t z(i) be the third derivative of 1/10*i**4 + 0*i - 62*i**2 + 0*i**3 - 1/300*i**5 - 1 - 1/50*i**6 + 1/1050*i**7. Factor z(s).
s*(s - 12)*(s - 1)*(s + 1)/5
Suppose 0 = -3*v + 107*t - 112*t + 86, 3*t - 58 = -5*v. Factor -41/4*y - 5 - 11/2*y**v - 1/4*y**3.
-(y + 1)**2*(y + 20)/4
Let b = -5397/677 + -8840931/23695. Let n = -1904/5 - b. What is c in 8/7*c - n*c**2 - 8/7 = 0?
2
Let d(k) be the second derivative of k**6/60 + 11*k**5/8 + 363*k**4/8 + 9317*k**3/12 + 14641*k**2/2 + 8111*k. Find r such that d(r) = 0.
-22, -11
Let z(g) = -g**4 - 2*g**3 + g**2 - 2*g. Let w(n) = 3*n**4 - 20*n**3 - 42*n**2 + 3*n + 6. Let j(t) = w(t) - 5*z(t). Suppose j(v) = 0. What is v?
-2, -1/4, 1/2, 3
Let t be ((-2)/(-10)*-8)/(86/(-215)). Let a be ((-2)/t)/(12/(-48)). Suppose 82*v**2 - 20 + v**3 - 5*v**4 - 57*v**a - v**3 = 0. What is v?
-2, -1, 1, 2
Let k(g) = g**3 + g**2 - 159*g + 164. Let a(b) = 6*b**2 + 2*b - 1. Let s(o) = 5*a(o) - 5*k(o). What is c in s(c) = 0?
-11, 1, 15
Factor -160*d**2 + 215*d**2 + 410*d - 57*d**2.
-2*d*(d - 205)
Let s(i) = 2*i**2 + i - 1. Let v(l) = 454*l**2 + 1562*l + 1350. Let t(j) = 2*s(j) - v(j). Find m such that t(m) = 0.
-26/15
Let h(o) be the third derivative of o**6/1020 + 59*o**5/102 + 871*o**4/102 + 136*o**3/3 + 3928*o**2. Suppose h(k) = 0. Calculate k.
-289, -4, -2
Suppose -55 - 24 = 90*f - 79. Let f + 0*z + 2/9*z**2 - 1/9*z**4 - 1/9*z**3 = 0. Calculate z.
-2, 0, 1
Let g(p) be the third derivative of p**5/20 + 409*p**4/2 + 334562*p**3 + p**2 - 21*p - 43. Factor g(w).
3*(w + 818)**2
Let n(m) = -2*m**2 - 12*m + 32. Let d(q) = -3*q**2 - 11*q + 32. Suppose 0 = 19*k - 22*k - 12. Let x(a) = k*d(a) + 5*n(a). What is i in x(i) = 0?
4
Let m = -1264 - -1268. Let k(p) be the third derivative of 0 + 2/75*p**5 + 0*p**3 + 0*p - 16*p**2 - 1/20*p**m - 1/300*p**6. Determine u so that k(u) = 0.
0, 1, 3
Let b(w) = -w**3 - w**2 - w - 1. Let v(h) = -727*h**3 - 1279*h**2 - 228*h + 331. Let a(d) = -21*b(d) + 3*v(d). Solve a(r) = 0 for r.
-13/12, 2/5
Factor -16/13 + 8/13*j + 4/13*j**2 - 2/13*j**3.
-2*(j - 2)**2*(j + 2)/13
Suppose 71*z - 66*z - p = 20, 31 = 2*z - 5*p. Factor -9*s - 26*s**z - 20*s**2 + 23*s**2 - 21*s**3 + 16*s**3 + 7*s**4 + 30*s**2.
s*(s - 3)*(s - 1)*(7*s - 3)
Let r be (-4)/(-8)*6 - 4 - 35. Let d be (-129)/(-9) - (-3)/(r/(-8)). Factor 70*t**2 - 15*t**4 - d - 105*t**3 + 5*t**2 + 0*t**2 + 55*t**4 + 5*t.
5*(t - 1)**3*(8*t + 3)
Let q(h) = -h**2 - 126*h - 389. Let i(l) = -2*l**2 - 186*l - 583. Let n(o) = 5*i(o) - 7*q(o). Solve n(k) = 0.
-8
Let v be ((-27)/(-1020) - 495/2805)/((-2)/1450). Factor -3/4*z**5 + 624*z - 384 - 114*z**2 - v*z**3 - 33/2*z**4.
