) = s*y(p) + z*d(p). Determine u, given that r(u) = 0.
0
Let q(x) be the third derivative of x**9/80640 + x**8/26880 - x**7/3360 - x**5/3 - 31*x**2. Let b(o) be the third derivative of q(o). Factor b(r).
3*r*(r - 1)*(r + 2)/4
Let k(a) be the second derivative of a**8/1680 + a**7/840 + 3*a**3 - 7*a. Let r(j) be the second derivative of k(j). Factor r(m).
m**3*(m + 1)
Let m be (-30100)/18 + 20/(-10) - 1. Let i = m - -1677. Factor -56/9*x + 16/9 + 76/9*x**2 - 50/9*x**3 + i*x**4 - 2/9*x**5.
-2*(x - 2)**3*(x - 1)**2/9
Let m(y) be the third derivative of y**5/360 - 7*y**4/144 - 46*y**2. Factor m(g).
g*(g - 7)/6
Let b = -517/14 + 37. Let y(t) be the first derivative of 4/7*t**2 + 0*t + 8/21*t**3 + b*t**4 - 3. Factor y(n).
2*n*(n + 2)**2/7
Determine b so that -38/7*b**2 + 0 + 8/7*b**5 + 18/7*b - 58/7*b**4 - 122/7*b**3 = 0.
-1, 0, 1/4, 9
Let p(l) be the first derivative of -l**4/8 - 10*l**3 - 117*l**2/4 - 29*l + 243. Factor p(d).
-(d + 1)**2*(d + 58)/2
Suppose -3*u + 14 = -0*t + t, 0 = -4*u + 5*t - 13. Let z be (0/8)/((3 - 1) + 0). Factor 8/7*x + 2/7*x**u + 8/7*x**2 + z.
2*x*(x + 2)**2/7
Let h(o) = o**3 + 9*o**2 + o + 13. Let l be h(-9). Let j be (1/(-3))/(1/(-66)). Suppose 2*b**2 - 22 - l*b + j = 0. Calculate b.
0, 2
Let g(z) be the first derivative of -9*z**4 - 4*z**2 - 11 - 2/3*z**6 + 28/3*z**3 + 4*z**5 + 0*z. Factor g(m).
-4*m*(m - 2)*(m - 1)**3
Factor -1/2*t**3 + 0 + 3/2*t**2 - t.
-t*(t - 2)*(t - 1)/2
Suppose -89*h - 40 = -97*h. Let j(i) be the third derivative of 1/20*i**h + 5*i**2 + 1/2*i**4 + 3/2*i**3 + 0*i + 0. Factor j(n).
3*(n + 1)*(n + 3)
Suppose 0 = 3*a + a - 8. Suppose a*t - 5*m = -t + 24, 4*m + 24 = 4*t. Factor 1 + 4*c + 0 - 2*c**2 + 0*c**2 - t.
-2*(c - 1)**2
Let u(d) be the second derivative of -6*d + 1/20*d**5 + 0*d**2 + 0*d**3 - 1/90*d**6 + 0 + 1/9*d**4. Factor u(k).
-k**2*(k - 4)*(k + 1)/3
Let m(p) = 11*p**2 + 6*p - 2. Let v(u) = 21*u**2 + 12*u - 4. Let y(g) = 10*m(g) - 6*v(g). Let n(z) = -z**2 - z - 1. Let i(o) = 12*n(o) - y(o). Factor i(x).
4*(x - 2)*(x + 2)
Suppose -g = -2*g + 3306. Solve -3306*h - h**2 + g*h - 2*h**3 = 0 for h.
-1/2, 0
Suppose 0 = -2*c - 2*c + 16. Let f = -2 + c. Solve 3*p**2 + 0*p - f*p + 2*p = 0.
0
Let n(d) = 5*d**4 - 23*d**3 + 5*d**2 + 107*d - 88. Let a(b) = 60*b**4 - 275*b**3 + 60*b**2 + 1285*b - 1055. Let x(j) = -2*a(j) + 25*n(j). Factor x(t).
5*(t - 3)**2*(t - 1)*(t + 2)
Factor 11/4*r**3 + 99/8*r**2 + 13/2 - 1/8*r**4 + 16*r.
-(r - 26)*(r + 1)**2*(r + 2)/8
Let u(p) be the first derivative of p**5/50 - p**4/15 + p**3/15 - 20*p - 23. Let o(r) be the first derivative of u(r). Factor o(b).
2*b*(b - 1)**2/5
Let n(x) = x**3 - 8*x**2 + x - 3. Let v be n(8). Let g = 25723/7 - 3667. Factor 3*t - g*t**2 - 3/7 + 66/7*t**3 - 39/7*t**4 + 9/7*t**v.
