 + 1)
Suppose -10 = -3*h - 2*a, 0*h - 11 = -2*h + 3*a. Factor 0*j + 0*j**2 - 1/4*j**5 + 0*j**3 + 0 - 1/4*j**h.
-j**4*(j + 1)/4
Suppose -b - 12 = -14. Let l be (-3)/(3 + -12) - 0/b. Factor 0 + 4*v**2 - 8/3*v - 2*v**3 + l*v**4.
v*(v - 2)**3/3
Factor 390*f - 5*f**2 - 602 - 67 - 144 + 53.
-5*(f - 76)*(f - 2)
Let h = 275/294 - 64/147. Find c such that -3/4*c**4 + h*c**2 - 1/4*c**5 + 3/4*c - 1/2*c**3 + 1/4 = 0.
-1, 1
Let m(l) = -l. Let a(n) = -n**3 + n**2 + 4*n. Let v = 66 - 62. Let f(y) = v*m(y) + a(y). Factor f(o).
-o**2*(o - 1)
Let f(t) = -t**2 - t + 1. Let q(a) = 3*a**3 + 95*a**2 - 100*a + 1. Let k(h) = -f(h) + q(h). Determine p so that k(p) = 0.
-33, 0, 1
Let p(g) = -48*g - 2*g**3 - 24*g - 6*g + 12*g**3 - 16*g**2 - 28. Let a(d) = 3*d**3 - 5*d**2 - 26*d - 9. Let s(t) = 8*a(t) - 3*p(t). Factor s(c).
-2*(c - 3)*(c + 1)*(3*c + 2)
Suppose -81/2*x - 3/8*x**2 - 2187/2 = 0. What is x?
-54
Solve 1/6*g**2 - 2/3*g**3 + 2/3*g - 1/6*g**4 + 0 = 0 for g.
-4, -1, 0, 1
Factor 13/4*y**2 + 3/2*y**3 + 1/4*y**4 + 1 + 3*y.
(y + 1)**2*(y + 2)**2/4
Let g(s) be the second derivative of s**7/126 - s**6/18 - s**5/30 + 5*s**4/18 + s**3/18 - 5*s**2/6 - 3*s - 134. Determine u so that g(u) = 0.
-1, 1, 5
Let r(k) = k**2 - 2*k. Let i be r(-1). Factor -8/7*u**i + 4/7 - 4/7*u**4 + 0*u**2 + 8/7*u.
-4*(u - 1)*(u + 1)**3/7
Let b = 54 - 51. Factor -2*l**2 + 3*l**5 - 278*l**b + 2*l**4 + 276*l**3 - l**5.
2*l**2*(l - 1)*(l + 1)**2
Let v(k) = 8*k**2 - 4 + k - 9*k**2 - 8*k. Let w be v(-6). Let 7 - 36*y - 18*y**w - 23 - y**3 - 2*y**3 - 8 = 0. What is y?
-2
Let z(j) be the third derivative of 9*j**8/448 - 9*j**7/280 + j**5/60 + 89*j**2. Determine g so that z(g) = 0.
-1/3, 0, 2/3
Let h(g) be the first derivative of -2*g**3/45 + 11*g**2/15 + 76. Factor h(d).
-2*d*(d - 11)/15
Let j(s) be the third derivative of 1/12*s**4 + 16*s**2 - 1/30*s**5 + 0*s + 2/3*s**3 + 0. Determine l, given that j(l) = 0.
-1, 2
Let j = -2334 - -2339. Let v(u) be the third derivative of 0*u**3 + 0*u + 1/96*u**4 - 11*u**2 + 1/240*u**j + 0. Suppose v(c) = 0. What is c?
-1, 0
Suppose v + m = 4, -5*v + 2*v + 8 = -m. Suppose -v = -4*c + 3*c. Find x such that 5*x**3 + 0*x**4 - c*x**4 + 0*x**4 + x**3 = 0.
0, 2
Suppose -78*c - 99 = -111*c. Factor -1 - 1/4*b**4 + 1/2*b**c + 3/4*b**2 - b.
-(b - 2)**2*(b + 1)**2/4
Let i(j) be the second derivative of j**5/20 - 4*j**4/3 - j**3/6 + 8*j**2 - j + 2. Suppose i(l) = 0. Calculate l.
-1, 1, 16
Suppose 55*m = 58*m + 216. Let j be 95/63 - (-16)/m. What is t in 0 + 3/7*t**2 + j*t = 0?
-3, 0
Suppose 0 + 1323*k**2 + 63*k**3 + 0*k + 3/4*k**4 = 0. Calculate k.
-42, 0
Find k, given that 9/5*k - 21/5 + 6*k**2 = 0.
-1, 7/10
Let q(w) be the third derivative of w**5/240 - 7*w**4/48 - 3*w**3 - 2*w**2 - 357. Solve q(x) = 0.