-3*(z - 1)**2*(z + 8)**3/4
Let p(l) be the second derivative of 21*l**5/100 - 13*l**4/10 + 2*l**3 + 12*l**2/5 + 1244*l. Let p(v) = 0. What is v?
-2/7, 2
Let q(n) be the second derivative of -36501/4*n**2 + 3/40*n**5 + 182 + 1587/4*n**3 - 69/8*n**4 + 2*n. Factor q(u).
3*(u - 23)**3/2
Let n be (720/84)/(0 + (-4)/(-42)). Let i be (-210)/22 - n/(-9). Let i*c + 3/11 + 1/11*c**2 - 1/11*c**3 = 0. Calculate c.
-1, 3
Suppose -70*p = -75*p + 120. Determine c so that -6*c**3 - 3*c - 7*c**3 - 2*c**3 + p*c**3 - 6 + 6*c**2 - 6*c**3 = 0.
-2, -1, 1
Let n(z) be the second derivative of -3*z**5/40 + 10289*z**4/24 - 8820245*z**3/12 - 2941225*z**2/4 + 8949*z. What is d in n(d) = 0?
-1/3, 1715
Suppose 2*h = -46*t + 45*t - 4, 4*t - 20 = 4*h. Let g(k) be the second derivative of -17*k - 50*k**t + 0 - 1/12*k**4 + 10/3*k**3. Find u such that g(u) = 0.
10
Factor 1/9*q**3 - 1840/9*q - 3712/9 - 224/9*q**2.
(q - 232)*(q + 4)**2/9
Let g(q) be the third derivative of -23*q**6/180 + q**5/30 + 4*q**3 + 54*q**2. Let i(l) be the first derivative of g(l). Let i(z) = 0. What is z?
0, 2/23
Let l(m) be the second derivative of -m**7/168 + 3*m**6 - 1215*m**5/2 + 60750*m**4 - 2733750*m**3 + 6171*m. Let l(p) = 0. Calculate p.
0, 90
Factor 128*o**2 - 4*o - 223*o**2 + 393*o**3 + 7*o - 301*o**2.
3*o*(o - 1)*(131*o - 1)
Let t(g) be the third derivative of g**6/810 + g**5/45 + 5*g**4/54 - 89*g**3/6 + 2*g**2 - 1. Let s(u) be the first derivative of t(u). Solve s(n) = 0 for n.
-5, -1
Let j(o) = -10*o - 27. Let s be j(-7). Let c = -41 + s. Factor -15*b + 6*b**4 - 5*b**3 - b**4 + 5*b**c - 29*b**2 - b**2.
5*b*(b - 3)*(b + 1)**2
Suppose -2402*d + 2406*d = -5*i + 66, -7*i = -3*d + 28. Let o be ((-2)/18)/((-1)/2). Find s such that -o + 4/9*s**i - 2/9*s = 0.
-1/2, 1
Let o(g) be the first derivative of -g**4/3 + 23*g**3/6 + 3*g**2 - 38*g - 34. Let b(x) be the first derivative of o(x). Let b(h) = 0. Calculate h.
-1/4, 6
Let b(j) = -45*j**2 - 2154*j + 701. Let r(g) = g - 4. Let q(z) = -b(z) + 6*r(z). Factor q(w).
5*(3*w - 1)*(3*w + 145)
Let n(s) = 11*s**2 - 2*s + 30. Let x(b) = -185*b**2 + 35*b - 500. Let m(u) = -50*n(u) - 3*x(u). Determine f so that m(f) = 0.
0, 1
Factor 3/8*m**2 + 0 - 495/8*m.
3*m*(m - 165)/8
Let f be (-12)/8*(-8)/6. Factor -896 + 6*a**f - a**2 + 956 - 35*a.
5*(a - 4)*(a - 3)
Find z, given that -18 + 5 - 23*z**2 - 3 - z**3 + 49*z + 3 - 12 = 0.
-25, 1
Let b be 3 + (-28)/(-56)*(1 - 1). Suppose -5*v + a - 4 = -2, -8 = -4*a. Determine y so that 10*y - 138 + v*y - y**2 + 144 - b*y**2 = 0.
-1/2, 3
Factor 5 + 5 + 20*c + 4*c**2 - 9 + 7 + 8.
4*(c + 1)*(c + 4)
Find q, given that -21/5*q - 18 + 3/5*q**2 = 0.
-3, 10
Let b(q) be the first derivative of -5*q**5/24 + 65*q**4/72 + 29*q**3/36 + q**2/4 - 12*q + 95. Let s(n) be the first derivative of b(n). Factor s(m).
