 1)
Let d(z) = 13*z**3 + 109*z**2 + 75*z - 197. Let y(w) = -20*w**3 - 164*w**2 - 112*w + 296. Let p(n) = -8*d(n) - 5*y(n). Factor p(i).
-4*(i - 1)*(i + 2)*(i + 12)
Let p(z) be the first derivative of 1/6*z**2 - 9 + 0*z - 1/12*z**4 + 0*z**3. Factor p(r).
-r*(r - 1)*(r + 1)/3
Suppose r + v - 17 = -6, -4*r + 2*v = -20. Suppose -2*x - 2*a + 9 = -r, 4*a + 40 = 4*x. Factor -3*m**2 + 4*m**2 - x*m - 4*m**3 + 10*m + 2*m**2.
-m*(m - 1)*(4*m + 1)
Let w(d) = 3*d**3 + 2*d**2 - 11*d + 5. Let k be 12/15*(-30)/4. Let s(u) = 3*u**3 + 3*u**2 - 12*u + 6. Let m(i) = k*w(i) + 5*s(i). Factor m(v).
-3*v*(v - 2)*(v + 1)
Let h(p) = -4*p**5 - 4*p**4 - 2*p**3 + 4*p. Let f(x) = x**5 - x**4 - x**3 - 2*x. Let o(y) = -4*f(y) - 2*h(y). Factor o(d).
4*d**3*(d + 1)*(d + 2)
Let x(o) be the third derivative of -o**5/450 + o**4/30 + 8*o**3/9 - 33*o**2. Find p, given that x(p) = 0.
-4, 10
Let n = 15/86 + 14/43. Factor 1/4*k**3 + 0 - n*k - 1/4*k**2.
k*(k - 2)*(k + 1)/4
Let p(v) be the first derivative of 2*v**3/9 + 17*v**2/3 - 76*v/3 - 225. Factor p(g).
2*(g - 2)*(g + 19)/3
Factor 2/11 - 6/11*o**2 - 4/11*o**4 - 2/11*o + 10/11*o**3.
-2*(o - 1)**3*(2*o + 1)/11
Factor -147456 - 1/6*s**3 - 4608*s - 48*s**2.
-(s + 96)**3/6
Let j(r) = 2*r**3 - 45*r**2 - 19*r + 45. Let o(d) = -d**3 + 15*d**2 + 7*d - 15. Let g(v) = -6*j(v) - 17*o(v). Determine x, given that g(x) = 0.
-3, -1, 1
Let g(u) be the second derivative of u**4/48 + 59*u**3/12 + 3481*u**2/8 + 176*u. Find d, given that g(d) = 0.
-59
Let h(a) = 21*a**3 - 29*a**2 - 61*a - 22. Let l(u) = 4*u**3 - 6*u**2 - 12*u - 4. Let r be ((-22)/32)/((-7)/28)*-4. Let q(m) = r*l(m) + 2*h(m). Factor q(j).
-2*j*(j - 5)*(j + 1)
Let f(l) = l**4 + 20*l**4 + 7*l**2 - 33*l**3 + 18*l**4 + 14*l**2. Let q(r) = 20*r**4 - 16*r**3 + 11*r**2. Let c(v) = 5*f(v) - 9*q(v). Factor c(n).
3*n**2*(n - 1)*(5*n - 2)
Suppose -2*h = -2 - 6. Factor -3*v**h + 11*v**4 + 3*v**2 - 2*v**3 - 4*v**3 - 5*v**4.
3*v**2*(v - 1)**2
Let i(v) be the second derivative of -v**7/11340 + v**6/3240 + v**5/270 + 2*v**4 + 20*v. Let t(h) be the third derivative of i(h). Solve t(c) = 0.
-1, 2
Let r = -21 + 23. Factor -2/9*i**r - 8/9 - 10/9*i.
-2*(i + 1)*(i + 4)/9
Let g(z) be the third derivative of 2*z**2 - 41*z + 0 + 1/60*z**6 + 1/15*z**5 - 1/4*z**4 + 0*z**3. Suppose g(u) = 0. What is u?
-3, 0, 1
Determine s, given that -1/3*s + 1/6*s**3 + 0 + 1/6*s**2 = 0.
-2, 0, 1
Let s(o) be the first derivative of 0*o**2 + 0*o**3 + 1/126*o**7 + 5 + 0*o**5 + 1/90*o**6 + 0*o**4 - 2*o. Let r(u) be the first derivative of s(u). Factor r(t).
t**4*(t + 1)/3
Let h(n) be the second derivative of -n**7/126 - n**6/45 + n**4/18 + n**3/18 - 3*n + 10. Factor h(g).
-g*(g - 1)*(g + 1)**3/3
Let i(c) be the first derivative of -3*c**5/25 + 3*c**4/5 - c**3 + 3*c**2/5 - 24. Factor i(w).
