w**3 - w**2 - 2/3*w.
-w*(w + 1)*(w + 2)/3
Suppose -5*v + 3*w = -25, 0 = -v - 5*w + w - 18. Factor -1/7*r + 1/7*r**v + 0.
r*(r - 1)/7
Let z(s) be the third derivative of -s**9/12096 + s**8/2016 - s**7/1008 - 14*s**5/15 + 8*s**2 + 2. Let d(a) be the third derivative of z(a). Factor d(p).
-5*p*(p - 1)**2
Suppose -4*g = -3 - 1. Suppose -g = y - 4. Suppose 48*b**y + 15*b**4 + 33*b**2 - 3*b + 9*b + 6*b**4 = 0. Calculate b.
-1, -2/7, 0
Suppose -2*a - 5*y = -35, 0 = -a - 4*a - 4*y + 79. Let z be -1*5/a*0. Factor -3/2*j**2 + 3/2 + z*j.
-3*(j - 1)*(j + 1)/2
Let o(d) be the first derivative of -d**3 + 42*d**2 - 588*d + 5. Factor o(i).
-3*(i - 14)**2
Let z(m) = 4*m**4 + m**3 + 8*m - 13. Let b(a) = -a**4 - 2*a + 3. Let d = -52 - -50. Let y(g) = d*z(g) - 9*b(g). Determine k so that y(k) = 0.
-1, 1
Let z be 5 - 2*(-21)/(-9). Solve 1/3 - 1/6*u**3 - z*u**2 + 1/6*u = 0.
-2, -1, 1
Let t be -1 - -11 - 36736/3690. Let v(w) be the third derivative of 0*w**3 + 0*w + 0 - 2/105*w**7 - 11*w**2 - 1/45*w**5 + 0*w**4 + t*w**6. Factor v(p).
-4*p**2*(p - 1)*(3*p - 1)/3
Factor 27648/7 - 2/7*d**3 + 144/7*d**2 - 3456/7*d.
-2*(d - 24)**3/7
Let c(f) be the second derivative of -2/15*f**5 + 12*f - 1/126*f**7 + 0*f**2 + 1/9*f**4 + 1/18*f**6 + 0 + 0*f**3. Suppose c(i) = 0. Calculate i.
0, 1, 2
Let o(m) be the second derivative of m**3/6 - 3*m**2/2 - 14*m. Let d be o(6). Solve 0*y + 3/2*y**d + 0 + 0*y**2 + 3/2*y**4 = 0 for y.
-1, 0
Factor 32*v**2 - 720 + 610*v - 632*v + 2*v**3 - 732.
2*(v - 6)*(v + 11)**2
Let s = -4108/5 - -822. Factor 2/5*r**2 + s - 4/5*r.
2*(r - 1)**2/5
Let r = -29 - -33. Suppose 15*q**r + 92*q + 30*q**2 - 92*q - 55*q**3 = 0. What is q?
0, 2/3, 3
Let m(c) be the third derivative of -c**5/150 + c**4/20 - 2*c**3/15 + 124*c**2. Let m(w) = 0. Calculate w.
1, 2
Let q be 166/(-72)*3 - -7. Let x(r) be the first derivative of -q*r**3 + 0*r**2 + 1/16*r**4 + 10 + 0*r. Factor x(n).
n**2*(n - 1)/4
Factor 47/3*y**2 - 784/3 - 1/3*y**4 - 2*y**3 + 56*y.
-(y - 4)**2*(y + 7)**2/3
Let t(u) be the third derivative of 17*u**7/525 - 49*u**6/300 + 3*u**5/10 - 11*u**4/60 - 2*u**3/15 - 119*u**2. Factor t(i).
2*(i - 1)**3*(17*i + 2)/5
Let c = -4437/1204 - -2/301. Let x = c + 31/7. Find i, given that -1/4 - 3/4*i**2 - x*i - 1/4*i**3 = 0.
-1
Let t(f) be the second derivative of -1/5*f**4 + 0 + 0*f**3 + 1/25*f**5 + 8/5*f**2 + 12*f. Factor t(q).
4*(q - 2)**2*(q + 1)/5
Let x(f) = 4*f**2 - 2*f - 2. Let o(k) = -k**3 + 9*k**2 - 14*k - 2. Let a be o(7). Let t(p) = -p**2 + p. Let l(n) = a*x(n) - 4*t(n). Suppose l(z) = 0. What is z?
-1, 1
Let x be (-1)/((-918)/96) + -1*(-8)/68. Factor 0 + 8/9*m + x*m**3 - 17/9*m**2.
m*(m - 8)*(2*m - 1)/9
Let o(i) be the third derivative of 0 + 0*i**3 + 1/30*i**5 + 0*i + 8*i**2 + 0*i**4. Determine k so that o(k) = 0.
