(i). Solve w(j) = 0 for j.
1, 5
Let m be -6 + 41/4 + (-1)/4. Suppose 0 = 4*c + 4*i - 6*i - m, i = 4*c - 6. Factor -8/5 + 2/5*u**c - 6/5*u.
2*(u - 4)*(u + 1)/5
Let d(x) be the third derivative of x**5/390 - x**4/78 + x**3/39 - 120*x**2. Factor d(q).
2*(q - 1)**2/13
Let o(l) be the second derivative of 0 + 11*l + 0*l**2 - 2/75*l**6 + 0*l**3 + 2/15*l**4 + 1/25*l**5. Factor o(m).
-4*m**2*(m - 2)*(m + 1)/5
Suppose 2*q - 4 = -2*c + 6, q - 3*c + 7 = 0. Suppose -x + 4 = -4*p - 0*p, q*p = -2. Determine r so that 2*r - 7*r**2 + x*r + 4*r + 4*r**2 = 0.
0, 2
Let a(t) be the second derivative of 2/7*t**2 + 0 - 1/7*t**3 - 2/21*t**4 + 3/35*t**5 - 5*t - 1/49*t**7 + 2/105*t**6. Determine o, given that a(o) = 0.
-1, 2/3, 1
Let p(u) be the first derivative of 2/15*u**5 + 0*u**2 + 0*u**3 + 7/18*u**6 + 0*u**4 + 0*u - 10. Determine m, given that p(m) = 0.
-2/7, 0
Let m(o) = -8*o**3 - 6*o**2 - 16*o - 10. Let h(d) = -d**3 - d**2 - 1. Let j(w) = -10*h(w) + m(w). What is c in j(c) = 0?
-4, 0, 2
Let l(v) be the third derivative of 0*v**3 + 1/96*v**4 + 1/160*v**6 + 1/80*v**5 + 0 + 1/840*v**7 + 0*v - 11*v**2. Let l(y) = 0. Calculate y.
-1, 0
Let a(u) be the second derivative of -2*u**6/15 - 125*u**5/12 + 65*u**4/4 + 35*u**3/6 - 53*u**2/6 + u + 8. Find d, given that a(d) = 0.
-53, -1/3, 1/4, 1
Let i(t) be the third derivative of -t**8/23520 - t**7/2940 + t**6/630 - 7*t**4/12 + 5*t**2. Let h(f) be the second derivative of i(f). Factor h(k).
-2*k*(k - 1)*(k + 4)/7
Let -110/9*i - 212/9 - 2/9*i**2 = 0. What is i?
-53, -2
Factor 2*x**3 - 5628 - 3*x**3 - 22*x**2 + 5628 + 0*x**3.
-x**2*(x + 22)
Let r be 32/(-5) - (-14)/35. Let p(y) = 3*y**2. Let i(b) = -3*b**2 - b + 0*b**2 + 1 + 1 + 8*b**2. Let f(s) = r*p(s) + 3*i(s). Factor f(a).
-3*(a - 1)*(a + 2)
Suppose 4 = -9*s + 10*s. Let d(w) be the third derivative of -1/240*w**5 + 0 + 0*w**s + 0*w + 0*w**6 + 2*w**2 + 1/1680*w**7 + 1/48*w**3. Factor d(h).
(h - 1)**2*(h + 1)**2/8
Let r(l) be the third derivative of l**8/252 - 22*l**7/315 - 13*l**6/45 - 32*l**2 + 6. Factor r(k).
4*k**3*(k - 13)*(k + 2)/3
Let l = 3175 + -25367/8. Suppose 3*v**2 - l*v + 9/8 = 0. What is v?
3/8, 1
Suppose z - 9 = -2*z + 2*w, 3*z = w + 9. Let g(h) be the second derivative of -2*h + 4/15*h**z - 1/30*h**4 + 0 - 3/5*h**2. What is u in g(u) = 0?
1, 3
Suppose 3*b - 7 = 2*s, -5*b - 5*s - 11 + 56 = 0. Let t(r) be the first derivative of 81/2*r**2 - 243/4*r - 27/2*r**3 - 3/20*r**5 - b + 9/4*r**4. Factor t(h).
-3*(h - 3)**4/4
Solve -2178/7 - 2/7*d**2 - 132/7*d = 0 for d.
-33
Let b(y) = 6*y**3 - 2*y**2 + 1. Let a be b(1). Suppose 21 = a*d - 69. What is n in -n**2 + 3*n**2 - 21*n - 5*n**2 + d*n = 0?
-1, 0
Let z(g) be the first derivative of -12/7*g - 51 + 16/7*g**2 - 8/7*g**3 + 0*g**4 + 4/35*g**5. Factor z(h).
