2 - 29. Determine u, given that n(u) = 0.
-1, 4
Let x(l) = 13*l**2 + 13*l - 11. Suppose t = 4*g + 5, 4*t + 43 = 3*g + 11. Let z(a) = -7*a**2 - 7*a + 6. Let w(c) = t*z(c) - 6*x(c). Factor w(u).
-u*(u + 1)
Let j = 15 + -12. Let x be 0 + 1 - j - -20. Suppose 1 - 1 + 3 + x*g - 5*g + 14*g**2 = 0. What is g?
-1/2, -3/7
Suppose 20 = -181*z + 185*z. Factor 3*c**4 + 2*c**3 + 619*c**5 - 617*c**z + c**4.
2*c**3*(c + 1)**2
Let q(b) = -442*b - 1764. Let h be q(-4). Determine o, given that -h*o + 0 + 4/7*o**2 = 0.
0, 7
Determine l, given that 5*l**4 + l**2 - 12*l**3 + 932*l - 922*l + 15 - 21*l**2 + 2*l**3 = 0.
-1, 1, 3
Let o(q) be the third derivative of q**6/180 + 29*q**5/90 + 7*q**4/9 + 290*q**2. Factor o(x).
2*x*(x + 1)*(x + 28)/3
Let a = 1106 - 1102. Let n(z) be the third derivative of -7*z**2 + 0*z**a + 0 + 0*z**3 - 1/10*z**5 + 0*z + 1/40*z**6. Factor n(s).
3*s**2*(s - 2)
Let u be (-4)/8*8/1. Let v(c) = -7 - c + 5*c**2 - 4*c + 3 - 4*c**2. Let z(k) = k**2 - k - 1. Let g(b) = u*z(b) + 2*v(b). Factor g(y).
-2*(y + 1)*(y + 2)
Let x be 1/16*(-3)/(-15). Let s(m) be the third derivative of 0*m + 0*m**3 - m**2 + 0 + 1/32*m**4 - 1/280*m**7 - 1/160*m**6 + x*m**5. Factor s(k).
-3*k*(k - 1)*(k + 1)**2/4
Let b(t) be the third derivative of -t**8/26880 + t**6/960 + t**5/240 + t**4/8 + 9*t**2. Let x(u) be the second derivative of b(u). Let x(k) = 0. Calculate k.
-1, 2
Let k(f) = -f - 4. Let x be k(-14). Suppose 2*y + y - 3*g + 15 = 0, x = 4*y + 2*g. Determine u, given that y + 4/3*u - 2/3*u**2 = 0.
0, 2
Let z(w) = w**5 - 2*w**3 + 2*w**2 - w + 2. Let c(u) = 3*u**5 - 6*u**3 + 7*u**2 - 4*u + 7. Let k = -12 - -33. Let b(q) = k*z(q) - 6*c(q). Factor b(x).
3*x*(x - 1)**2*(x + 1)**2
Let h(u) = -11*u**4 - 11*u**3 + 5*u**2 + 11*u. Let l(d) = 10*d**4 - 41*d - 15*d**3 + 25*d**3 - 5*d**2 + 31*d. Let f(r) = -5*h(r) - 6*l(r). Factor f(v).
-5*v*(v - 1)*(v + 1)**2
Find m such that 4/23*m**2 - 30/23 - 2/23*m = 0.
-5/2, 3
Let t(g) be the second derivative of g**4/12 + 10*g**3/3 + 50*g**2 - g + 1. Factor t(y).
(y + 10)**2
Let k = 58 + -54. Find b, given that -29*b - 11*b - 6*b**2 - 242 - k*b + 4*b**2 = 0.
-11
Let n(z) = 2*z**3 - z - 1. Let d(u) = -10*u**3 - 10*u**2 + 20*u + 100. Let f(x) = -d(x) - 4*n(x). Factor f(h).
2*(h - 3)*(h + 4)**2
Let m(i) = -10*i**4 - 5*i**3 + 67*i**2 + 17*i - 117. Let p(z) = -z**2 - z + 1. Let a(n) = m(n) - 3*p(n). Find u, given that a(u) = 0.
-2, 3/2, 2
Let p = 6 - 3. Factor 27*m**2 + 18*m**3 - 3 + 3 + 12*m + p*m**4.
3*m*(m + 1)**2*(m + 4)
Let u(n) be the second derivative of n**4/12 + 11*n**3/10 - 7*n**2/5 + 54*n. Suppose u(x) = 0. What is x?
-7, 2/5
Let k(w) = w**3 + 3*w**2 - 2*w + 2. Let x(t) = -1 - 4*t**2 + t + 0 - 8*t**2 + 11*t**2. Let o(j) = -3*k(j) - 6*x(j). Factor o(q).
