5*s**2 - 7 + 1 + g*s = 0.
-3, 1
Let f(b) be the first derivative of b**4/12 + 16*b**3/3 + 128*b**2 + 4096*b/3 - 21. Factor f(h).
(h + 16)**3/3
Suppose 328*h + 6*h = 0. Factor h + 16/3*o**2 + 20/3*o - 4/3*o**3.
-4*o*(o - 5)*(o + 1)/3
Let g(l) = -l - 18 + 7 + 5. Let u be g(-6). Determine z so that -1/3*z - 1/3*z**2 + u + 1/3*z**4 + 1/3*z**3 = 0.
-1, 0, 1
What is s in -18/7*s - 1/7*s**4 - 8/7*s**3 - 3*s**2 + 0 = 0?
-3, -2, 0
Let w(j) be the first derivative of 2*j**3/45 + 2*j**2/5 + 2*j/3 - 17. Factor w(t).
2*(t + 1)*(t + 5)/15
Let c(h) = h**3 + h**2. Let i(k) = -7*k**3 - 10*k**2 + 5*k. Let v(z) = -6*c(z) - i(z). Factor v(n).
n*(n - 1)*(n + 5)
Let s(j) be the second derivative of -1/14*j**7 + 1/5*j**6 + 1/2*j**3 - 1/2*j**4 - 12*j + 0*j**5 + 0 + 0*j**2. Find l such that s(l) = 0.
-1, 0, 1
Suppose -5*y + 4*u = 9 + 1, y = 3*u - 13. Find c, given that 13*c**y + 3*c**3 - 22*c**2 + 7*c - c = 0.
0, 1, 2
Suppose -1/2*z**4 + 0 + 0*z + 13/4*z**3 - 1/4*z**5 - 5/2*z**2 = 0. Calculate z.
-5, 0, 1, 2
Find d, given that 36/7*d + 22/7*d**2 + 0 + 2/7*d**3 = 0.
-9, -2, 0
Suppose 9*u + 5 - 5 = 0. Let c(r) be the first derivative of 3 + 0*r**2 - 2/3*r**3 - 2/5*r**5 + u*r - r**4. Factor c(s).
-2*s**2*(s + 1)**2
Let i(w) be the first derivative of 1/66*w**4 - 2/33*w**3 + w + 4 + 1/11*w**2. Let f(g) be the first derivative of i(g). Factor f(c).
2*(c - 1)**2/11
Let u(q) be the second derivative of q**4/102 - 88*q**3/51 + 1936*q**2/17 + 2*q - 2. Find l such that u(l) = 0.
44
Let -468*g**3 + 921*g**3 - 459*g**3 - 2*g**4 + 4*g**5 = 0. What is g?
-1, 0, 3/2
Find r such that -20/3*r**2 + 5 - 5/3*r = 0.
-1, 3/4
Let a(t) be the second derivative of -11*t**4/3 - 65*t**3/9 + t**2/3 - 282*t. Factor a(n).
-2*(n + 1)*(66*n - 1)/3
Let j(w) be the first derivative of 2/15*w**3 + 7/5*w**2 + 12 + 4*w. Determine k, given that j(k) = 0.
-5, -2
Let k = -12/79 - -1616/237. Factor k*l + 2/3*l**2 + 50/3.
2*(l + 5)**2/3
Suppose 6 = 4*g - 2*k, 4*g + 6 = 5*k + 21. Factor 1/2*m - 1/4*m**2 + g.
-m*(m - 2)/4
Let d(r) be the first derivative of 15 + 12*r + 5/2*r**4 - 5*r**2 - 14/3*r**3 + 2/5*r**5. Factor d(n).
2*(n - 1)**2*(n + 1)*(n + 6)
Let g be 3/2 + 9/6. Let h be (-1 - (-30)/36)*24/(-10). Factor 0*d - h*d**4 - 2/5 + 4/5*d**2 + 0*d**g.
-2*(d - 1)**2*(d + 1)**2/5
Let q be (-12)/(4/(32/(-12))). Suppose -q*i + i = -6*i. Factor 1/3*v**2 + i - 1/3*v**3 + 0*v.
-v**2*(v - 1)/3
Suppose -359*t + 53*t = -918. Let 12/5*g + 0 - 4/5*g**t - 8/5*g**2 = 0. What is g?
-3, 0, 1
Suppose -2*v - 62 = -62. Let h(l) be the third derivative of 1/12*l**4 + 0*l - 1/30*l**5 + 8*l**2 + 0 + v*l**3. Suppose h(a) = 0. What is a?
0, 1
Solve -201*m**3 + 548*m**2 + 9680 + 1017*m**2 + 51*m**3 + 5*m**4 - 6600*m = 0 for m.
4, 11
Let f(r) be the second derivative of 15*r**7/14 + 43*r**6/6 + 53*r**5/4 + 65*r**4/12 - 5*r**3 - 121*r + 1. Suppose f(h) = 0. What is h?
