4)
Let t be 325/35 + (-2)/7. Suppose -5*m = -4*j - 15, 3*m + 3*j = j + t. Factor 10*v**m - 4*v**2 - 8*v**3 + 5 - 5.
2*v**2*(v - 2)
Let l = 6119 + -6114. Let d(a) be the third derivative of 0 + 79/12*a**l + 7/4*a**6 + 0*a - 10/3*a**3 - 5/2*a**4 - 2*a**2. Find r, given that d(r) = 0.
-2, -1/6, 2/7
Let a(x) be the second derivative of x**5/210 + 53*x**4/42 + 2809*x**3/21 + 134*x**2 + x + 16. Let i(l) be the first derivative of a(l). Factor i(n).
2*(n + 53)**2/7
Let o(f) = -3*f**3 + 33*f**2 - 81*f + 79. Let j(l) = -l**3 + 11*l**2 - 28*l + 26. Let a(q) = 7*j(q) - 2*o(q). Suppose a(r) = 0. What is r?
1, 4, 6
Let i(j) = 3*j**3 - 2*j**2 + 3*j - 2. Let n be i(1). Suppose -n*b + 0*b + 36 = 0. Factor 0*a**4 + a**4 + b*a - a**2 - 18*a.
a**2*(a - 1)*(a + 1)
Let b(s) be the third derivative of 9*s**6/40 - 69*s**5/10 + 91*s**4/2 + 676*s**3 - 202*s**2. Solve b(x) = 0 for x.
-2, 26/3
Let r = -1884 + 1941. Let m = r + -55. Determine y so that 1/2*y + 2/3*y**m + 1/6*y**3 + 0 = 0.
-3, -1, 0
Let o be (111/(-21) - -1)*(-44996)/14463. Solve 0*r - 20/3*r**2 + 0*r**3 + 5/6*r**4 + o = 0 for r.
-2, 2
Let k(x) be the first derivative of -x**6/24 - 27*x**5/20 - 281*x**4/16 - 1393*x**3/12 - 1617*x**2/4 - 686*x - 100. Factor k(c).
-(c + 2)*(c + 4)*(c + 7)**3/4
Let s(y) = -8*y - 2*y + 14*y - 3*y. Let t(u) be the second derivative of -u**4/4 + 3*u. Let d(m) = 15*s(m) + t(m). Solve d(j) = 0 for j.
0, 5
Let h(v) be the first derivative of -v**6/54 + 127*v**5/3 - 403225*v**4/12 + 256047875*v**3/27 + 5142. Find l, given that h(l) = 0.
0, 635
Let k(h) be the first derivative of 151 + 32/3*h**3 + 0*h + 24*h**2 + h**4. Let k(y) = 0. What is y?
-6, -2, 0
Let u(r) = -23*r + 164. Let f be u(7). Let h(j) be the second derivative of -21*j + 1/20*j**5 - 5/2*j**2 + 0 - 1/6*j**f + 5/12*j**4. Factor h(v).
(v - 1)*(v + 1)*(v + 5)
Let p(c) be the second derivative of c**4/18 - 1376*c**3/9 + 473344*c**2/3 - c - 1148. Factor p(z).
2*(z - 688)**2/3
Suppose -2*d - 2 = 2*d + 5*a, a - 4 = -3*d. Suppose -v + 0 = -d, 2*t + v - 10 = 0. Find k such that 3*k + t*k + 12*k + 10 - 4*k - 5*k**3 = 0.
-1, 2
Let j(f) = -f**3 - 54*f**2 - 45*f + 428. Let l be j(-53). Let s(i) be the second derivative of 0 - 1/4*i**2 + 31*i + 1/72*i**l - 1/18*i**3. Solve s(t) = 0.
-1, 3
Let -162/5*t**2 + 0*t + 1/5*t**4 + 0 + 161/5*t**3 = 0. What is t?
-162, 0, 1
Let 18*u + 41*u + 83*u - 5*u**2 - 680 - 8*u - 9*u = 0. Calculate u.
8, 17
Let k be (-1)/(6/(-18)) - 1. Suppose -4913 - 156*j**2 + k*j**3 + 867*j + 105*j**2 - j**3 = 0. Calculate j.
17
Suppose -2/9*r**5 + 64*r + 1792/9 - 976/9*r**2 + 236/9*r**3 - 2/3*r**4 = 0. What is r?
-14, -1, 4
Let v(t) be the third derivative of -t**6/480 - 193*t**5/16 - 931225*t**4/32 - 898632125*t**3/24 + 2974*t**2. Factor v(i).
-(i + 965)**3/4
Let v(z) = -8*z**2 + 1008*z + 2224. Let q(a) = 7*a**2 - 1032*a - 2224. Let i(m) = 4*q(m) + 3*v(m). Factor i(n).
