(j) = 4*j**2 + 23*j - 67. Let n(g) = h*p(g) + 5*b(g). Factor n(u).
4*(u - 2)*(u + 9)
Let o(a) = -5*a**2 - 884*a - 702. Let q be o(-176). Factor -98/13 - 28/13*c - 2/13*c**q.
-2*(c + 7)**2/13
Let f(k) be the third derivative of k**5/15 + 3*k**4/2 + 40*k**3/3 - 944*k**2. Factor f(n).
4*(n + 4)*(n + 5)
Factor 1/5*c**2 - 288/5 - 93/5*c.
(c - 96)*(c + 3)/5
Let n(g) be the second derivative of g**5/30 + 29*g**4/9 + 896*g**3/9 + 1568*g**2/3 - 109*g. Factor n(y).
2*(y + 2)*(y + 28)**2/3
Suppose -u + 3 = 1. Suppose 0 = -9*z - 490 + 2173. Suppose 95*t**2 - 15*t**3 + 97*t**u + 6*t**4 + 4*t**4 - z*t**2 = 0. What is t?
0, 1/2, 1
Let s be ((-8)/10)/((-5 - 306/(-60))*-4). Let b(t) be the third derivative of 0 + t**3 + 1/5*t**5 + 5/8*t**4 + 1/40*t**6 - 6*t**s + 0*t. Factor b(w).
3*(w + 1)**2*(w + 2)
Let s(x) = -x**2 + 17*x - 12. Let l be s(16). Suppose 0*w = l*w + 16, w - 56 = -n. Find p, given that -25*p - 9 - 7 - 38*p + 15*p + n*p**2 - 16*p**3 = 0.
-1/4, 2
Let z = 1664/523 - -36088/5753. Let -z*g - 1352/11 - 2/11*g**2 = 0. Calculate g.
-26
Let t(d) be the third derivative of -d**6/24 + 19*d**5/4 - 135*d**4/4 + 2*d**2 + 161*d. Factor t(l).
-5*l*(l - 54)*(l - 3)
Let v(w) be the first derivative of 2*