4*(h - 1)**3*(h + 3)/7
Let h(c) be the third derivative of 0 + 2/5*c**6 + 0*c - 2/15*c**7 - 1/3*c**4 - 1/5*c**5 + 0*c**3 - 2*c**2. Suppose h(o) = 0. What is o?
-2/7, 0, 1
Let m(l) be the third derivative of -l**6/780 - 2*l**5/195 + 5*l**4/156 + 59*l**2. Factor m(g).
-2*g*(g - 1)*(g + 5)/13
Let -15123/2*k - 357911/2 - 213/2*k**2 - 1/2*k**3 = 0. Calculate k.
-71
Let b(y) = -66*y**3 + 184*y**2 - 160*y + 32. Let h(j) = 100*j**3 - 276*j**2 + 240*j - 48. Let x(z) = 8*b(z) + 5*h(z). Factor x(l).
-4*(l - 2)*(l - 1)*(7*l - 2)
Let u(t) = -t**2 + 20*t - 2. Let i be u(19). Determine j so that 10*j - i*j**2 + 5*j**4 - 8*j**2 + 0*j + 20*j**3 - 10*j**4 = 0.
0, 1, 2
Let r(t) = -2*t**4 - 4*t**3 - 4*t**2 + 4*t. Let s(g) = 3*g**4 + 2*g**2 + 3*g**3 + g**2 - g**4 - 5*g + 2*g. Let n(q) = 5*r(q) + 6*s(q). Factor n(b).
2*b*(b - 1)**2*(b + 1)
Let t be 167/51 + ((-42)/(-27))/(52/(-78)). Find w, given that t*w**2 + 8/17*w + 0 + 2/17*w**4 + 10/17*w**3 = 0.
-2, -1, 0
Let p(b) be the first derivative of -b**5/5 + b**4 - 5*b**3/3 + b**2 - 53. Determine a, given that p(a) = 0.
0, 1, 2
Let c = -95 + 98. Factor -15 + 5*q + 37*q**3 - 42*q**3 + 13*q**2 + 5*q**2 - c*q**2.
-5*(q - 3)*(q - 1)*(q + 1)
Let y(t) = -t**5 + t**4 + t**2 - 1. Let l(a) = 20*a**5 - 134*a**4 + 276*a**3 + 127*a**2 - 480*a - 187. Let o(s) = l(s) + 5*y(s). Find w, given that o(w) = 0.
-1, -2/5, 2, 4
Let d = 2549 - 2543. Let l(g) be the first derivative of 16*g**2 - 8/3*g**3 + 16*g + 9/5*g**5 - d*g**4 - 8. Factor l(h).
(h - 2)**2*(3*h + 2)**2
Suppose 0 = -83*b + 88*b - 2*p - 25, -b - 12 = 3*p. Factor 6/7*u - 6/7*u**2 - 2/7 + 2/7*u**b.
2*(u - 1)**3/7
Let a(j) be the third derivative of 0*j + 5/6*j**4 + 1/30*j**6 + 0 + 4/3*j**3 + 4/15*j**5 - 29*j**2. Factor a(k).
4*(k + 1)**2*(k + 2)
Let v(m) be the second derivative of m**7/5670 + 13*m**4/12 - 10*m. Let j(l) be the third derivative of v(l). Find i such that j(i) = 0.
0
Let q(p) be the first derivative of -5*p**6/6 - 10*p**5 - 75*p**4/2 - 100*p**3/3 + 155*p**2/2 + 150*p - 101. Let q(n) = 0. What is n?
-5, -3, -2, -1, 1
Let o be ((-28)/42)/((-4)/18). Let z be 4/22 + (-288)/(-2288). Solve -6/13*c**o + 4/13*c**2 - z + 6/13*c = 0.
-1, 2/3, 1
Factor 6*t + 45/4*t**3 + 107/4*t**2 + 0 + t**4.
t*(t + 3)*(t + 8)*(4*t + 1)/4
Suppose -g = u - 3661 + 3652, 0 = -3*g - 5*u + 35. What is b in 1/6*b**g - 2*b**3 + 2/3*b**4 + 11/6*b + 1/3*b**2 - 1 = 0?
-6, -1, 1
Suppose 5*q - j - 32 = 0, q + j + 4*j - 22 = 0. Find g such that -g**2 - 2 - q*g - 2*g**2 + 6*g + 4*g**2 = 0.
-1, 2
Let l(n) = -3*n - 12. Let h be l(-6). Let m(c) = -3*c**2 + 2*c**2 - c - h*c**2. Let a(f) = -27*f**2 - 3*f. Let p(d) = -4*a(d) + 15*m(d). Factor p(u).
3*u*(u - 1)
Let d = 1702772/7 - 242793. Let f = -459 + d. What is s in -2/7*s**2 + f*s - 8/7 = 0?