4*(n - 278)*(n + 2)
Let v(q) = 26*q + 206. Let b be v(-6). Suppose 94*s - b = 69*s. Determine m, given that 5/6*m**s - m - 4/3 = 0.
-4/5, 2
Let k = 36805/12 + -3067. Let j(x) be the third derivative of 1/90*x**5 + 0*x - k*x**4 + 2/9*x**3 + 0 - 7*x**2. Suppose j(i) = 0. What is i?
1, 2
Let y(p) be the first derivative of p**6/14 + 3*p**5/35 - 3*p**4/14 + 393. Solve y(o) = 0.
-2, 0, 1
Find g, given that -5471*g**3 - 154*g + 6225/2*g**4 + 5625*g**5 - 6221/2*g**2 - 2 = 0.
-1, -1/2, -2/75, 1
Suppose 2362*i**5 + 2211*i**5 + 90*i**2 + 500*i**4 + 1971*i**5 + 2405*i**3 - 40 - 1060*i - 7339*i**5 = 0. What is i?
-1, -2/53, 2/3, 2
Let b(s) be the second derivative of 1 - 17/30*s**4 - 3/5*s**2 - 4/75*s**6 + 2*s - 1/210*s**7 - 6/25*s**5 - 23/30*s**3. Suppose b(z) = 0. Calculate z.
-3, -2, -1
Let l(u) = -u**2 - 1897*u - 1869. Let w(r) = -8*r**2 - 13284*r - 13078. Let m(c) = 44*l(c) - 6*w(c). Factor m(n).
4*(n - 942)*(n + 1)
Let w be (10 - (-272)/(-51)) + -4. Let z(x) be the second derivative of -1/36*x**4 + 0 - 17*x - w*x**2 - 5/18*x**3. Find d such that z(d) = 0.
-4, -1
Suppose -311/5*l**2 - 236/5 + 5*l**4 - 948/5*l + 294*l**3 = 0. What is l?
-59, -2/5, 1
Let r(t) be the first derivative of 5/6*t**6 + 0*t**2 + 0*t**3 + 0*t**4 + 106 + 0*t - 2*t**5. Factor r(z).
5*z**4*(z - 2)
Let t be 0/84830 - (0 - (1 + (-18)/(-4))). Suppose 14*v - t*v**2 - 6 = 0. What is v?
6/11, 2
Let c = 68447 - 68445. Find x, given that 0 + 0*x - 4/9*x**3 - 2/3*x**c + 2/9*x**4 = 0.
-1, 0, 3
Suppose 2*f**2 + 47/3 + 283/3*f = 0. Calculate f.
-47, -1/6
Let q(o) be the first derivative of 2*o**5/15 + 6*o**4 - 50*o**3/3 + 38*o**2/3 + 1188. Find d, given that q(d) = 0.
-38, 0, 1
Suppose 0 = -5*y + 2*l - 12, 11*y - 14*y = -2*l + 16. Factor -2/7*s**y - 36/7*s - 162/7.
-2*(s + 9)**2/7
Let c be (-6078)/(-315) + 718/(-7539). Factor 256/5*n**2 + 9/5 + c*n.
(16*n + 3)**2/5
Let d = 1845435/1090492 - -1/83884. Solve -4/13*r**4 - d*r**2 + 8/13 - 18/13*r**3 + 0*r = 0.
-2, -1, 1/2
Let c = -28 - -53. Let s be c/(-100) + 13/4. Factor 847*g**5 - 3*g**2 + 4*g**4 - s*g**3 - 844*g**5 - g**4.
3*g**2*(g - 1)*(g + 1)**2
Let w(s) be the third derivative of s**8/392 - 5*s**7/294 - s**6/120 + 3*s**5/28 + s**4/168 - 10*s**3/21 + 1813*s**2. Suppose w(l) = 0. What is l?
-1, -5/6, 1, 4
Let a(t) be the first derivative of -10/3*t**3 + 0*t**2 - 3 + 0*t**4 - 1/540*t**5 - 1/1620*t**6 + 0*t. Let u(s) be the third derivative of a(s). Factor u(f).
-2*f*(f + 1)/9
Suppose -1963*p = 169*p + 235*p - 4734. Find g such that 4 - 15/4*g - 1/4*g**p = 0.
-16, 1
Let i(y) be the third derivative of y**5/210 + 127*y**4/42 + 24*y**3 + 41*y**2 + 2*y + 7. Determine o, given that i(o) = 0.
-252, -2
Factor -1437 + 4132 - 21*z**2 - 1825*z + 975 + 8*z**2 + 8*z**2.