-3*q**2*(q + 1)
Let n = 15729 - 15727. Find c, given that 2/3*c**3 + 4/3*c**4 - 4/3 - 4*c**n - 14/3*c = 0.
-1, -1/2, 2
Let h be 64/(-96)*(-1)/(-2) + 21/9. Solve 1/5 - 1/5*s**h + 0*s = 0.
-1, 1
Find i such that 1/2*i**2 + 2 + 2*i = 0.
-2
Let o(j) be the third derivative of j**6/480 + 19*j**5/120 + 73*j**4/96 + 3*j**3/2 - 35*j**2 - 1. Factor o(z).
(z + 1)**2*(z + 36)/4
Suppose 2*x = -0*x - 5*o + 5, -1 = -4*x - o. Let c be 8/36 - x/(-1). Factor c*q**5 - 20/9*q**2 - 10/9*q**4 + 10/9*q - 2/9 + 20/9*q**3.
2*(q - 1)**5/9
Let u = -17030 - -17032. Factor -1/2*j + 17/8*j**u - 5/2*j**3 + 0 + 1/2*j**4.
j*(j - 4)*(2*j - 1)**2/8
Let s = -49 + 54. Factor 0*k**5 + 6*k**3 + k**5 - 6*k**4 - 9*k**3 - 4*k**s.
-3*k**3*(k + 1)**2
Factor 48*s**2 + 15*s + s - 32*s**3 - 237*s**5 - 11*s**4 + 4*s**4 - 5*s**4 + 244*s**5.
s*(s - 2)**2*(s + 2)*(7*s + 2)
Let l(q) be the third derivative of q**7/1470 + 13*q**6/840 + 11*q**5/420 - 13*q**4/168 - 2*q**3/7 + 38*q**2 - q. Factor l(s).
(s - 1)*(s + 1)**2*(s + 12)/7
Let f(q) be the third derivative of q**5/480 + 23*q**4/192 + 15*q**3/8 + 477*q**2. Suppose f(t) = 0. Calculate t.
-18, -5
Let c(f) be the second derivative of -f**5/100 + 7*f**4/15 + f**3/30 - 14*f**2/5 + 4*f + 15. Find q such that c(q) = 0.
-1, 1, 28
Solve -15/8*i**3 + 3/2*i - 3/8*i**4 - 9/4*i**2 + 3 = 0 for i.
-2, 1
Let i(x) be the first derivative of -2*x**3/33 + 9*x**2/11 - 16*x/11 - 59. Let i(h) = 0. What is h?
1, 8
Factor -1/7*l**4 + 3/7*l**2 - 9/7*l**3 + 29/7*l + 18/7.
-(l - 2)*(l + 1)**2*(l + 9)/7
Let z(d) be the first derivative of d**6/840 + 33*d**2/2 + 28. Let v(q) be the second derivative of z(q). Factor v(y).
y**3/7
Let c(o) = -35*o**2 - 1700*o - 47030. Let b(t) = -11*t**2 - 566*t - 15677. Let d(w) = 10*b(w) - 3*c(w). Let d(x) = 0. Calculate x.
-56
Let b(j) be the first derivative of j**5 + 25*j**4/2 + 40*j**3/3 - 25*j**2 - 45*j - 313. Find n, given that b(n) = 0.
-9, -1, 1
Let s(y) be the third derivative of y**5/110 + 19*y**4/22 + 361*y**3/11 - 86*y**2. Let s(m) = 0. What is m?
-19
Factor 25*d**4 - 23 + 2063*d**3 - 61*d**2 - 13 - 1843*d**3 - 148*d.
(d - 1)*(d + 9)*(5*d + 2)**2
Let q(o) be the third derivative of o**5/240 - 5*o**4/16 + 29*o**3/24 + 805*o**2. Find a such that q(a) = 0.
1, 29
Let r be 33 + -3*(-10)/15. Solve 19*k**2 + 10 + 5*k**2 + k**2 - r*k = 0 for k.
2/5, 1
Factor 1824 - 5*d**2 - 26945 + 630*d + 5276.
-5*(d - 63)**2
Let b(p) be the first derivative of p**5 + 15*p**4/2 + 20*p**3 + 20*p**2 + 445. Solve b(q) = 0.
-2, 0
Factor 0 - 12/5*k**3 - 22/5*k**2 - 12/5*k - 2/5*k**4.
-2*k*(k + 1)*(k + 2)*(k + 3)/5
Let i(y) be the third derivative of -23/105*y**7 + 6/5*y**5 - 8/3*y**4 + 1/56*y**8 - 14*y**2 + 28/45*y**6 + 0*y - 64/9*y**3 + 0. What is h in i(h) = 0?