2
Let h(m) be the first derivative of -2*m**3/21 - 348*m**2/7 - 60552*m/7 - 646. Factor h(v).
-2*(v + 174)**2/7
Let g(m) = -22*m**4 - 34*m**3 + 78*m**2 + 34*m - 56. Let l(v) = 2*v**4 + 3*v**3 - 7*v**2 - 3*v + 5. Let d = 79 - 73. Let o(w) = d*g(w) + 68*l(w). Factor o(q).
4*(q - 1)**2*(q + 1)**2
Let r(h) = -h**2 - 13*h - 20. Let z be (2/(-6))/(5/165). Let n be r(z). Factor -3/2*a + 3/2*a**n - 3.
3*(a - 2)*(a + 1)/2
Determine k, given that -11*k + 1/6*k**2 + 363/2 = 0.
33
Factor 21*s**2 - 102 + 165/2*s - 3/2*s**3.
-3*(s - 17)*(s - 1)*(s + 4)/2
Let x(t) be the first derivative of t**6/24 + 3*t**5/20 + t**4/16 - t**3/4 - t**2/4 + 128. Factor x(q).
q*(q - 1)*(q + 1)**2*(q + 2)/4
Let u = -1168 - -8185/7. What is v in -12/7*v - 3/7*v**2 - u = 0?
-3, -1
Let s = 12745/21 + -4155/7. Factor -16/3 - s*y - 2*y**3 - 28/3*y**2.
-2*(y + 2)**2*(3*y + 2)/3
Let n(o) = 3*o**2 + 3*o + 2. Let v(g) = g**2 + g. Let a(u) = -n(u) + 4*v(u). Let h be a(-3). Factor 0 - 2/5*l**3 + 2/5*l - 2/5*l**h + 2/5*l**2.
-2*l*(l - 1)*(l + 1)**2/5
Let z(o) be the first derivative of o**6/42 - o**5/5 - o**4/28 + o**3/3 + 108. Determine n so that z(n) = 0.
-1, 0, 1, 7
Let j(w) = -11*w**3 - 6*w**2 + 12*w + 5. Let g(q) = -8*q**3 - 4 - 6 + 13 + 2*q**3 - 3*q**2 + 6*q. Let f(a) = -5*g(a) + 3*j(a). Find i such that f(i) = 0.
-2, 0, 1
Let f = 137/1818 - 2/101. Let s(u) be the first derivative of -2/27*u**3 - 2 - f*u**4 + 0*u + 2/9*u**2. Factor s(j).
-2*j*(j - 1)*(j + 2)/9
Let w be 16/2 + -4 + -6. Let r be -3 - (14/w + 4). Factor r - 1/3*f**5 + 2/3*f**2 + 0*f - 5/3*f**3 + 4/3*f**4.
-f**2*(f - 2)*(f - 1)**2/3
Suppose -35*m - 158 = -114*m. Find f such that 32/5*f - 64/5 - 4/5*f**m = 0.
4
Let l(d) be the second derivative of -d**4/3 + 28*d**3/3 - 98*d**2 + 179*d. Find k such that l(k) = 0.
7
Let u be (1 - 14/(-4))*230/483. Factor -9/7 + 3/7*s**3 + 3*s - u*s**2.
3*(s - 3)*(s - 1)**2/7
Solve -33/4*t - 3/4*t**5 - 9/2 + 3*t**4 + 3/2*t**2 + 9*t**3 = 0 for t.
-1, 1, 6
Let o be 1/(-4) - (-2)/8. Suppose 4*h = 4*j + 28, 103*j - 88*j = 3*h - 81. Suppose 0*u + 3/4*u**4 + 0*u**3 + o*u**h + 0 = 0. Calculate u.
0
Suppose -10*f + 3*f = 245. Let d = f - -107/3. Factor 2/3*p**2 - 2/3*p**3 + 2/3*p - d.
-2*(p - 1)**2*(p + 1)/3
Let o(t) be the second derivative of -t**8/1920 + t**7/315 - t**6/360 - t**4/6 + t. Let b(u) be the third derivative of o(u). Suppose b(i) = 0. Calculate i.
0, 2/7, 2
Let l = -137 - -4111/30. Let n(w) be the second derivative of 1/3*w**3 + 0*w**2 + l*w**6 - 2*w + 5/12*w**4 + 0 + 1/5*w**5. Let n(j) = 0. What is j?
-2, -1, 0
Let a(k) be the second derivative of 0 + 0*k**2 - 1/189*k**7 + 2/135*k**6 + 0*k**5 + 1/27*k**3 - 1/27*k**4 + 19*k. Suppose a(g) = 0. What is g?
-1, 0, 1
Let a(j) be the first derivative of 2*j**4 + 382*j**3/3 + 140*j**