3*(t - 1)**4*(3*t - 1)/7
Let f(q) = 13*q**2 + 38*q + 367. Let x(w) = 2*w**2 + 1. Let t(k) = -f(k) + 6*x(k). Factor t(y).
-(y + 19)**2
Let y(n) be the third derivative of 4/1155*n**7 - 5*n**2 + 1/165*n**6 + 0*n**3 + 0*n**4 + 0*n + 0 + 1/330*n**5. Factor y(u).
2*u**2*(2*u + 1)**2/11
Let o(f) be the third derivative of f**7/560 - 11*f**5/80 - 3*f**4/8 + 45*f**3/16 - 34*f**2 - 6. Find y such that o(y) = 0.
-3, 1, 5
Let j be 1/(-5) + (-2261)/95. Let n(l) = -9*l**2 + 4*l + 3. Let t be (2 - 1) + 9 + -5. Let k(g) = -44*g**2 + 20*g + 16. Let b(y) = j*n(y) + t*k(y). Factor b(h).
-4*(h - 2)*(h + 1)
Find b such that 3*b**2 + 0 + 8/3*b + 1/3*b**3 = 0.
-8, -1, 0
Let s(w) be the third derivative of 1/210*w**5 - 1/168*w**4 + 0 + 0*w**3 + 5*w**2 + 0*w - 1/840*w**6. Find k, given that s(k) = 0.
0, 1
Let s(u) be the third derivative of u**7/840 + 7*u**6/480 + u**5/60 - u**4/8 + 196*u**2 - u. What is v in s(v) = 0?
-6, -2, 0, 1
Factor 1/6 + 2/3*t**3 - 7/6*t**2 + 1/3*t.
(t - 1)**2*(4*t + 1)/6
Suppose -38*x + 187 - 73 = 0. Suppose -f - 2*p - 4 = 3*f, 5*f + 6 = -3*p. Solve -2/3*k + 0 + f*k**2 + 2/3*k**x = 0 for k.
-1, 0, 1
Let b(c) = c**2 + 4. Let j(q) = -2*q**2 - 12*q - 83. Let o(l) = 5*b(l) + j(l). Factor o(w).
3*(w - 7)*(w + 3)
Let a be -3 + -1 + -10 + 1184/48. Let l(f) be the first derivative of -10 - 4/3*f**4 - 2/15*f**5 - a*f - 16/3*f**3 - 32/3*f**2. Factor l(m).
-2*(m + 2)**4/3
Let t = -41 - -21. Let o(v) = 45*v**5 - 80*v**4 + 65*v**3 - 10*v**2 + 20*v. Let g(c) = c**5 - c**4 + c**3 + c. Let d(s) = t*g(s) + o(s). Factor d(w).
5*w**2*(w - 1)**2*(5*w - 2)
Let u = -13 - -68/5. Let a be (-1 + 0)*(-38)/95. Let -1/5*r**4 + a*r**2 - 1/5 + u*r**5 - 6/5*r**3 + 3/5*r = 0. What is r?
-1, 1/3, 1
Suppose 0 = 8*z - 0*z - 56. Suppose 5*j = z*j. Find d, given that -2/9*d**5 - 2/3*d**3 - 2/9*d**2 - 2/3*d**4 + j + 0*d = 0.
-1, 0
Let b(w) = w**2 + 1. Let d(a) = 8*a**2 - 394*a + 38816. Let v(q) = -21*b(q) + 3*d(q). Find n such that v(n) = 0.
197
Factor 230/3 + 35*c - 5/3*c**2.
-5*(c - 23)*(c + 2)/3
Let o be (6/(-14))/(9/(-63)). Let w(m) be the second derivative of 5*m + 1/9*m**o + 0 - 1/189*m**7 + 1/9*m**2 + 1/27*m**4 - 1/45*m**6 - 1/45*m**5. Factor w(v).
-2*(v - 1)*(v + 1)**4/9
Let b = -8549 + 25649/3. Let 2*x**2 - 4/3*x**3 - b + 0*x = 0. What is x?
-1/2, 1
Let y be ((-3)/(1 + 17))/(2/(-5)). Let k(g) be the first derivative of 2/3*g + 6 - y*g**4 + 1/15*g**5 - 7/6*g**2 + g**3. Factor k(r).
(r - 2)*(r - 1)**3/3
Factor -2/15*k**5 + 0*k - 6/5*k**3 + 8/15*k**2 + 4/5*k**4 + 0.
-2*k**2*(k - 4)*(k - 1)**2/15
Let w be (-12 - 132/(-9))/(4/((-24)/(-14))). Suppose 0*m + 0*m**4 + 0 - 12/7*m**3 + w*m**2 + 4/7*m**5 = 0. What is m?
-2, 0, 1
Let q be (-177)/27 - 39/(-26). Let f = 11/2 + q. Determine i so that -f*i**2 + 0*i + 0 + 4/9*i**4 - 2/3*i**3 = 0.
