1)
Let r(g) be the second derivative of -4/17*g**2 - 3*g + 8/51*g**3 + 0 + 5/102*g**4. Determine m, given that r(m) = 0.
-2, 2/5
Let s = -223 - -223. Solve 2/3*i**2 + 0 + s*i - 5/3*i**3 = 0.
0, 2/5
Let z = 1366 + -4097/3. Factor 0 - 1/3*m - z*m**3 + 2/3*m**2.
-m*(m - 1)**2/3
Let l(f) be the first derivative of -8*f**4 - 688*f**3 - 513*f**2 - 128*f - 1059. What is q in l(q) = 0?
-64, -1/4
Let c(m) be the third derivative of -m**6/900 - 7*m**5/150 - 3*m**4/4 - 27*m**3/5 + 219*m**2. Solve c(t) = 0.
-9, -3
Let x(y) = -2*y**5 + 8*y**4 - 4*y**3 - 6*y**2 + 4*y. Let u(b) = -2*b**5 + 9*b**4 - 5*b**3 - 6*b**2 + 4*b. Let f(a) = 4*u(a) - 6*x(a). Solve f(n) = 0 for n.
-1, 0, 1, 2
Let p(n) = 2*n. Let x = 6 - 5. Let o be p(x). Factor -2*v - 2*v - 4 + 12 - 4*v**o.
-4*(v - 1)*(v + 2)
Let b(w) be the first derivative of -1/4*w**4 + 2/3*w - w**2 + 1/30*w**5 + 13/18*w**3 - 2. Let b(a) = 0. What is a?
1, 2
Let z(n) be the second derivative of 1/40*n**5 + 1/48*n**4 + 1/42*n**7 + 0*n**3 - 7/120*n**6 + 0 - 36*n + 0*n**2. Find p, given that z(p) = 0.
-1/4, 0, 1
Let q = 66/245 - -3/98. Let m = q - 1/20. Find o such that 1/4*o + 0*o**2 + 0 - m*o**3 = 0.
-1, 0, 1
Factor -5*j**4 + 105*j**2 + 0*j**4 + 40*j - 86*j**3 - 100 + 55*j - 9*j**3.
-5*(j - 1)**2*(j + 1)*(j + 20)
Let x = -1968685/15666 - 3/5222. Let p = -125 - x. Factor -p*n**3 - 4/3*n**2 + 0*n + 0.
-2*n**2*(n + 2)/3
Let q(p) = 11*p**2 - 238*p + 5019. Let k(l) = -4*l**2 + 79*l - 1672. Let x(z) = 8*k(z) + 3*q(z). Factor x(n).
(n - 41)**2
Let n = 140 - 107. Let w be (n/9 + -5)*(-27)/48. Factor -1/8*d**2 + w*d - 9/8.
-(d - 3)**2/8
Let c(u) be the first derivative of u**6/360 + u**5/24 + 26*u**3/3 - 15. Let l(v) be the third derivative of c(v). Solve l(k) = 0 for k.
-5, 0
Let q = 4 - 0. Let d be 92/192*q + 2/(-8). Factor 1/3*m**3 + 4/3*m**2 + 2/3 + d*m.
(m + 1)**2*(m + 2)/3
Let d = 40 + -38. Factor -46 - l**d + 44 + 2*l**2 + l**2.
2*(l - 1)*(l + 1)
Suppose 8 = -s + 11. Factor -15*z**2 + 12*z**3 - 5*z**s - 17*z**3 + 5*z**4.
5*z**2*(z - 3)*(z + 1)
Suppose 4*p + 4 = 32. Suppose 15 - 1 = p*g. Factor 0*q - 2/3*q**g + 0*q**3 + 0 + 2/3*q**4.
2*q**2*(q - 1)*(q + 1)/3
Factor 50/3*f**2 + 14/3*f**4 + 32/3*f + 2/3*f**5 + 38/3*f**3 + 8/3.
2*(f + 1)**3*(f + 2)**2/3
Let r(f) be the second derivative of f**7/1260 + f**6/360 - 11*f**4/12 + 13*f. Let x(l) be the third derivative of r(l). Factor x(i).
2*i*(i + 1)
Suppose -85*k + 83*k = -3*x + 41, -49 = -3*x + 4*k. Suppose -24/5*w**2 + 2/5 + w - 28/5*w**4 - x*w**3 = 0. What is w?
-1, -1/4, 2/7
Let u = 63 - 30. Suppose 11*r**3 + 3 + 0*r - u*r**2 - 47*r**3 + 6*r = 0. What is r?
-1, -1/4, 1/3
Suppose -2*n - 4*p - 12 = 0, 3*p = 27*n - 30*n - 3. Solve -1/2*i**n - 1/4*i**3 + 0*i**2 + 0*i + 0 - 1/4*i**5 = 0 for i.
