- 1)
Let k(g) be the second derivative of g**6/30 - 3*g**5/20 + 1963*g. Factor k(r).
r**3*(r - 3)
Let j be 113*(510/45 - 3/9). Let x = -1237 + j. Solve -x + 18*h - 3/2*h**2 + 15/2*h**4 - 18*h**3 = 0 for h.
-1, 2/5, 1, 2
Let h(d) = -d**3 + 46*d**2 - 39*d - 265. Let b be h(45). Suppose -5*w = -15, -9*i + 13*i - b = w. Factor -2/5 - 2/5*q + 12/5*q**i.
2*(2*q - 1)*(3*q + 1)/5
Let w(g) be the third derivative of -g**8/112 - 33*g**7/50 - 133*g**6/100 + 93*g**5/50 + 271*g**4/40 + 9*g**3/2 + g**2 - 1888. Suppose w(f) = 0. Calculate f.
-45, -1, -1/5, 1
Let n(s) = 2*s**4 + s**3 - 3*s**2 + 6. Let i(f) = 88*f**2 - 2*f**3 - 10 - 82*f**2 - 2*f**4 - 5*f**3 + 4*f**3 - f**4. Let l(p) = 3*i(p) + 5*n(p). Factor l(g).
g**2*(g - 3)*(g - 1)
Let x(f) be the first derivative of 4*f**3/3 - 116*f**2 + 3364*f + 247. Factor x(c).
4*(c - 29)**2
Let q(n) = -2*n - 20. Let c be q(-12). Suppose -3*l + 78 = 5*y + 7, -2*l + c = 0. Factor 31*s + 4 - 25*s - s**2 - y.
-(s - 3)**2
Suppose -5*x + 650*c = 653*c + 11, 0 = 3*x + 2*c + 8. Factor -34/3*f + 0 + 2/3*f**x.
2*f*(f - 17)/3
Suppose 5*j - 144 = -4*m, 0 = -m + 3*j + 28 + 8. Solve -12*k + 6*k + 24*k**4 + m*k**2 - 4*k - k + 68*k**3 + 3*k = 0 for k.
-2, -1, 0, 1/6
Let g(z) be the first derivative of z**5/480 - z**4/192 - z**3/8 - 97*z**2 + 115. Let r(l) be the second derivative of g(l). Factor r(f).
(f - 3)*(f + 2)/8
Let j be (3 - 1) + 1/(-3)*-9. Let n = 0 + j. Find k, given that -87*k - 93*k + 5*k**n - 20*k**4 + 185*k + 30*k**3 - 20*k**2 = 0.
0, 1
Let m(g) be the second derivative of -g**8/3360 + 13*g**7/3780 - g**6/270 - 5*g**4/6 - g**3/3 - 45*g. Let t(d) be the third derivative of m(d). Factor t(w).
-2*w*(w - 4)*(3*w - 1)/3
Let j(o) = o - 22. Let k be j(9). Let s = k - -24. Solve -y**2 + s + 9 - 20 - y**3 = 0 for y.
-1, 0
Let i(d) = -3*d + 43. Let z be i(8). Suppose -21 = -8*x + z. Factor 4*a**x - 118*a**4 + 53*a**4 + 16*a**2 - 12*a + 8*a**3 + 49*a**4.
4*a*(a - 3)*(a - 1)**2*(a + 1)
Let z(i) be the third derivative of i**8/2016 - 8*i**7/105 + 23*i**6/180 + 29*i**5/36 - 53*i**4/16 + 95*i**3/18 - 1249*i**2 + 2*i. Let z(w) = 0. Calculate w.
-2, 1, 95
Let s(z) = z**2 - 9. Let t(u) = -10*u**2 + 3409*u - 3311. Let o(y) = -22*s(y) - 2*t(y). Factor o(c).
-2*(c - 1)*(c + 3410)
Let o(i) = 60*i**2 - 695*i + 635. Let b(c) = -5*c**2 + 58*c - 53. Let g(k) = -4*k - 59. Let d be g(-6). Let x(j) = d*b(j) - 3*o(j). Find y, given that x(y) = 0.
1, 10
What is d in -48/7*d + 3/7*d**2 - 780/7 = 0?
-10, 26
Determine q so that 294*q**4 + 2598994*q**5 - 2597600*q + 1868655*q**2 + 2451*q**4 - 2598999*q**5 - 383555*q**3 + 1109760 = 0.
1, 3, 272
Let c(v) be the third derivative of v**6/160 + 357*v**5/10 + 127449*v**4/2 + 2479*v**2 - v. Solve c(d) = 0 for d.
-1428, 0
Let f = -593 + 201. Let v = -386 - f. Factor -3/5*g**2 - 15 - v*g.