-1/2, 0, 2
Let v be -1 + 1406/6*2. Let m = -435 + v. Factor -176/3*q - 350/3*q**2 - m*q**3 - 8.
-2*(q + 3)*(7*q + 2)**2/3
Suppose 2*v - 5*m + 12 = 147, 4*m = 5*v - 329. Let q be (52/v)/(4/10). Let -11 + 4*n**q - n**2 - 1 = 0. What is n?
-2, 2
Let z(u) = 3*u**2 - u. Let t be z(-1). Suppose 0 = -2*v + 10. Let -3*d**t + d**3 + 3*d**v - 2*d**3 - 2*d**3 + 3*d**2 = 0. What is d?
-1, 0, 1
Let k be (-272)/(-51) + 3*12/(-27). Let l(j) be the second derivative of 0 - j**3 + 0*j**2 + 6*j + 1/4*j**k. Factor l(c).
3*c*(c - 2)
Let p(h) be the second derivative of -3/2*h**3 + 1/2*h**4 + 1/14*h**7 + 3/10*h**5 - 8*h - 3/10*h**6 + 0 + 3/2*h**2. Solve p(g) = 0.
-1, 1
Let j(k) be the third derivative of -k**7/70 - 13*k**6/280 - k**5/28 + k**4/56 + 14*k**2. Factor j(w).
-3*w*(w + 1)**2*(7*w - 1)/7
Let a(q) be the second derivative of -7*q**5/5 - 23*q**4/3 - 4*q**3 + 113*q. What is h in a(h) = 0?
-3, -2/7, 0
Factor -31*c**2 - 2*c**2 - 27*c**2 + 8 - 10*c**2 - 136*c.
-2*(c + 2)*(35*c - 2)
Let r(u) = 5*u**2 - 6*u + 5. Let i be r(4). Let l = -547/9 + i. Factor 0*o + l*o**2 - 2/9.
2*(o - 1)*(o + 1)/9
Let u(k) be the first derivative of -8*k**2 + 2/3*k**3 - 27 - 18*k. Suppose u(q) = 0. What is q?
-1, 9
Suppose -c - 2*k = -1, -k = -2*c - 3*k - 4. Let r(o) = o + 1. Let p(t) = 9*t**3 + 19*t**2 + 5*t - 5. Let s(g) = c*p(g) - 30*r(g). Find y, given that s(y) = 0.
-1, -1/9
Let c(q) be the third derivative of q**5/20 + 129*q**4/4 + 16641*q**3/2 + 76*q**2. Factor c(r).
3*(r + 129)**2
Let o(p) be the second derivative of p**4/3 - 2*p**3 - 36*p**2 + 3*p + 6. Factor o(n).
4*(n - 6)*(n + 3)
Suppose -1761 + 403 = -7*a. Let n = 196 - a. Solve -1/2*g + 1/4*g**n + 1/4 = 0.
1
Let c be ((-2)/54*-9)/(1/6). Factor -4/3*t - 1/3*t**c + 5/3.
-(t - 1)*(t + 5)/3
Let f(b) = b**2 - b + 4. Let y be f(0). Let 26*j - 2*j**4 + 8 + 0*j + 14*j**3 + 30*j**2 + y*j**4 = 0. What is j?
-4, -1
Suppose -3*c + 8 = c. Let v = 3 - -9. Factor c + v*h**2 + 9*h**2 - 20*h**2 - 4 - h.
(h - 2)*(h + 1)
Let m(h) be the second derivative of -3*h**5/20 + 7*h**4/4 - 15*h**3/2 + 27*h**2/2 - 40*h. Factor m(p).
-3*(p - 3)**2*(p - 1)
Let i = 31/21 + -19/21. Find n, given that -12/7*n**2 + 8/7 + 4/7*n**4 + i*n - 4/7*n**3 = 0.
-1, 1, 2
Let s(u) be the third derivative of -2*u**7/105 - 19*u**6/10 - 37*u**5/5 - 55*u**4/6 - 915*u**2 + 2*u. Determine c, given that s(c) = 0.
-55, -1, 0
Let q(j) be the second derivative of 1/48*j**4 - 1/80*j**5 - 5*j + 0 + 1/6*j**3 - 1/2*j**2. Factor q(l).
-(l - 2)*(l - 1)*(l + 2)/4
Let u(l) = 4*l**4 + 4*l**3 - 2*l**2 - 4*l - 2. Let o(k) = k**5 - k**3 + k**2 + 2*k + 1. Let i(d) = -2*o(d) - u(d). Factor i(j).
-2*j**3*(j + 1)**2
Let t(i) = 38*i**3 + 116*i**2 + 137*i + 51. Let h(y) = 191*y**3 + 578*y**2 + 687*y + 256. Let o(p) = 6*h(p) -