-1, 0
Suppose 35*i = 32*i + 9. Let d(m) = -m - 2. Let o be d(-4). Factor -2*f**o - 3*f**3 - 2*f**3 + 0*f**i + 2*f**5 + 3*f**3 + 2*f**4.
2*f**2*(f - 1)*(f + 1)**2
Let s = -6324 + 18973/3. Factor s*u - 1/2 + 1/6*u**2.
(u - 1)*(u + 3)/6
Factor -2*i + 4*i + 76*i**2 - 72*i**2 - i**3 + 19*i.
-i*(i - 7)*(i + 3)
Factor 48/5*w**2 - 6/5*w**3 - 42/5*w + 0.
-6*w*(w - 7)*(w - 1)/5
Suppose 4*j = -d + 18, -3*d + 0*j = 4*j - 22. Factor 17*q**3 + 44*q**2 + 7*q**d + 28*q**3 + 6*q.
3*q*(q + 1)*(15*q + 2)
Let a(m) be the third derivative of m**8/28 + 8*m**7/35 + m**6/8 - 19*m**5/20 + 3*m**4/4 + 51*m**2. Let a(u) = 0. What is u?
-3, -2, 0, 1/2
Let m(y) be the third derivative of y**5/20 + 7*y**4/8 + 5*y**3 + 99*y**2. Solve m(i) = 0.
-5, -2
Let s(r) be the second derivative of r**7/420 + r**6/240 - r**5/40 + 2*r**4/3 - 8*r. Let z(m) be the third derivative of s(m). Suppose z(o) = 0. Calculate o.
-1, 1/2
Let k(l) = -l**2 + 7*l + 3. Let h be (2/(-8) + (-112)/(-64))*-2. Let d(s) = 8*s**2 - 64*s - 28. Let w(m) = h*d(m) - 28*k(m). Factor w(q).
4*q*(q - 1)
Let g be (-195)/(-63) + 156/(-21) + 7. Let p(i) be the first derivative of g*i**3 + 1 + i**2 + 0*i. Factor p(d).
2*d*(4*d + 1)
Let w(c) be the third derivative of c**9/15120 - c**8/1008 + c**7/210 + 17*c**5/30 - 14*c**2. Let a(b) be the third derivative of w(b). Factor a(p).
4*p*(p - 3)*(p - 2)
Let c(l) = -l**2 + 9*l + 38. Let m be c(12). Factor 7*w**2 + 30 - 84*w - m*w**2 + 109*w.
5*(w + 2)*(w + 3)
Let h(m) be the second derivative of -m**7/5040 - m**6/720 - 5*m**4/4 + 3*m. Let d(r) be the third derivative of h(r). Factor d(j).
-j*(j + 2)/2
Let q(k) be the first derivative of k**7/2100 - k**6/300 + k**5/150 - 23*k**3/3 - 14. Let g(z) be the third derivative of q(z). Find c such that g(c) = 0.
0, 1, 2
Let s(x) be the third derivative of x**5/20 - 31*x**4/8 - 16*x**3 + 37*x**2 - 8*x. Find k, given that s(k) = 0.
-1, 32
Factor -1/2*s**2 + 3*s - 4.
-(s - 4)*(s - 2)/2
Suppose 4*p - 48 = -0*p. Suppose 7 = -p*w + 31. Find h, given that 2/5*h**w + 6/5*h + 0 = 0.
-3, 0
Let a(m) = 45*m**3 - 820*m**2 + 1340*m - 730. Let v(l) = 5*l**3 - 91*l**2 + 149*l - 81. Let o(z) = -6*a(z) + 55*v(z). Factor o(x).
5*(x - 15)*(x - 1)**2
Let k(w) be the first derivative of -4*w**3 - 66*w**2 - 363*w + 55. Solve k(g) = 0 for g.
-11/2
Let x(w) be the second derivative of w**4/54 + 50*w**3/27 + 625*w**2/9 + 2*w - 7. Factor x(c).
2*(c + 25)**2/9
Let f(u) = 2*u**2 - 3*u + 1. Let l be f(2). Suppose l*x - 2*b = 10 - 1, -5*b + 3 = x. Factor -5*y - x*y**3 + 12*y**2 - 3*y + 6 + 0*y**3 - 7*y.
-3*(y - 2)*(y - 1)**2
Let 2/3*z**2 + 0 - 4/9*z - 2/9*z**3 = 0. What is z?
0, 1, 2
Let z = 2683 + -2683. Let b = 1 + 1. Solve z + 1/4*w**b + 0*w = 0.
0
Let z(i) be the third derivative of -19/6*i**5 - 20/3*i**3 + 0*i - 35/6*i**4 + 0 - 4/21*i**7 - 5/336*i**8 - 25/24*i**6 + 12*i**2. Factor z(m).