0
Let x = -21 + 23. Factor -14*f**2 + 28*f + 4*f**3 + 2*f**x - 8 - 4*f**2 - 8*f.
4*(f - 2)*(f - 1)**2
Let r = -12472/65 - -2510/13. Factor -1 - r*h - 1/5*h**2.
-(h + 1)*(h + 5)/5
Let x = -17 - -13. Let b be 1 - (-4 + (-1 - x)). Find w such that 5 + 13 - 10*w**b + 21*w + w**2 = 0.
-2/3, 3
Factor 0*v - 1/2*v**3 + 0 - 1/4*v**4 - 1/4*v**2.
-v**2*(v + 1)**2/4
Suppose -5*w - 3*r - 27 = 0, -7*w - 3*r = -3*w + 24. Let j be (-5 + (-15)/w)/(-1). Factor 2/15*m + j - 2/15*m**2.
-2*m*(m - 1)/15
Let l(a) = a**2 + a. Let k(m) = 39*m**2 + 30*m**2 - 49*m**2 + 24*m. Let n = -4 + -12. Let v(w) = n*l(w) + k(w). Factor v(f).
4*f*(f + 2)
Let w be (-1)/((-2)/(-8)*-2). Let t be ((-5)/4)/((2755/152)/(-29)). Factor w*u**3 + 14/3*u**4 - 2*u**2 + t*u**5 + 0 - 4/3*u.
2*u*(u + 1)**3*(3*u - 2)/3
Let h(x) be the second derivative of -x**6/10 + 3*x**5/20 + x**4/4 - x**3/2 - 254*x. Solve h(w) = 0 for w.
-1, 0, 1
Solve -1696*h**3 + 4*h**2 - 91 - 305*h + 1701*h**3 + 36*h**2 + 351 = 0.
-13, 1, 4
Factor 112/13 + 2/13*x**2 - 114/13*x.
2*(x - 56)*(x - 1)/13
Let s(v) be the second derivative of 10*v + 0*v**2 + 0 + 1/105*v**6 + 5/42*v**4 - 2/21*v**3 - 2/35*v**5. Factor s(d).
2*d*(d - 2)*(d - 1)**2/7
Let l(g) be the first derivative of -1/5*g - 1/20*g**4 + 1/15*g**3 + 8 + 1/10*g**2. Suppose l(r) = 0. Calculate r.
-1, 1
Let b(w) be the third derivative of -w**6/630 - 2*w**5/105 + 5*w**4/42 - 14*w**3/3 + 17*w**2. Let a(r) be the first derivative of b(r). Factor a(i).
-4*(i - 1)*(i + 5)/7
Let g(q) be the third derivative of -1/1848*q**8 + 0 - 3/44*q**4 + 2/55*q**5 - 4/1155*q**7 + 0*q + 18*q**2 + 0*q**3 + 1/330*q**6. Find m such that g(m) = 0.
-3, 0, 1
Factor 0*c**4 - 5*c**3 + 52*c + 3*c**2 - c**4 - 43*c + 2*c**4.
c*(c - 3)**2*(c + 1)
Let g = 13/7 - 12/7. Let l(x) be the second derivative of g*x**2 - 6*x + 0 + 1/42*x**4 - 2/21*x**3. Suppose l(w) = 0. Calculate w.
1
Let m(d) be the second derivative of -1/51*d**3 - 3/170*d**5 + 0 + 0*d**2 - 7*d - 1/255*d**6 - 1/34*d**4. Find r, given that m(r) = 0.
-1, 0
Let p(a) = a**2 + 8*a - 17. Let c be p(-10). Factor -c*n - n - 27*n**2 + 2*n**2 - 6*n - 15*n**3.
-5*n*(n + 1)*(3*n + 2)
Let 4/7*i**3 + 16/7*i**2 + 0 + 12/7*i = 0. What is i?
-3, -1, 0
Let i(o) = o**4. Let y(z) = -9*z**4 - 24*z**3 - 27*z**2. Let m(g) = -12*i(g) - y(g). Factor m(v).
-3*v**2*(v - 9)*(v + 1)
Let k(a) = -a**3 + 14*a**2 + 15*a + 5. Let h be k(15). Let p(d) be the first derivative of -4*d**3 - 6*d - 3/4*d**4 - 15/2*d**2 + h. Find r such that p(r) = 0.
-2, -1
Solve 16*g**3 + 193*g**4 + 16*g**2 - 191*g**4 + 2*g**3 = 0 for g.
-8, -1, 0
Let z(c) = -c**3 + 5*c**2 + 10. Let k be z(5). Suppose 0 = -3*h - 2*h + k. Suppose 10*n**2 - n**h + 3*n + 10 - 12 = 0. What is n?