-3*(g + 5)**2/5
Let z be -2 + 14 - (4/6 + 240/18 + -4). Determine t, given that 675/2 + 3/2*t**z + 45*t = 0.
-15
Let w(n) = -584*n**2 - 2328*n + 34. Let v be w(-4). Suppose -2/19*b + 2/19*b**3 - 2/19 + 2/19*b**v = 0. Calculate b.
-1, 1
Let x(r) = r**3 + 4*r**2 - r - 4. Let c be x(-4). Let h be ((-10)/70)/(c - 1). Suppose -1/7*m**2 - 2/7*m + 0 + h*m**3 = 0. What is m?
-1, 0, 2
Factor 1280 + 2368/7*p + 2/7*p**3 + 172/7*p**2.
2*(p + 8)**2*(p + 70)/7
Let g = -649181 - -649183. Find u such that 2/7*u**4 + 4 + 22/7*u**3 + 66/7*u**g + 74/7*u = 0.
-7, -2, -1
Let l(s) be the first derivative of 2*s**3/3 - 34*s**2 - 144*s + 3456. Determine x, given that l(x) = 0.
-2, 36
Let d(p) be the first derivative of -p**3/6 - 619*p**2/4 - 309*p - 3263. Let d(u) = 0. What is u?
-618, -1
Let f(b) be the third derivative of 4*b**4 - 4/45*b**6 + 1/315*b**7 + 9*b**3 + 23/45*b**5 + 0*b + 112 - b**2. Factor f(m).
2*(m - 9)**2*(m + 1)**2/3
Let r be 1*((-47)/9 - (-18)/81). Let t be 3*(r - -1 - 3477/(-855)). Factor -1/5*i**4 + 13/5*i + 7/5*i**2 + 6/5 - t*i**3.
-(i - 3)*(i + 1)**2*(i + 2)/5
Let i(t) be the second derivative of -t**6/105 - 67*t**5/35 + 6375*t. Factor i(c).
-2*c**3*(c + 134)/7
Suppose 10 = -10119*k + 10118*k + 12*w, 0 = -5*w + 5. Factor -2/11*s**3 + 12/11*s - 2/11*s**k + 0.
-2*s*(s - 2)*(s + 3)/11
Let q(m) = 56*m**4 - 2034*m**3 - 8794*m**2 - 34*m - 34. Let j(t) = -5*t**4 + 185*t**3 + 799*t**2 + 3*t + 3. Let g(h) = 68*j(h) + 6*q(h). Factor g(k).
-4*k**2*(k - 98)*(k + 4)
Factor 156/5*h**3 + 0 + 0*h**2 + 84/5*h**4 + 3/5*h**5 + 0*h.
3*h**3*(h + 2)*(h + 26)/5
Suppose 763*t = 761*t - 3534. Let d = -1735 - t. Determine p, given that d + 8*p + 1/2*p**2 = 0.
-8
Determine u so that 1167*u - 58*u**3 + 2 + 61*u**3 - 396*u**2 - 776 = 0.
1, 2, 129
Let h(v) be the third derivative of -v**6/30 - 6*v**5/5 + 31*v**4/2 + 220*v**3/3 - 2*v**2 - v + 174. Factor h(n).
-4*(n - 5)*(n + 1)*(n + 22)
Let i = -15093 - -1177321/78. Let v = i + 38/39. Factor v*q + 1/3*q**2 - 1.
(q + 6)*(2*q - 1)/6
Suppose 0 = 2*a - 3*u - 179 + 657, 4*u = -4*a - 996. Let q be -3*(a/(-45) - 6)*1. Factor 1/3*z**2 + q*z + 2.
(z + 2)*(z + 3)/3
Let b be (21/(-14))/(8/112). Let t(d) = d**2 + 23*d + 44. Let m be t(b). Factor -2/3*y**m - 2/3*y + 4/3.
-2*(y - 1)*(y + 2)/3
Let n(c) be the first derivative of -c**3/3 + 85*c**2/2 + 174*c - 372. Factor n(w).
-(w - 87)*(w + 2)
Suppose -26*n + 345 = 293. Let z(y) be the second derivative of -1/12*y**4 - 5*y - 2/3*y**3 - 3/2*y**n + 0. Find d such that z(d) = 0.
-3, -1
Let i = 1/21363 + 769061/149541. Factor i*f**2 + 6/7*f**3 + 48/7 + 72/7*f.
6*(f + 2)**3/7
Suppose 42 = 9*z - 2*z. Suppose -z*y = -7*y + 2. Find n, given that -2*n**4 - 2*n**3 - 250 + 4*n**2 + 10*n + 254 + 2*n**y = 0.