-3*w*(w - 2)*(w - 1)**2/5
Let x(r) = 9*r**2 - 8*r + 63. Let y(s) = 11*s**2 - 7*s + 62. Let j(z) = 6*x(z) - 5*y(z). Determine h, given that j(h) = 0.
-17, 4
Let g(b) be the second derivative of -b**7/1155 + b**6/220 - b**5/165 + 2*b**2 - 4*b. Let q(k) be the first derivative of g(k). Factor q(f).
-2*f**2*(f - 2)*(f - 1)/11
Let j = -3859 + 11579/3. Factor -1/2*v**2 - 1/6*v**4 + j + 2/3*v - 2/3*v**3.
-(v - 1)*(v + 1)*(v + 2)**2/6
Let z(i) be the third derivative of 0 + 1/18*i**3 + 1/48*i**4 + 1/360*i**5 + 17*i**2 + 0*i. Let z(m) = 0. What is m?
-2, -1
Let k(d) be the second derivative of 2*d**4/3 - 2*d**3/3 - 46*d. Solve k(j) = 0.
0, 1/2
Let i = 262/27 - 443/54. Factor i*s**3 + 0 - 3*s**2 + 3/2*s.
3*s*(s - 1)**2/2
Suppose y = -3*v + 91, 2*y = -2*v - v + 194. Let 63*u**5 - 57*u**3 + 24*u**2 + y*u**3 + 186*u**4 + 86*u**3 = 0. What is u?
-2, -2/3, -2/7, 0
Let b be (6/(-9))/((-8)/72) - 528/104. Suppose -10/13 - 2/13*d**2 - b*d = 0. Calculate d.
-5, -1
Let v be (24/(-10) - -1)*-1. Let k = 759 + -754. Factor 0 - 9/5*p**3 - 1/5*p**k + v*p**2 + p**4 - 2/5*p.
-p*(p - 2)*(p - 1)**3/5
Let c(o) = o**2 + 63*o + 838. Let r be c(-19). Factor -7/4*x**3 - r*x**2 + 0 + 5/4*x**4 + x.
x*(x - 2)*(x + 1)*(5*x - 2)/4
Let y = -953/6 + 159. Let d(a) be the second derivative of 5*a + 0*a**2 + 0*a**3 + 0 - y*a**4. Factor d(v).
-2*v**2
Let m(c) be the first derivative of 2/5*c**5 + 0*c - 3/2*c**2 + c**4 + 13 - 2/3*c**3 - 1/6*c**6. Factor m(u).
-u*(u - 3)*(u - 1)*(u + 1)**2
Let x(g) be the second derivative of g**7/42 - 4*g**6/15 + 19*g**5/20 - g**4 - 2*g + 256. Factor x(l).
l**2*(l - 4)*(l - 3)*(l - 1)
Let d(b) be the second derivative of -3*b**5/100 - 3*b**4/2 - 28*b**3/5 - 81*b. Factor d(r).
-3*r*(r + 2)*(r + 28)/5
Let j(v) be the first derivative of -3*v**6/2 + 3*v**5 + 31*v**4/4 + 43*v**3/9 + v**2 - 239. What is g in j(g) = 0?
-2/3, -1/3, 0, 3
Let k be ((-108)/8 - 3)/((-4)/8). Suppose -16*j + k = -5*j. Solve 2/7*w**j - 2/7*w - 2/7*w**4 - 4/7 + 6/7*w**2 = 0.
-1, 1, 2
Solve -32/3*x + 32/3 - 1/3*x**3 + 10/3*x**2 = 0 for x.
2, 4
Factor 1/6*o**2 + 1250/3 + 50/3*o.
(o + 50)**2/6
Let k = -1144 + 1146. Let n(p) be the first derivative of -28/3*p**3 + 0*p - 5*p**4 - 11 - 4*p**k. Factor n(r).
-4*r*(r + 1)*(5*r + 2)
Let w(b) be the third derivative of b**7/1680 - b**5/80 - b**4/24 - 25*b**3/6 - 2*b**2. Let q(a) be the first derivative of w(a). Let q(d) = 0. What is d?
-1, 2
Let f = -424/23 + 4000/207. Let 0 + 40/9*m**3 - 50/9*m**4 - f*m**2 + 0*m = 0. Calculate m.
0, 2/5
Let f(k) be the first derivative of 4*k**3/3 - 244*k**2 + 14884*k + 157. Solve f(a) = 0.
61
Let g(y) be the second derivative of y**4/24 - 35*y**3/6 + 1225*y**2/4 - 191*y. Let g(h) = 0. What is h?
35
Factor -47 + 26 + 354*b**2 + 57*b - 352*b**2 - 37 - b.
