d**4 + 9/4*d**2 - k*d**3 + 1/2 - 7/4*d.
(d - 2)*(d - 1)**3/4
Suppose 73 = 15*q - 77. Suppose 3*t + 5*m - 34 = 0, m = -0*t + 5*t - q. Factor 0 - 2/9*v - 2/3*v**2 - 2/9*v**4 - 2/3*v**t.
-2*v*(v + 1)**3/9
Let u be (-6)/(252/125) + (3 - 0). Let j(g) be the third derivative of 3*g**2 + 0 + 1/7*g**3 - u*g**4 - 1/210*g**5 + 0*g. Factor j(a).
-2*(a - 1)*(a + 3)/7
Let k be -22*(-16)/264 - 8/6. Let x(y) be the first derivative of k*y**2 + 0*y - 4/5*y**5 - 2*y**4 + 7 + 2*y**6 + 0*y**3. Suppose x(j) = 0. Calculate j.
-2/3, 0, 1
Let t(a) = 2*a + 73. Let r be t(-17). Let 4*s**2 + 11 - 8*s + 4 - r + 12 = 0. Calculate s.
-1, 3
Let s = -3102/5 - -9311/15. Factor 32/3*g - 16/3 - 8*g**2 + 8/3*g**3 - s*g**4.
-(g - 2)**4/3
Let s = -3 - -2. Let b be (0 - -1 - 3)*s. Factor -4 + 7*m**b - 4*m**2 + 6*m + 4.
3*m*(m + 2)
Let b(k) = -k**3 + 2*k**2 + 5*k - 3. Let h be b(3). Let 16*t**2 - t**h + 36 + 9*t + 23*t + 10*t + 3*t**3 = 0. What is t?
-3, -2
Let g = -121 + 123. Let u(b) be the second derivative of -3*b + 1/10*b**5 + 2*b**g + 0 - 1/3*b**3 - 1/3*b**4. Factor u(v).
2*(v - 2)*(v - 1)*(v + 1)
Let a = 14 + -12. Suppose -3 = -5*q + a*q. Suppose 2*u**2 - 1 + q + 0 = 0. Calculate u.
0
Solve 1562*w**2 - 6017*w**2 - 7243*w**3 + 500 + 8673*w**3 - 1700*w + 4225*w**4 = 0.
-10/13, 1/5, 1
Let g(d) = -d**3 - 12*d**2 - 40*d. Suppose 3*u = -6, -f + 0 = -4*u - 5. Let l(q) = q**3 + 12*q**2 + 39*q. Let j(v) = f*g(v) - 4*l(v). Solve j(r) = 0.
-6, 0
Suppose -8*v + 3*v = -20. Suppose 2*h - 28 = v*o, 3*h = -3*o + 2*o + 7. Find x such that 2*x**3 - x - 3*x - 2*x + h - 8 = 0.
-1, 2
Let m be 328 - (1 - (-3 + 4)). Let o = m - 2272/7. Let -o*f - 36/7 - 4/7*f**2 = 0. What is f?
-3
Let a be 25/50*(3/(-9))/(14/(-12)). Factor 1/7*z - 2/7 + a*z**2.
(z - 1)*(z + 2)/7
Let z be (-9 - -2) + 825/110. Let j = 2 + 0. What is w in z - 3/4*w**j + 5/4*w = 0?
-1/3, 2
Let h = 1088 + -4317/4. Let b = -103/12 + h. What is r in b*r**2 + 0*r - 1/6 = 0?
-1, 1
Factor 62/3 - 62/3*v**2 - 1/3*v**3 + 1/3*v.
-(v - 1)*(v + 1)*(v + 62)/3
Let r(a) = 28*a**2 + 544*a - 1125. Let z(u) = -68*u**2 - 1360*u + 2812. Let k(d) = 12*r(d) + 5*z(d). Solve k(o) = 0.
-70, 2
Let t(o) be the third derivative of -o**7/840 + o**5/120 + 13*o**3/6 - 9*o**2. Let q(m) be the first derivative of t(m). Factor q(s).
-s*(s - 1)*(s + 1)
Factor -4*a**2 + 68*a + 142 - 24*a - 94.
-4*(a - 12)*(a + 1)
Let l = 2977/24 + -195/8. Let a = l - 77. Suppose -a*q**4 - 40/3*q**3 + 0 + 14*q**5 + 16/3*q**2 + 0*q = 0. What is q?
-2/3, 0, 2/7, 2
Let v(n) be the first derivative of -n**6/1440 - n**5/96 - n**4/24 - 8*n**3/3 - 9. Let p(x) be the third derivative of v(x). Determine z, given that p(z) = 0.
