ppose -4*o + 16 = -4*l, 2*o - 5*l = -0*l + 5. Factor 5*t**2 + 27*t**3 - t**o + 2*t**2 - 3*t**4 - 4 - 26*t**3.
-(t - 1)**2*(t + 1)*(t + 2)**2
Let r(q) be the second derivative of -q**5/4 - 25*q**4/3 + 230*q**3/3 - 240*q**2 + 345*q. Factor r(u).
-5*(u - 2)**2*(u + 24)
Suppose -5*j - 5*m + 10 = -8*m, 0 = m. Let x(i) be the third derivative of 1/30*i**4 + 0 + 4*i**j - 1/150*i**5 + 0*i**3 + 0*i. Factor x(c).
-2*c*(c - 2)/5
Factor 2/9*v**2 + 4/3 - 14/9*v.
2*(v - 6)*(v - 1)/9
Let b = -155 + 1087/7. Suppose -6*s + 10*s = 0. Factor -10/7*d**2 + 4/7*d + b*d**4 + s - 2/7*d**5 + 6/7*d**3.
-2*d*(d - 1)**3*(d + 2)/7
Let l(h) be the first derivative of -h**4/2 - 26*h**3/3 - 30*h**2 - 90. Suppose l(b) = 0. What is b?
-10, -3, 0
Let b be 114/144 - (3 + (-115)/40). Let -8/3*m - 8/3 - b*m**2 = 0. What is m?
-2
Let p = 5885/2 - 11769/4. Factor -7*d**2 + 9*d + 9/4*d**3 - 4 - p*d**4.
-(d - 4)*(d - 2)**2*(d - 1)/4
Factor 97*z**2 - 214*z**2 + 3*z + 7*z + 72*z**2 + 20*z**3.
5*z*(z - 2)*(4*z - 1)
Let q(v) be the second derivative of v**6/10 - 123*v**5/10 + 1597*v**4/4 + 1722*v**3 + 2646*v**2 + v + 82. What is c in q(c) = 0?
-1, 42
Suppose -2*m**4 + 6804*m - 2146*m**2 - m**4 + 126*m**3 + 499*m**2 - 8748 = 0. Calculate m.
3, 18
Let h(y) be the first derivative of 2*y**5/15 - 5*y**4/6 + 4*y**3/9 + 8*y**2/3 - 237. Solve h(z) = 0 for z.
-1, 0, 2, 4
Let w(x) = 3*x**2 - 18*x + 37. Let y(g) = 10*g**2 - 56*g + 113. Let k(m) = -7*w(m) + 2*y(m). Factor k(l).
-(l - 11)*(l - 3)
Suppose -3*l - 5*x = -22, 12 - 2 = 3*l - x. Suppose -l*p = -3 - 9. Determine n so that -1 - 2 + 3*n**2 - 3*n - p + 0*n = 0.
-1, 2
Let k(u) be the third derivative of u**8/504 + 8*u**7/315 - u**6/18 - 4*u**5/45 + u**4/4 + 153*u**2 - 1. Find f such that k(f) = 0.
-9, -1, 0, 1
Suppose 0 = j - 12 - 10. Let h = 27 - j. Factor -2/7*v**3 + 0 + 0*v**4 + 0*v**2 + 2/7*v**h + 0*v.
2*v**3*(v - 1)*(v + 1)/7
Let c(j) be the third derivative of -j**7/8820 - j**6/1260 - 3*j**4/8 + 6*j**2. Let q(n) be the second derivative of c(n). Suppose q(o) = 0. Calculate o.
-2, 0
Let f(y) be the third derivative of y**7/4200 + y**6/1200 - 5*y**4/24 + y**2. Let j(t) be the second derivative of f(t). Factor j(c).
3*c*(c + 1)/5
Let v be 3/(-16)*-4*4. Factor 2*r**5 + 11*r**4 - 30*r**4 - 12*r + v*r**4 + 8*r**3 + 16*r**2 + 2*r**5.
4*r*(r - 3)*(r - 1)**2*(r + 1)
Let o = -4/5 - -13/10. Let w(g) be the first derivative of 0*g**3 - 9 - 3*g**2 + 4*g + o*g**4. Suppose w(a) = 0. Calculate a.
-2, 1
Suppose 5*k - 33 = -2*a, -3*a - 2*a + 5 = -3*k. Let -4*c**k - 28*c**2 - 4*c**4 - 34*c**2 + 62*c**2 = 0. Calculate c.
-1, 0
Let a be 1 + -4 - -6 - (-186)/(-63). Let r(f) be the second derivative of -1/70*f**5 - 5*f - a*f**3 + 0 + 0*f**2 - 1/21*f**4. Factor r(b).
-2*b*(b + 1)**2/7
Let i(z) = -15*z**2 - 6210*z - 961015. Let u(d) = -7*d**2 - 3104*d - 480506. Let n(g) = -2*i(g) + 5*u(g). Factor n(v).