-4, 18
Let a(k) = k**2 + 14*k. Let f be a(-14). Let h(g) be the first derivative of f*g**3 - 5 + g**2 + 0*g - 1/2*g**4. Let h(j) = 0. What is j?
-1, 0, 1
Let l(m) = -m**4 - m**3 - m - 1. Let y(a) = 3*a**4 + 6*a**3 + 3*a**2 + 4*a + 4. Let x(g) = 4*l(g) + y(g). Find p, given that x(p) = 0.
-1, 0, 3
Let u(a) be the second derivative of 2/27*a**3 + 0 + 1/54*a**4 - a - 8/9*a**2. Factor u(z).
2*(z - 2)*(z + 4)/9
Let i(c) be the second derivative of c**6/240 - c**4/96 + c + 25. Solve i(o) = 0 for o.
-1, 0, 1
Let h(x) = 9*x**3 - 9*x + 12. Let m(l) = -17*l**3 + 18*l - 23. Let i(v) = -11*h(v) - 6*m(v). Factor i(c).
3*(c - 1)**2*(c + 2)
Suppose 3*k - 5*a = 6*k - 30, -2*k - 3*a + 20 = 0. Factor 5*u**2 - 11*u**3 + 6*u**3 + 5*u**2 + k*u**2.
-5*u**2*(u - 4)
Suppose -2*l - 2*j + 13 = j, -5*j = 2*l - 19. Find m such that -44*m**l + 49*m**2 - 5*m - 5*m - 15 = 0.
-1, 3
Solve 71675 - 669*h - 233147 - 590*h - 133*h - 3*h**2 = 0.
-232
Let h(d) be the first derivative of -5*d**3 + 20*d**2 - 20*d + 62. Factor h(c).
-5*(c - 2)*(3*c - 2)
Let v(r) be the third derivative of r**6/540 + r**5/270 - 25*r**4/108 - 25*r**3/27 - 156*r**2. Let v(p) = 0. Calculate p.
-5, -1, 5
Let j(q) be the second derivative of -3*q**5/40 - q**4/2 + q**3/4 + 3*q**2 + 35*q + 1. What is m in j(m) = 0?
-4, -1, 1
Let g(r) be the third derivative of r**5/390 - r**4/156 - 2*r**3/13 - 2*r**2 + 5. Factor g(k).
2*(k - 3)*(k + 2)/13
Let u(f) = f**4 + 191*f**3 + 518*f**2 + 481*f + 153. Let d(l) = -96*l**3 - 260*l**2 - 240*l - 76. Let o(i) = 7*d(i) + 4*u(i). Factor o(x).
4*(x + 1)**3*(x + 20)
Let -18*x - 3/5*x**2 - 135 = 0. What is x?
-15
Let f(a) be the first derivative of a**4/20 + 11*a**3/15 + 12*a**2/5 - 36*a/5 + 91. Factor f(c).
(c - 1)*(c + 6)**2/5
Find l such that -20444*l - 20442*l + 5*l**3 + 40870*l + 38*l**2 = 0.
-8, 0, 2/5
Let d(h) be the second derivative of h**6/15 + 2*h**5/5 - h**4/2 - 10*h**3/3 + 8*h**2 - 418*h + 1. Determine w so that d(w) = 0.
-4, -2, 1
Solve 4*d**2 - 17 - 15 + 0*d - 8*d = 0 for d.
-2, 4
Factor 56/5 + 2/5*z**3 + 64/5*z + 22/5*z**2.
2*(z + 2)**2*(z + 7)/5
Suppose l + 3*l - 28 = 0. Suppose 0 = 3*j + 2*j - 10. Factor 8*n + 3 + n**j + 1 - 4*n**2 + l*n**2.
4*(n + 1)**2
Let l(s) be the first derivative of 3*s**4/32 + 13*s**3/8 - 12*s**2 + 51*s/2 - 39. Determine r so that l(r) = 0.
-17, 2
Let a(c) be the second derivative of c**5/100 + 19*c**4/60 + 8*c**3/3 - 10*c**2 + 204*c. Determine k so that a(k) = 0.
-10, 1
Let h(t) = 5*t**2 + 4*t + 20. Let l(w) be the third derivative of 3*w**5/20 + 3*w**4/8 + 13*w**3/2 - 5*w**2. Let d(j) = 7*h(j) - 4*l(j). Factor d(r).
-(r + 4)**2
Determine c, given that -32/7 + 2*c**2 + 2/7*c**3 + 16/7*c = 0.
-4, 1
Let v(s) be the first derivative of s**6/240 - s**4/16 + s**3/6 - 10*s**2 + 1. Let i(w) be the second derivative of v(w). Factor i(c).