2*(b - 1)*(b + 29)
Find n, given that -8*n**3 - 20*n**2 - 65*n - 65*n + 20*n**4 + 138*n = 0.
-1, 0, 2/5, 1
Suppose -1/3*r**3 + 17/3*r + 16/3*r**2 + 0 = 0. Calculate r.
-1, 0, 17
Let i be 2*-1*1/(11/(-33)*39). Factor 2/13*v**4 + 0 - 6/13*v**3 + 6/13*v**2 - i*v.
2*v*(v - 1)**3/13
Let i(o) = -4*o**2 + 47*o - 22. Let g(k) = 2*k**2 - 1. Let l(t) = 5*g(t) + 5*i(t). Factor l(u).
-5*(u - 23)*(2*u - 1)
Factor 58/17*l**2 + 10/17*l**4 - 44/17*l**3 + 0 - 24/17*l.
2*l*(l - 1)**2*(5*l - 12)/17
Suppose -10 = -5*x + 3*s, 0 = -2*x + 2*s + 4. Factor -2*d**x + 36*d - 45*d + 5*d**2.
3*d*(d - 3)
Factor -3/7*l**2 + 18 + 33/7*l.
-3*(l - 14)*(l + 3)/7
Suppose 68/5*x + 12/5*x**2 + 8 = 0. What is x?
-5, -2/3
Solve -2/3*a**2 - 2/3*a**3 - 4/15*a**5 - 4/15 + 14/15*a + 14/15*a**4 = 0 for a.
-1, 1/2, 1, 2
Suppose 0 + 16/9*i + 4/9*i**4 - 4/9*i**3 - 16/9*i**2 = 0. Calculate i.
-2, 0, 1, 2
Let m(u) = -8*u**2 - 92*u - 112. Let v(z) = 3*z**2 + 30*z + 37. Let l(x) = -5*m(x) - 14*v(x). Find s, given that l(s) = 0.
-1, 21
Let t be 5/(-2)*2/(-30). Suppose -26 + 58 = 4*a + 12*a. Determine w, given that -t*w + 1/6*w**a + 0 = 0.
0, 1
Let s(f) be the second derivative of 1/70*f**5 - 1/147*f**7 + 4/7*f**2 + 0 + 1/35*f**6 - 22*f - 1/6*f**4 + 0*f**3. Let s(p) = 0. What is p?
-1, 1, 2
Let n(u) be the second derivative of 0 - 1/4*u**5 - 25/12*u**4 - 15/2*u**2 - 35/6*u**3 - 29*u. Factor n(i).
-5*(i + 1)**2*(i + 3)
Let q(u) = -2*u - 25. Let t be q(-14). Factor t*x**2 - 6262*x + 6262*x.
3*x**2
Let f(q) = q**3 + 13*q**2 - 6. Let d be f(-13). Let z(x) = -x**3 - 6*x**2 - x - 4. Let l be z(d). Factor -5*y**l - 2*y**2 - 2*y**2 - 2 - 2 - 12*y.
-(3*y + 2)**2
Let v(o) be the first derivative of -o**4/8 - 16*o**3 - 768*o**2 - 16384*o - 33. Find w such that v(w) = 0.
-32
Suppose -7*v + 4*v = -15. Factor -16*h**2 - 16*h**3 - 3*h**4 + v*h + 45*h**3 - 16*h**3 - h.
-h*(h - 2)**2*(3*h - 1)
Suppose 6 = 8*r - 10. Let h(n) be the first derivative of -2/5*n**3 + 6/25*n**5 + 0*n + r - 3/10*n**2 + 0*n**4 + 1/10*n**6. Factor h(d).
3*d*(d - 1)*(d + 1)**3/5
Let u(l) be the second derivative of 1/6*l**4 - 1/60*l**5 + 0 - 1/2*l**3 + 0*l**2 - 22*l. Determine k, given that u(k) = 0.
0, 3
Let u = 1888 + -1879. Let y(d) be the third derivative of 0*d - u*d**2 + 0 - 1/24*d**6 - 5/6*d**3 + 5/24*d**4 + 1/12*d**5. Determine s, given that y(s) = 0.
-1, 1
Let t be (150/(-420) - (-1)/(-7)) + 1. Let y be 15/18 + (-1)/3. Factor y*c**2 - t + 3/4*c.
(c + 2)*(2*c - 1)/4
Let a(m) be the third derivative of m**5/120 + m**4/24 - m**3/4 + 2*m**2 + 9*m. Find z, given that a(z) = 0.
-3, 1
Let q = 398 - 109. Solve -4*l**3 + 293*l**4 - l - l**5 - q*l**4 + l = 0.
0, 2
Let g(y) be the second derivative of -y**6/40 + 3*y**5/40 + 3*y**4/16 - y**3/2 - 3*y**2/2 + 61*y. S