-(m - 3)*(5*m + 1)**2/6
Let j be (-24)/(432/63)*(-1 + (-9)/(-21)). Let d(z) be the first derivative of 15 + 1/2*z**4 + 0*z - 16/3*z**3 + 16*z**j. Suppose d(t) = 0. What is t?
0, 4
Let n be 70/14 - (-143)/(-8). Let i = -1941/152 - n. Suppose 0*y - i*y**2 - 2/19*y**3 + 0 = 0. Calculate y.
-1, 0
What is d in 0 + 1676/21*d**2 - 2/21*d**3 + 0*d = 0?
0, 838
Let h(z) = -25*z**2 - 640*z + 470. Let k(o) = o**2 - o + 5. Let t(p) = -h(p) - 5*k(p). Factor t(x).
5*(x + 33)*(4*x - 3)
Let o(s) = -s**5 - 4*s**4 + 34*s**3 - 40*s**2 + 11*s + 4. Let l(n) = -n**5 - 9*n**4 + 69*n**3 - 80*n**2 + 21*n + 9. Let w(u) = 4*l(u) - 9*o(u). Factor w(z).
5*z*(z - 1)**3*(z + 3)
Let x(t) be the second derivative of t**7/420 - t**6/60 + 25*t**3/3 - 63*t. Let l(g) be the second derivative of x(g). What is j in l(j) = 0?
0, 3
Let n(h) be the second derivative of h**7/14 - 4*h**6 + 231*h**5/20 - 19*h**4/2 + 1115*h. Factor n(i).
3*i**2*(i - 38)*(i - 1)**2
Factor -5*i**2 - 17*i - 2423*i - 893*i - 288*i - 1429*i - 1275125.
-5*(i + 505)**2
Let k = 372 - 163. Determine u so that k - 48*u**2 - 86*u + 110 - 4*u**3 + 2*u + 73 = 0.
-7, 2
Suppose 0 = 20*z - 17*z + 126. Let s be 122/z + 0 + -3 + 6. Factor s*w**2 - 8/21 + 2/7*w.
2*(w - 1)*(w + 4)/21
Let v(z) be the first derivative of 2/3*z**3 - 25/24*z**4 + 0*z + 12 + 1/12*z**5 + 0*z**2 - 1/360*z**6. Let u(i) be the third derivative of v(i). Factor u(w).
-(w - 5)**2
Suppose 0 = 31*r - 32*r + 15. Suppose 17*g - 8 = r*g. Find a such that 108*a**2 + 98*a**g - 182*a**3 + 16/7 - 184/7*a = 0.
2/7, 1
Let q(h) = -h**2 - 4*h + 5. Let s be q(-4). Suppose 18*n + 7*n**2 - 5*n**2 - s*n**2 + n**2 = 0. Calculate n.
0, 9
Let g = -48 - -52. Suppose g*k - 2*q = 0, 4*q - 5 = 3*k + 5. What is h in 9*h**4 + 2*h**2 + 21*h**3 + h**k + 12*h**2 + 3*h = 0?
-1, -1/3, 0
Factor 78*r + 3/2*r**2 + 1665/2.
3*(r + 15)*(r + 37)/2
Let h(l) be the third derivative of l**6/24 + 10*l**5/3 + 185*l**4/8 - 2*l**2 - 1224. Let h(u) = 0. What is u?
-37, -3, 0
Suppose -o - 6 = -3*o. Suppose -2*y - 81*n + 250 = -78*n, 0 = y + n - 126. Suppose -y*r**3 + 134*r**3 - o*r**4 + r**4 = 0. What is r?
0, 3
Let z(g) be the third derivative of g**5/360 - 31*g**4/16 + 706*g**2 + 2*g. Find j, given that z(j) = 0.
0, 279
Let k(s) be the second derivative of s**4/114 + 13*s**3/19 + 390*s + 13. Find u, given that k(u) = 0.
-39, 0
Suppose -7 = 7*b - 42. Let m = 7 - b. Factor 20 + 5*i + 25*i - 4*i**m - 46*i.
-4*(i - 1)*(i + 5)
Let p(u) = 2*u**2 - 76*u - 148. Let y be p(-2). Let i(j) be the first derivative of y*j**2 + 32*j + 16 + 4/3*j**3. Factor i(w).
4*(w + 2)*(w + 4)
Suppose -94*z - 115 + 417 = -74. Let g(r) be the second derivative of -1/36*r**z + 5*r + 1/9*r**3 + 0 + 0*r**2. Determine y so that g(y) = 0.
0, 2
Let m(j) be the second derivative of -j**5/12 + 5*j**4/4 - 20*j**3/3 + 137*j**2/2 - 68*j. Let t(k) be the first derivative of m(k). Find g,