-2/3, 1/3
Let k(f) = 25*f**4 - 155*f**3 - 95*f**2 + 85*f - 35. Let j(l) = -2*l**4 + 13*l**3 + 8*l**2 - 7*l + 3. Let r(b) = 35*j(b) + 3*k(b). What is a in r(a) = 0?
-1, 0, 1, 2
Let l(p) be the first derivative of -p**4/38 + 8*p**3/57 - 5*p**2/19 + 4*p/19 - 71. Factor l(z).
-2*(z - 2)*(z - 1)**2/19
Let g(b) be the third derivative of -b**5/60 + 77*b**4/12 - 5929*b**3/6 + 144*b**2. Suppose g(f) = 0. Calculate f.
77
Suppose 4*i - 3*w - 639 = 0, -4*w + 221 + 601 = 5*i. Let d = 649/4 - i. Determine x so that -1/2 - d*x**2 - 3/4*x = 0.
-2, -1
What is c in 5 + 3*c**2 - 1571*c + 1550*c + 13 = 0?
1, 6
Let n be (1 - -21) + 60 + -70. Let z(i) be the first derivative of 0*i + 0*i**2 + 1/14*i**4 + 0*i**3 + n. Solve z(t) = 0.
0
Factor -17/3*n - 1/6*n**3 + 0 - 19/6*n**2.
-n*(n + 2)*(n + 17)/6
Suppose -4*x + 20 = 4*y, 591*x - y = 588*x + 7. Let u(a) be the first derivative of -10/7*a**2 - 50/7*a + 4 - 2/21*a**x. Factor u(p).
-2*(p + 5)**2/7
Let b(a) be the third derivative of -a**8/2240 - 3*a**7/1120 + a**5/40 - 4*a**3 + 11*a**2. Let n(g) be the first derivative of b(g). Factor n(j).
-3*j*(j - 1)*(j + 2)**2/4
Let s(p) be the first derivative of 2*p**2 + 3*p + 2 + 1/3*p**3. Factor s(i).
(i + 1)*(i + 3)
Let -58/7 - 60/7*s**2 + 1/7*s**3 + 117/7*s = 0. What is s?
1, 58
Suppose -3*y + y - 4*x = 2, 8 = 4*y + 2*x. Find k, given that 49 + y*k - k**2 - 106 + 55 = 0.
1, 2
Let n be (-4)/(-1)*(-140)/(-5 + 9). Let r = n + 145. Find h such that 4/13*h - 2/13*h**r + 6/13*h**2 - 2/13*h**3 - 6/13*h**4 + 0 = 0.
-2, -1, 0, 1
Let t be 1 - 156/32*24/(-18). Let d(a) be the first derivative of -5 - t*a**2 + 6*a + 2*a**3. Let d(z) = 0. What is z?
1/2, 2
Let b be (-360)/(-84) - (-8)/(-28). Let w(x) be the third derivative of 1/30*x**5 + 0*x + 1/12*x**b + 0*x**3 + 0 + 6*x**2. Factor w(h).
2*h*(h + 1)
Let n(c) = c**3 - 112*c**2 + 696*c - 998. Let k(t) = t**3 + 113*t**2 - 694*t + 997. Let l(y) = -2*k(y) - 3*n(y). Let l(x) = 0. Calculate x.
2, 10
Let r(y) be the first derivative of 25*y**4/4 - 30*y**3 - 165*y**2/2 - 50*y - 43. Factor r(z).
5*(z - 5)*(z + 1)*(5*z + 2)
Let d(s) be the third derivative of -s**7/1260 + s**6/90 - s**5/15 - s**4/8 - 16*s**2. Let y(b) be the second derivative of d(b). Factor y(w).
-2*(w - 2)**2
Let h(q) be the second derivative of q**5/210 + 4*q**4/63 + 16*q**3/63 - 2*q - 2. Factor h(v).
2*v*(v + 4)**2/21
Factor -11/3*n**2 - 40/3*n + 1/3*n**3 - 28/3.
(n - 14)*(n + 1)*(n + 2)/3
Suppose 8*w - 12 = 4*w. Suppose -t = -3 - w. Factor -7*m - 4*m + 2*m**2 + t*m**3 + 5*m - 4 + 2*m**4.
2*(m - 1)*(m + 1)**2*(m + 2)
Let a(g) be the third derivative of -5*g**8/168 - 5*g**7/42 - g**6/24 + g**5/6 - 16*g**2 - 3. Solve a(n) = 0 for n.
-2, -1, 0, 1/2
Let a(b) = 3*b**4 - 9*b**3 + 6*b**2 + 32*b - 32. Let c(k) = 4*k**4 - 10*k**3 + 6*k**2 + 32*k - 32. Let l(g) = 5*a(g) - 