-2/3, 1, 4
Let c(z) be the second derivative of -z**6/120 - 21*z**5/80 - 5*z**4/2 - 25*z**3/6 - 104*z + 2. Suppose c(m) = 0. What is m?
-10, -1, 0
Let i be ((24/(-14))/3)/(8/(-28)). Factor -16*b + 18*b**i - 4*b**3 + 4*b**3 - 4*b**3 + 2*b**2.
-4*b*(b - 4)*(b - 1)
Suppose -5*o = -68 + 58. Let m(h) be the second derivative of -1/6*h**3 + 0*h**o - 1/3*h**4 + 0 - 2*h. Solve m(x) = 0 for x.
-1/4, 0
Let z(c) be the second derivative of c**4/54 - 2*c**3/27 - c**2/3 + 79*c. Factor z(h).
2*(h - 3)*(h + 1)/9
Let l be (-2 - -1)/((-15)/45) + 2. Suppose -1 = -l*i - 2*m + 3, -2*m - 8 = -i. Factor p + 1/2 + 1/2*p**i.
(p + 1)**2/2
Let p(t) be the first derivative of t**4 + 152*t**3/3 + 640*t**2 - 3200*t - 180. Factor p(x).
4*(x - 2)*(x + 20)**2
Suppose -27 - 3 = -4*c + u, 4*c + 5*u - 42 = 0. Suppose -11*x + 7*x + c = 0. Factor 8/3 + 2/3*s**x + 8/3*s.
2*(s + 2)**2/3
Let h(o) be the first derivative of -o**6/51 + 12*o**5/85 + 5*o**4/17 - 104*o**3/51 - 105*o**2/17 - 100*o/17 + 68. What is l in h(l) = 0?
-2, -1, 5
Let f(g) = 2*g**3 + 70*g**2 + 716*g + 652. Let s(y) = y**2 + y - 1. Let o(n) = f(n) + 4*s(n). Let o(v) = 0. What is v?
-18, -1
Let t(o) = -9*o + 713. Let d be t(79). Factor 4/5 - 2/5*w**d - 2/5*w.
-2*(w - 1)*(w + 2)/5
Suppose 2*d + 1 = -3*h + 11, 0 = 5*d + 5. Determine r so that -2*r**3 + 3*r - 2*r - 850*r**2 + r**3 + 847*r**2 + 3*r**h = 0.
-1, 0, 1/3, 1
Let g(r) be the third derivative of -r**9/7560 + r**7/1050 - r**5/300 - 13*r**3/6 + 24*r**2. Let z(b) be the first derivative of g(b). Factor z(o).
-2*o*(o - 1)**2*(o + 1)**2/5
Let q be 4/5 - 92/(-10). Factor 2*p - 5*p - 2*p + q + 3*p**2 - 8*p**2.
-5*(p - 1)*(p + 2)
Factor -2/5*u**3 + 0*u**2 + 0*u + 0.
-2*u**3/5
Let t(c) = c**3 + 6*c**2 + 4*c - 1. Let g be t(-3). Suppose 1 = 3*d - g. Let b - 3*b**2 + d*b - 3*b = 0. What is b?
0, 1
Let z(a) be the second derivative of -26*a - 3*a**3 + 0 - 1/4*a**4 + 21/2*a**2. Find n such that z(n) = 0.
-7, 1
Solve -4/3*q**2 - 28 + 88/3*q = 0.
1, 21
Suppose 4*r + 70*p - 37 = 65*p, -25 = -5*r - 2*p. Let -j**2 + 1/2*j**4 + 0*j + 1/2 + 0*j**r = 0. Calculate j.
-1, 1
Suppose -608 = -20*g + 4*g. Let k be g/(-228)*-2*(-2 + 4). Find h, given that 2/3*h**2 + k*h - 4/3 = 0.
-2, 1
Let f be ((-112)/24)/(28/(-24)). Factor -2*v**3 + 8/3*v + 8/3*v**2 + 0 + 2/3*v**5 - 4/3*v**f.
2*v*(v - 2)**2*(v + 1)**2/3
Let d be -3*(5 + (57/(-9) - 1)). Let j(w) be the second derivative of 9/7*w**2 + 11/14*w**4 - 23/14*w**3 + 0 + d*w - 3/28*w**5. Suppose j(f) = 0. What is f?
2/5, 1, 3
Let l(h) = 3*h**3 - 8*h**2 + h + 10. Let t(m) = m**3 + m + 1. Let w(b) = -l(b) + 2*t(b). What is o in w(o) = 0?
-1, 1, 8
Let -3/2*d**2 - 54 - 18*d = 0. Calculate d.
-6
Suppose 5*b - 2*t + 422 + 218 = 0, 3*t = 3*b + 375. Let k = -1039/8 - b. Determine x so that -k*x**2 + x - 2 = 0.
4
Let y = 5/839 - -2497/3356