(c - 1)**2*(c + 2)/2
Let q(c) be the second derivative of c**9/3024 - c**8/336 + c**7/105 - c**6/90 + 11*c**3/3 - 32*c. Let w(g) be the second derivative of q(g). Factor w(z).
z**2*(z - 2)**2*(z - 1)
Let k(h) be the first derivative of -h**3/3 - 2*h**2 + 4*h - 18. Let s be k(-4). Factor 12/7*v**2 + 2/7*v**s - 8/7*v + 2/7 - 8/7*v**3.
2*(v - 1)**4/7
Let i = -89 - -114. Let n be 3 + (i/4 - 4). Factor -21/4*v**3 + n*v + 3/2 - 3/2*v**2.
-3*(v - 1)*(v + 1)*(7*v + 2)/4
Let z(o) = -5*o - 33. Let k be z(-7). Factor 4*s**2 + 12*s + 7 - 2 + 4*s**k - 1.
4*(s + 1)*(2*s + 1)
Let d be -8*5/20*-2 - -1. Let u be (d + (-30)/6)/3. Factor -4/5*m**2 + u*m - 2/5*m**3 + 2/5*m**4 + 0.
2*m**2*(m - 2)*(m + 1)/5
Find j such that 3/4*j**3 + 0*j**2 + 0 - 3/4*j = 0.
-1, 0, 1
Let r(u) = u**2 + 3*u - 2. Let w = -25 - -21. Let t be r(w). Factor 6*a**4 + 6*a**3 - 20*a**4 + 8*a + 15*a**4 + 12*a**t.
a*(a + 2)**3
Let y(x) be the first derivative of -20*x**6/33 + 1486*x**5/55 - 7309*x**4/22 + 14972*x**3/33 - 252*x**2/11 - 1296*x/11 - 7. Solve y(z) = 0.
-1/4, 2/5, 1, 18
Let z(r) = 3*r**2 + 55*r + 114. Let a(x) = 2*x**2 + 55*x + 111. Let f(n) = -2*a(n) + 3*z(n). Factor f(m).
5*(m + 3)*(m + 8)
Let g be (-9402)/12600 + 9*6/72. Let n(a) be the third derivative of -10*a**2 + 0*a - 1/30*a**4 + 1/150*a**6 + 0 + 0*a**3 - 1/75*a**5 + g*a**7. Factor n(p).
4*p*(p - 1)*(p + 1)**2/5
Let q(u) = -2*u + 25. Let o be q(11). Find r, given that 0 - 1/3*r**o + 1/3*r**2 + 2/3*r = 0.
-1, 0, 2
Let a = 7549 + -22643/3. What is k in 0 + 1/12*k**3 + a*k + 2/3*k**2 = 0?
-4, 0
Let k(a) = 201*a - 1572. Let f be k(8). Solve 3/2*y**3 - f*y**2 + 288*y - 768 = 0 for y.
8
Let w(r) be the second derivative of r**4/48 - 7*r**3/12 + 3*r**2 - 300*r. Let w(k) = 0. Calculate k.
2, 12
Let b be 972/90 - (19 + -9). Let 0 - b*n - 6/5*n**2 - 2/5*n**3 = 0. Calculate n.
-2, -1, 0
Let h(z) = -z**2 - z + 1. Let c = -5 + 9. Let d(k) = 3*k - 2 + 5 + c*k**2 - 3 - 3. Let s(o) = d(o) + 3*h(o). Determine m so that s(m) = 0.
0
Let u be (-3 + 4 - 29)*(-12)/8. Let r be u/40 + 40/(-32) + 1. Factor 1/5*p**2 - 4/5*p + r.
(p - 2)**2/5
Let h be ((-2)/(-3))/((-7)/1680). Let k = -798/5 - h. Suppose -k + 2/5*l**2 - 2/5*l**3 + 2/5*l = 0. What is l?
-1, 1
Let n(d) be the second derivative of 1/168*d**7 - 1/6*d**4 + 1/60*d**6 + 12*d + 0 - 1/4*d**2 - 1/40*d**5 - 7/24*d**3. Factor n(p).
(p - 2)*(p + 1)**4/4
Let a = 69 + -67. Let k(m) be the first derivative of 1/3*m**3 - 3/8*m**a - 5 - 1/16*m**4 + 0*m. Factor k(s).
-s*(s - 3)*(s - 1)/4
Let n(d) = -d - 9. Let t be n(0). Let y(u) = u**2 + 12*u + 29. Let m be y(t). Factor 1/6*b**m + 0*b - 1/6*b**3 + 0.
-b**2*(b - 1)/6
Find l, given that -1/7*l + 6/7*l**4 + 2/7*l**3 + 6/7 - 12/7*l**2 - 1/7*l**5 = 0.
-1, 1