-5*(m + 1)**2*(m + 2)**3
Determine d, given that 1/3*d**2 + 14/3 - 5*d = 0.
1, 14
Let c(l) be the second derivative of l**5/4 - 5*l**4/12 - 5*l**3/3 + 2*l - 10. Find g such that c(g) = 0.
-1, 0, 2
Let n(d) be the first derivative of 2/21*d**3 - 15 - 1/7*d**2 + 0*d. Factor n(o).
2*o*(o - 1)/7
Let x(k) be the first derivative of k**5 + 45*k**4/2 + 545*k**3/3 + 630*k**2 + 980*k + 18. Solve x(f) = 0.
-7, -2
Factor 8*h - 8*h**2 + h**4 + 3*h + h**4 + 5*h + 3*h**3 - 7*h**3.
2*h*(h - 2)**2*(h + 2)
Let l(j) be the first derivative of -j**5/5 + j**2/2 - j + 9. Let o(f) = -f**4 + 24*f**2 - 2*f - 46. Let x(u) = -2*l(u) - o(u). Factor x(w).
3*(w - 2)**2*(w + 2)**2
Let p = 138 - 110. Let h = 31 - p. Factor 0 - h*g + 9/2*g**2 - 3/2*g**4 + 0*g**3.
-3*g*(g - 1)**2*(g + 2)/2
Suppose 24 + 25*h + 91*h**2 + 85*h**2 + 7*h - 162*h**2 + 2*h**3 = 0. What is h?
-3, -2
Let g be 398/(-3383) + 44/85. Solve 4/5 + g*m**3 - 4/5*m**2 - 2/5*m = 0.
-1, 1, 2
Solve 68*y**3 + 20*y**4 - 96 - 5*y + 33*y + 69*y**2 + 100 = 0 for y.
-2, -1/2, -2/5
Let c(t) be the first derivative of -56*t**3/15 - 13*t**2 + 36*t/5 + 723. Determine k so that c(k) = 0.
-18/7, 1/4
Let q(l) be the third derivative of -l**6/300 - l**5/50 - 16*l**2 - 16*l. Factor q(a).
-2*a**2*(a + 3)/5
Suppose -18*f = -15*f - 15. Let i(x) be the first derivative of 1/12*x**4 + 1/3*x**3 + 1/3*x + 1/2*x**2 + f. Factor i(k).
(k + 1)**3/3
Suppose z + 0*z = -4*f + 81, -3*z + 273 = -3*f. Let o = z - 177/2. Let 1/2*l**2 + l + o = 0. Calculate l.
-1
Let p(w) = 2*w**3 - w**2 - w + 1. Let k be p(1). Let l be (k - 4) + 6 + 0. Let -5 - 40*z - 3*z**2 - l + 16*z - 40 = 0. What is z?
-4
Let v(r) be the first derivative of 2*r**6/3 + 28*r**5/5 + 11*r**4 + 20*r**3/3 - 93. Solve v(i) = 0.
-5, -1, 0
Let z be -3*(-9)/(-216)*(-4)/210. Let h(b) be the third derivative of -1/120*b**5 + 0*b + 0*b**3 + 0*b**6 + 0*b**4 + z*b**7 - 3*b**2 + 0. Factor h(c).
c**2*(c - 1)*(c + 1)/2
Let d(j) be the third derivative of 7/150*j**6 - 8/75*j**5 - 2/175*j**7 + 0*j - 46*j**2 + 0 + 1/840*j**8 + 3/20*j**4 - 2/15*j**3. Factor d(h).
2*(h - 2)*(h - 1)**4/5
Suppose 0 = -r - 0*r + 3. Suppose 2*m + 28 = 9*m. Factor -3*f**5 + f + f**5 + 4*f**m - r*f**2 - f**2 + f.
-2*f*(f - 1)**3*(f + 1)
Let x be (420/630)/((-5)/(-12)). Determine t so that -2/5*t**5 + 0 - 8/5*t**2 - x*t**4 - 12/5*t**3 - 2/5*t = 0.
-1, 0
Let k be 602/70 + 6/(-10). Factor -11*r**5 - 12*r - r**5 + k - 2*r**2 + 11*r**5 + 7*r**3.
-(r - 2)*(r - 1)**2*(r + 2)**2
Let y = -968 + 2905/3. Let a(n) be the first derivative of 1/9*n**3 + y*n**2 + 1/3*n - 5. Factor a(u).
(u + 1)**2/3
Let r be -7 + 22/4 + 5/2 + 2. Let -2/9*k + 2/3 + 2/9*k**r - 2/3*k**2 = 0. Calculate k.
-1, 1, 3
Let h be (-129)/(