-1, 2
Let 847*j**2 + 878*j**2 - 1677*j**2 + 144 - 156*j - 3*j**3 = 0. Calculate j.
2, 12
Let k(s) be the first derivative of 4*s**2 - 16*s - 13 + 1/6*s**4 + 4/3*s**3. Let t(a) be the first derivative of k(a). What is g in t(g) = 0?
-2
What is t in 14/17*t + 2/17 - 36/17*t**2 = 0?
-1/9, 1/2
Let k(l) = 17*l**2 - 16*l**3 - 9 + 40 - 11 + 8*l - 15. Let u(n) = 23*n**3 - 25*n**2 - 13*n - 7. Let x(v) = 7*k(v) + 5*u(v). Factor x(t).
3*t*(t - 3)*(t + 1)
Determine d, given that 81/2*d**2 + 0*d + 0 - 243/2*d**3 - 21/2*d**5 + 135/2*d**4 = 0.
0, 3/7, 3
Let h(i) = 10*i**3 + 60*i**2 + 20*i - 6. Let a(d) = -10*d**3 - 59*d**2 - 28*d + 7. Let u(x) = 6*a(x) + 7*h(x). Determine r, given that u(r) = 0.
-7, 0, 2/5
Suppose 2182 - 609 = 714*d - 569. Suppose 5408*i + 2/3*i**d - 281216/3 - 104*i**2 = 0. Calculate i.
52
Suppose g - 6 = -3. Suppose l - 7 = -g. Determine r, given that 6*r**2 - 22*r**l + 9*r**4 + 16*r**4 + 9*r**3 = 0.
-2, -1, 0
Let u = 4506552484/15555 + -4925112/17. Let z = u + -4/183. Let z + 27/5*m + 3/5*m**2 = 0. What is m?
-8, -1
Suppose -1/8*r**3 + 5/4*r**2 + 4 - 4*r = 0. What is r?
2, 4
Let y(f) = -10*f**2 + 42*f + 30. Let m(k) = -26*k**2 + 84*k + 55. Let h(j) = 2*m(j) - 5*y(j). Factor h(g).
-2*(g + 1)*(g + 20)
Let o be 3/8*3/(-36*(-24)/128). Let q(n) be the third derivative of 0*n - 7/180*n**5 + o*n**3 - n**2 - 1/120*n**6 + 7/72*n**4 + 0. Factor q(d).
-(d - 1)*(d + 3)*(3*d + 1)/3
Let j = -237149 - -237152. Suppose -1/4*v**5 + v - v**4 + v**2 - 3/4*v**j + 0 = 0. What is v?
-2, -1, 0, 1
Determine n so that 1/9*n**2 - 28 - 19/9*n = 0.
-9, 28
Let z(v) be the second derivative of -7/12*v**4 + 1/10*v**6 + 0*v**2 - v**3 - 28*v + 0 - 1/42*v**7 + 3/20*v**5. Find d such that z(d) = 0.
-1, 0, 2, 3
Let i(c) be the first derivative of c**3/9 + 19*c**2/3 + 37*c/3 + 577. Suppose i(m) = 0. Calculate m.
-37, -1
Factor -149*g**4 + 16*g**2 - 85*g**3 - 151*g**2 - 35*g + 13*g**4 + 151*g**4.
5*g*(g - 7)*(g + 1)*(3*g + 1)
Let s(p) be the first derivative of 8*p**2 + 0*p + 11 + 1/150*p**5 + 0*p**4 - 1/15*p**3. Let f(a) be the second derivative of s(a). Factor f(t).
2*(t - 1)*(t + 1)/5
Let j(f) = -9*f**2 - 11*f + 48. Let n(h) = 5*h**2 + 5*h - 24. Let p = -152 - -149. Let b(o) = p*j(o) - 5*n(o). Let b(s) = 0. What is s?
-6, 2
What is m in 2/15*m**2 - 128/5 - 8/15*m = 0?
-12, 16
Let r = 24039/60110 + 1/12022. Let y = -37 + 187/5. Factor -2/5*q**3 - 2/5 + r*q + y*q**2.
-2*(q - 1)**2*(q + 1)/5
Let j = -242200 + 242203. Factor -16/7*i**j + 4/7*i**4 + 32/7*i + 2/7*i**5 + 64/7 - 32/7*i**2.
2*(i - 2)**2*(i + 2)**3/7
Let -64/7 + 1/7*x**5 + 115/7*x**3 - 19/7*x**4 + 208/7*x - 241/7*x**2 = 0. Calculate x.
1, 8
Factor -1428025/3 - 1/3*k**2 - 2390/3*k.
-(k + 1195)**2/3
Suppose q + 18 = 22. Factor 2*z**2 + 25*z**3 + 20*z +