-4, -1
Let t be (-14)/(-6)*30/175. Let y(g) be the first derivative of 1 - 2*g - g**4 - t*g**5 + 4/3*g**3 + g**2 + 1/3*g**6. Factor y(z).
2*(z - 1)**3*(z + 1)**2
Let j(n) be the first derivative of n**5 + 10*n**4 + 35*n**3/3 + 126. Find w such that j(w) = 0.
-7, -1, 0
Let r(g) be the second derivative of g**10/6048 - g**9/1512 + g**8/1344 + g**4/12 - 6*g. Let x(n) be the third derivative of r(n). Factor x(a).
5*a**3*(a - 1)**2
Factor -7913*c + c**2 + 29 + 0*c**2 + 7943*c + 0*c**2.
(c + 1)*(c + 29)
Factor -15552/5 - 3/5*g**2 - 432/5*g.
-3*(g + 72)**2/5
Let u be (332/249)/((-2)/(-6)). Let -2/9*n**u - 8/3*n**2 + 20/9*n + 4/3*n**3 - 2/3 = 0. Calculate n.
1, 3
Let d(l) be the second derivative of -l**5/40 - 5*l**4/12 - 17*l**3/12 - 2*l**2 - 304*l. Find n, given that d(n) = 0.
-8, -1
Factor 48 - 52*d + 12*d**2 + 144 - 69*d - 7*d + 16*d**2 - 2*d**3.
-2*(d - 6)*(d - 4)**2
Let k(z) be the third derivative of -z**6/60 - 7*z**5/15 + 80*z**2. Let k(h) = 0. Calculate h.
-14, 0
Let k be (0 - 0)/(-12 + 14). Let g(v) be the first derivative of -2/5*v**5 + 1/3*v**4 + 6 + 0*v**3 + 0*v**2 + k*v - v**6. Factor g(u).
-2*u**3*(3*u - 1)*(3*u + 2)/3
Let i be 108/14 - (-864)/(-144). Suppose 0 - i*d**3 - 8/7*d**4 - 12/7*d + 32/7*d**2 = 0. What is d?
-3, 0, 1/2, 1
Let h = -1906 - -11437/6. Solve 0*m - 1/6 + h*m**2 = 0 for m.
-1, 1
Let b(y) = 16*y**4 - 33*y**3 - 50*y**2 + 39*y + 43. Let f(v) = -28*v**4 + 67*v**3 + 98*v**2 - 77*v - 85. Let c(l) = -5*b(l) - 3*f(l). Factor c(i).
4*(i - 10)*(i - 1)*(i + 1)**2
Let b(t) be the first derivative of 10*t**3/3 - 25*t**2/2 + 15*t + 92. Suppose b(a) = 0. What is a?
1, 3/2
Let l(y) be the first derivative of 2*y**6/15 - 3*y**5/5 + 8*y**3/3 - 35*y - 28. Let i(u) be the first derivative of l(u). Suppose i(s) = 0. What is s?
-1, 0, 2
Suppose -8*d = -2*d - 72. Factor m + 12 - 26*m - 34*m + d*m**2 + 19*m.
4*(m - 3)*(3*m - 1)
Let i(p) be the third derivative of p**6/360 - p**5/60 - p**4/18 + 2*p**3/3 + 141*p**2. Suppose i(h) = 0. Calculate h.
-2, 2, 3
Let d(g) = -17*g**3 + 40*g**2 + 259*g + 201. Let k(i) = i**4 + 2*i**2 + i - 1. Let z(h) = -3*d(h) - 3*k(h). Factor z(s).
-3*(s - 10)**2*(s + 1)*(s + 2)
Let z(b) = -12*b**2 + 52*b - 30. Let u(k) = 23*k**2 - 103*k + 60. Let t be (-66)/21 + (-4)/(-28). Let s(o) = t*u(o) - 7*z(o). Factor s(j).
5*(j - 3)*(3*j - 2)
Let k(x) = 3*x**2 - 8*x + 2. Let h be k(3). Let -93 + 93 + h*u**2 - 5*u = 0. What is u?
0, 1
Let f(b) be the first derivative of b**6/4 + 2*b**5/5 - 19*b**4/8 - 4*b**3/3 + 3*b**2 + 457. Suppose f(o) = 0. What is o?
-3, -1, 0, 2/3, 2
Let x(w) be the first derivative of -4*w**5/15 + 8*w**4/3 - 28*w**3/3 + 44*w**2/3 - 32*w/3 + 350. Suppose x(g) = 0. Calculate g.
1, 2, 4
Let r(c) = c**3 + 9*c**2 - 102*c - 718. Let n be r(-6). Factor 133/2*x**n + 12*x - 2.