-5*(v + 310)**2
Let w = 25754 + -77252/3. Determine t so that 3 - 1/6*t**5 + w*t**2 - t**4 + 13/2*t - t**3 = 0.
-3, -1, 2
Let b(f) be the second derivative of 4*f**7/147 - f**6/35 - f**5/14 + f**4/14 + f**3/21 - 10*f. Determine d so that b(d) = 0.
-1, -1/4, 0, 1
Let -3*z - 10*z**2 - 13*z + 21*z**2 + 3*z - 2 + 4 = 0. What is z?
2/11, 1
Suppose -106*z + 140 = -36*z. What is u in 0 + 0*u + 0*u**z + 1/4*u**4 - 1/4*u**5 + 1/2*u**3 = 0?
-1, 0, 2
Let r = -4699 - -4699. Factor -4/15*o**2 + 16/15*o**4 + 0*o + 2/3*o**5 + 2/15*o**3 + r.
2*o**2*(o + 1)**2*(5*o - 2)/15
Factor 528*z**3 + 34320*z + 4*z**4 - 434236*z**2 - 673 + 17573 + 452180*z**2.
4*(z + 1)**2*(z + 65)**2
Suppose -99/5*q + 24/5*q**2 + 54/5 + 6*q**3 - 6/5*q**4 - 3/5*q**5 = 0. What is q?
-3, 1, 2
Suppose 8*k + 96 = 14*k. Factor 2 + 2 + 5*w**2 - 10*w**3 + 3*w**3 + k*w.
-(w - 2)*(w + 1)*(7*w + 2)
Let l = 2437/77 + -345/11. Factor 4/7*a**3 - 2/7*a + 0 + 0*a**4 - l*a**5 + 0*a**2.
-2*a*(a - 1)**2*(a + 1)**2/7
Factor 1/3*o**3 - 4/3*o**2 + 0 + 0*o.
o**2*(o - 4)/3
Factor -2/11*w**3 + 42/11*w**2 - 294/11*w + 686/11.
-2*(w - 7)**3/11
Factor 4*z**4 - 15/2*z**3 - 1/2*z**5 + 0*z + 0*z**2 + 0.
-z**3*(z - 5)*(z - 3)/2
Suppose -6*h = -16*h. Let o(n) be the first derivative of -2/15*n**5 + h*n - 1/3*n**2 - 1/2*n**4 - 2/3*n**3 + 4. Find v, given that o(v) = 0.
-1, 0
Let x(j) = j**2 + 4*j. Let l(t) = -t**2 + 4*t + 7. Let w be l(6). Let s be x(w). Factor 0*a**4 - 2*a**4 - 2*a**4 + s*a**3 - a**2.
-a**2*(a - 1)*(4*a - 1)
Let v = -15 - 5. Let k be (16/(-20))/(8/v). Suppose r**3 + 0*r**2 - 3*r**3 + 0*r**k - 8*r**4 = 0. Calculate r.
-1/4, 0
Let j(k) be the second derivative of -k**5/180 - 5*k**4/72 + k**3/3 + 6*k**2 - 2*k. Let r(z) be the first derivative of j(z). Factor r(q).
-(q - 1)*(q + 6)/3
Let q(a) be the first derivative of 3*a**5/20 + 3*a**4/4 - 25*a**3/4 - 21*a**2/2 - 226. Find g, given that q(g) = 0.
-7, -1, 0, 4
Factor 0 - 224/3*b - 52*b**3 - 328/3*b**2 + 1/3*b**5 - 22/3*b**4.
b*(b - 28)*(b + 2)**3/3
Let w(i) = -7*i**2 + 34*i + 4. Let d be w(5). Let q be (11/5 + d)/((-14)/(-35)). Factor -2/7*g + 0 + 5/7*g**2 - 4/7*g**q + 1/7*g**4.
g*(g - 2)*(g - 1)**2/7
Let a(x) = -x**2 + x + 4. Let i be a(-2). Let z be (-10)/105*(4 + i - 5). Factor -4/7*g - z*g**2 - 2/7.
-2*(g + 1)**2/7
Suppose 0 = 5*n + 260 - 270. Let s(l) be the first derivative of 1 - l**3 + 3/2*l**n + 6*l. Factor s(j).
-3*(j - 2)*(j + 1)
Let q be 5/(-2)*(-2 - 0). Suppose q*r + 2 = 12. Solve -r*g**4 + 1 - 3*g**4 - 2*g + 4*g**4 + 2*g**3 = 0 for g.
-1, 1
Let g(z) be the second derivative of -z**6/20 + 93*z**5/40 - 35*z**4 + 147*z**3 + 8*z + 58. Solve g(s) = 0.
0, 3, 14
Solve l + 1/6*l**2 + 0 = 0.