-5*(z - 2)*(z + 367)
Let q be (-5)/(-40)*480/144. Let j(u) be the first derivative of -43 + 2/3*u - q*u**2 + 1/18*u**3. Factor j(y).
(y - 4)*(y - 1)/6
Let i(f) = -2*f**4 + 1233*f**3 - 252147*f**2 + 17230247*f. Let y(x) = 10*x**4 - 6164*x**3 + 1260736*x**2 - 86151236*x. Let u(r) = 14*i(r) + 3*y(r). Factor u(t).
2*t*(t - 205)**3
Let r(z) = -12*z**3 + 1809*z**2 + 20889*z + 46782. Let o(i) = -i**3 + 113*i**2 + 1306*i + 2924. Let c(x) = 33*o(x) - 2*r(x). Factor c(p).
-3*(p + 4)**2*(3*p - 61)
Let r(y) = -11*y**3 - 2*y - 2. Let f be r(2). Let a = f + 143. Factor -a*z**3 + 1 + 54*z**3 - 15*z**2 + 5*z**5 - 1 + 15*z**4 - 10*z.
5*z*(z - 1)*(z + 1)**2*(z + 2)
Find w, given that 5965*w**3 + 180*w**4 - 106*w**2 - 22*w**5 + 26*w**2 - 3066*w**3 - 2491*w**3 = 0.
-2, 0, 2/11, 10
Suppose 3/8*y**4 - 429/4*y + 7668*y**2 + 429/4*y**3 - 61347/8 = 0. What is y?
-143, -1, 1
What is f in -64525*f**3 + f - 8*f**4 - f + 64401*f**3 = 0?
-31/2, 0
Suppose 264 = 6*s - 348. Let w be (3/(-4))/(s/340) - -5. Determine v so that w*v - 1/2*v**2 - 1/2*v**3 - 3/2 = 0.
-3, 1
Let y(s) = -24*s**2 + 1214*s - 306. Let c(n) = -16*n**2 + 810*n - 204. Let a(i) = 8*c(i) - 5*y(i). Factor a(d).
-2*(d - 51)*(4*d - 1)
Find g, given that -301/3 + 1/3*g**4 + 566/3*g - 38/3*g**3 - 76*g**2 = 0.
-7, 1, 43
Let w = 122630 - 122625. Let -4/7*r**2 - 8/7*r**4 + 0 - 2/7*r**w - 10/7*r**3 + 0*r = 0. What is r?
-2, -1, 0
Let r(c) = 2*c**2 - 6*c + 25. Let w be r(3). Suppose 24 = 37*t - w*t. Find n such that 1/3*n**t - 2/3 + n + 1/3*n**4 - n**3 = 0.
-1, 1, 2
Suppose 5 - 8 = -2*b + 3. Let l(j) be the second derivative of 0*j**2 + 3/160*j**5 + 1/16*j**b - 1/16*j**4 + 0 + 5*j. Factor l(s).
3*s*(s - 1)**2/8
Let i(g) be the second derivative of 6*g**2 + 0 - 3/65*g**5 - 5/39*g**3 - 7/52*g**4 + 18*g. Let h(c) be the first derivative of i(c). Find b such that h(b) = 0.
-5/6, -1/3
Suppose -85*r + 304 = -36. Let t(y) be the second derivative of 0 - y**r + 6/5*y**5 + 17*y - 3/4*y**2 - 7/4*y**3. Solve t(i) = 0.
-1/4, 1
Factor -76 + 78 + 194*a**2 + 222*a + 26*a**2.
2*(a + 1)*(110*a + 1)
Let w(c) = -154*c + 5240. Let r be w(34). Solve 0 + 24*s + 40*s**2 + 74/3*s**3 + 2/3*s**5 + 20/3*s**r = 0.
-3, -2, 0
Let w be 2/1*15/2. Suppose -14*u + w*u - 2 = 0. Factor 0*y**u - y**2 + 6 - 33*y + 32*y.
-(y - 2)*(y + 3)
Suppose -1 + 10 = 3*i. Let m be (5/i - 2)/(1/(-6)). Find r such that -51 - 4*r**m - 45 + 72 + 28*r = 0.
1, 6
Let s = -137 + 147. Find x such that -4*x**2 + s*x**4 - 1076*x + 1076*x - 6*x**3 = 0.
-2/5, 0, 1
Let h(a) = 9*a**5 - 28*a**4 + 42*a**3 - 4*a**2 - 57*a + 26. Let u(r) = r**5 - r**4 + r**3 - r**2 - 3*r + 1. Let o(x) = -h(x) + 6*u(x). Solve o(z) = 0.
-1, 1, 4/3, 5