(7*x + 2)*(19*x - 2)/2
Suppose 0 = -5*d - 4*o + 20, -o - 10 = -4*d - 15. Let z(j) be the second derivative of -1/84*j**4 + 0*j**3 - j + 0*j**2 + d. Factor z(x).
-x**2/7
Let v be 30 + -29 + (-1)/3. Let m(j) be the first derivative of v*j**3 - 14 + 2*j**2 + 2*j. Factor m(k).
2*(k + 1)**2
Let p(h) be the third derivative of h**8/1176 + 47*h**7/735 - 33*h**6/70 + 151*h**5/105 - 29*h**4/12 + 17*h**3/7 - 34*h**2 - 2. Factor p(o).
2*(o - 1)**4*(o + 51)/7
Let i(j) be the second derivative of 2*j**3 + 0*j**2 + 0 + 1/3*j**4 - 13*j. Factor i(f).
4*f*(f + 3)
Let h(u) be the second derivative of u**7/14 + u**6/2 + 267*u. Factor h(k).
3*k**4*(k + 5)
Let z(m) be the third derivative of m**5/90 - 23*m**4/18 + 529*m**3/9 + 159*m**2. Suppose z(q) = 0. What is q?
23
Solve -4*t**2 - 30*t**2 + 18*t**3 + 6*t + 16*t**4 + 2*t**3 + 0*t + 16*t**3 = 0.
-3, 0, 1/4, 1/2
Let a(v) be the third derivative of -v**9/3024 + v**8/1344 + v**7/504 - v**6/144 - 5*v**4/4 - 32*v**2. Let j(k) be the second derivative of a(k). Factor j(t).
-5*t*(t - 1)**2*(t + 1)
Let v(t) be the second derivative of t**8/30240 + t**7/3780 + t**6/1620 + t**4 + 16*t. Let u(p) be the third derivative of v(p). Suppose u(y) = 0. Calculate y.
-2, -1, 0
Let y(p) = -5*p**3 + 8*p**2 + 34*p + 15. Let f(j) = 6*j**3 - 6*j**2 - 34*j - 14. Let s(b) = 3*f(b) + 4*y(b). What is g in s(g) = 0?
-1, 9
Let l(o) be the second derivative of o**4/3 + 32*o**3/3 - 34*o**2 - 221*o. What is u in l(u) = 0?
-17, 1
Let r(f) = 3*f**2 + 11*f. Suppose 0 = -5*n + 2*o + 7 - 1, -4*o = -4*n. Let t(w) = 3*w**2 + 12*w. Let j(i) = n*t(i) - 3*r(i). Solve j(p) = 0 for p.
-3, 0
Let z be (-10)/15*(-3 + 0). Suppose 1/3*m**3 - 1/3*m**4 - 1/3*m**5 + 0 + 0*m + 1/3*m**z = 0. What is m?
-1, 0, 1
Let n be 268/52 + 1/(13/(-2)). Let u(q) be the third derivative of 1/160*q**6 + 2*q**2 + 0*q - 3/32*q**4 + 0 + 0*q**n + 1/4*q**3. Factor u(p).
3*(p - 1)**2*(p + 2)/4
Let o(r) = -r**2 + 18*r + 30. Let p(l) = -4*l**2 + 74*l + 119. Let v(y) = 9*o(y) - 2*p(y). Find j such that v(j) = 0.
-2, 16
Determine v, given that -4/5*v**3 - 52/5*v - 56/5*v**2 + 0 = 0.
-13, -1, 0
Let h be (-15)/(-9)*-1*12/(-70). Factor -2/7 + 0*i + h*i**2.
2*(i - 1)*(i + 1)/7
Let n(s) = s**5 + s**4 - s**3 + 1. Let q(x) = x**5 - 19*x**4 - 21*x**3 + 45*x**2 + 6. Let g(u) = -6*n(u) + q(u). Factor g(z).
-5*z**2*(z - 1)*(z + 3)**2
Let u = 447 - 200. Let i = u - 1233/5. Let -i*l**2 - 2/5*l**4 - 3/5*l**3 - 1/10*l + 0 - 1/10*l**5 = 0. What is l?
-1, 0
Let m(t) = -20*t**2 - 24*t - 31. Suppose 5*w = p - 4*p - 100, -4*p = -3*w - 31. Let b(y) = -7*y**2 - 8*y - 10. Let u(r) = w*b(r) + 6*m(r). Factor u(d).
-(d + 4)**2
Let g(x) be the second derivative of 3*x**5/80 - x**4/2 + 15*x**3/8 - 112*x. Factor g(w).
3*w*(w - 5)*(w - 3)/4
Let p(f) = -21*f - 12. Let s be p(-9). Let 9*i**3 - s*i**2 + 0*i**4 + 3*i**4 + 186*i**2 + 3*i = 0. Calcu