-6, 0
Suppose 777 + 1688 = -5*c. Let u be c/(-145) + (-2)/(-5)*-1. Factor -10/3*d**u - 2/3*d - 16/3*d**2 + 4/3.
-2*(d + 1)**2*(5*d - 2)/3
Suppose -4*d - 16 = 2*h - 0*h, -d = -h + 4. Suppose h = -8*x - 4*x + 24. Determine o so that -40/7*o**2 + 16/7*o - x*o**4 + 2/7*o**5 + 0 + 36/7*o**3 = 0.
0, 1, 2
Let p = -15 - -9. Let b be (-2)/p - (-68)/12. Suppose l**3 - 4*l**2 + l**3 + b*l**2 = 0. What is l?
-1, 0
Let p be (-6 + 2)/((-2)/3). Suppose 4*t = -2*i, -i - 4*t + t = 1. Determine n, given that i*n**2 - 2*n**2 + p*n + 3*n**2 = 0.
-2, 0
Suppose -2*a - 2 = -h, 15*a + h - 16 = 10*a. Factor -4/3*m**a - 4*m + 0.
-4*m*(m + 3)/3
Factor 328/5*i - 13448/5 - 2/5*i**2.
-2*(i - 82)**2/5
Let q(n) be the third derivative of 0*n - 1/20*n**5 + 10*n**2 + 0 + n**3 + 1/8*n**4. Solve q(x) = 0.
-1, 2
Let y be (2/(-8))/((-10)/8). Factor -y*d**2 + 0 - 1/5*d.
-d*(d + 1)/5
Factor 7*u + 147/2 + 1/6*u**2.
(u + 21)**2/6
Let r = 26 - 24. Find p, given that p + 3*p**r + 2*p + 0*p**2 = 0.
-1, 0
Let d be -4 - -8 - (2/2 - 2). Let t be 279/54 - d/30. Suppose 2/5*g**t + 0*g**2 + 0*g**4 + 0 + 0*g - 2/5*g**3 = 0. What is g?
-1, 0, 1
Suppose 8 = 142*q - 138*q. Factor 16/3*n**q + 16/3*n + 4/3*n**3 + 0.
4*n*(n + 2)**2/3
Let y(d) be the second derivative of 0 + 0*d**3 + 1/54*d**4 + 1/15*d**5 + 1/15*d**6 + 4/189*d**7 + 17*d + 0*d**2. Factor y(m).
2*m**2*(m + 1)**2*(4*m + 1)/9
Factor -2/15*a**2 - 34/5*a + 104/15.
-2*(a - 1)*(a + 52)/15
Factor -361/4 + 38*m - 4*m**2.
-(4*m - 19)**2/4
Let t(s) be the second derivative of s**7/26460 + s**4 + 11*s. Let k(i) be the third derivative of t(i). Factor k(g).
2*g**2/21
Let v(m) be the first derivative of -m**3/4 + 21*m**2/2 + 45*m - 314. What is o in v(o) = 0?
-2, 30
Let q(o) = -27*o**3 + 97*o**2 + 53*o - 57. Let v(j) = -14*j**3 + 49*j**2 + 26*j - 29. Let w(h) = -4*q(h) + 7*v(h). Factor w(n).
5*(n - 5)*(n + 1)*(2*n - 1)
Suppose 0 = -9*q + 7*q + 8. Let j(v) = v - 4. Let s be j(q). Find h such that -2/9*h**2 + s + 2/9*h**5 + 2/9*h**4 - 2/9*h**3 + 0*h = 0.
-1, 0, 1
Factor -2 + 2/9*z**2 - 2*z + 2/9*z**3.
2*(z - 3)*(z + 1)*(z + 3)/9
Suppose -3*h + 36 = -4*s, -12 = 3*s - 3. Let -h + 4*t - 1/2*t**2 = 0. Calculate t.
4
Let c(k) be the third derivative of 3*k**8/224 + 2*k**7/15 + k**6/20 - 12*k**5/5 - 4*k**4/3 + 721*k**2 - 1. Determine o so that c(o) = 0.
-4, -2/9, 0, 2
Suppose -5*n - 4 = a, -a - 5*n = 4*a - 60. Suppose a = 4*u - 2*u. Factor 2 + 3*w - u*w**2 + 4 + 0*w**2 + 5*w**2.
-3*(w - 2)*(w + 1)
Let o = 13306 + -13304. Find s, given that 0 + 4/5*s**o + 0*s = 0.
0
Let o be 2/40 + 1 + -1. Let w(k) be the first derivative of 1/4*k - 6 + o*k**5 + 1/2*k**3 + 1/4*k**4 + 1/2*k**2. Let w(b) = 0. What is b?
-1
Let a(m) be the first derivative of 0*m**2 + 1/5*m**5 - 15 - 1/2*m**4 + 0*m + 0*m**3 + 1/6*