-3, -1, 0, 2/9
Let b(w) = 3 + 8*w**2 + 6*w - 6*w**2 - w**2. Let n be b(-6). Determine x, given that -6*x**2 - 9*x**3 + 0*x**5 + 0*x**5 - 3*x**5 - 9*x**4 + n*x**2 = 0.
-1, 0
Let g = -51 - -53. Factor -2*s**g + 30*s + 17 - 17 - 26*s.
-2*s*(s - 2)
Factor -18*v - 54 - 3/2*v**2.
-3*(v + 6)**2/2
Suppose -2*y - 28 = 3*f - 13, -4*y - 25 = 5*f. Let p(r) be the second derivative of 0 + 0*r**3 + 1/60*r**6 + 0*r**2 + 0*r**5 + y*r**4 + 3*r. Factor p(v).
v**4/2
Let n(s) be the second derivative of s**8/840 + s**7/126 + s**6/90 - 11*s**4/4 - 22*s. Let o(v) be the third derivative of n(v). Solve o(i) = 0 for i.
-2, -1/2, 0
Let a(g) be the second derivative of -7*g**5/34 + 199*g**4/102 - 124*g**3/51 + 20*g**2/17 + 2*g + 12. Determine b so that a(b) = 0.
2/7, 2/5, 5
Let j = 17 - 14. Factor -6 + 4063*s - 4052*s + 2 + j*s**2.
(s + 4)*(3*s - 1)
Find p, given that 100*p**3 + 7 - 84*p**2 + 12*p + 0 - 36*p**4 + 1 + 0 = 0.
-2/9, 1
Let s be (5 + 2)/7 + -1. Factor s + 1/4*k**2 + 0*k.
k**2/4
Let r be (24/6 - 2)/(84/(-31)). Let m = 5/6 + r. Factor 2/21*l**3 - 2/7*l**2 - 10/21*l + m*l**4 - 4/21.
2*(l - 2)*(l + 1)**3/21
Determine h so that 10/3*h**3 + 2/3*h**4 + 2*h + 14/3*h**2 + 0 = 0.
-3, -1, 0
Suppose 61*j - 180 + 65 = 129. Suppose 45*i**2 + 25/2*i - 5 - 40*i**j - 45/2*i**5 + 10*i**3 = 0. Calculate i.
-1, 2/9, 1
Let l(n) = n**3 - 6*n**2 + 3. Let x be l(6). Solve 3*z**2 - 5*z**5 + 21*z**3 + 3*z**5 - 6 - x*z**4 - 15*z - 4*z**5 + 6*z**4 = 0.
-1, -1/2, 1, 2
Let v be (5 - (0 + 13)) + 8. Let n(m) be the first derivative of -10 - 1/2*m**3 + v*m + 3/4*m**2. Factor n(u).
-3*u*(u - 1)/2
Let q(u) = 4*u**2 + 5*u + 5. Let a be q(-1). Let d(w) be the first derivative of 1/6*w**a + 2 + 2/3*w**3 + w**2 + 2/3*w. Solve d(l) = 0.
-1
Let -2/5*u**3 + 8/15*u - 22/15*u**2 + 0 = 0. What is u?
-4, 0, 1/3
Let o(a) be the first derivative of -a**6/252 - 2*a**5/105 + a**4/21 + a**3 - 20. Let p(j) be the third derivative of o(j). Determine k, given that p(k) = 0.
-2, 2/5
Let g(h) be the first derivative of 10*h**2 - 5/4*h**4 - 9*h + 1/4*h**5 + 0*h**3 + 1. Let s(b) be the first derivative of g(b). Factor s(l).
5*(l - 2)**2*(l + 1)
Let p(m) be the third derivative of -m**5/30 - m**4 - 20*m**3/3 + 114*m**2. Factor p(o).
-2*(o + 2)*(o + 10)
Let s be -4*(-2)/8*4/(-4). Let d be s*4 - (9/3 - 7). Factor d + 2/9*n**3 + 2/9*n - 4/9*n**2.
2*n*(n - 1)**2/9
Suppose 0*j - 2*j = -6. Let -4*d**4 + 8*d**2 - 3*d**2 - 2*d**3 - 3*d**2 + 0*d**j = 0. What is d?
-1, 0, 1/2
Let y be (-209)/1045 - (-30014)/70. Factor -900/7*w + 90/7*w**2 - 3/7*w**3 + y.
-3*(w - 10)**3/7
Let a(m) be the first derivative of -m**4 + 8*m**3/3 + 18*m**2 - 72*m + 164. Factor a(z).
-4*(z - 3)*(z - 2)*(z + 3)
Let l(q) be the second derivative of 2*q**7/63 + 4*q**6/45 - q**5/5 - 4*q + 49. Factor l(i).
4*i**3*(i - 1)*(i + 3)/3
Let v(f) be the first derivative of -f**6/4 + 27*f**5/10 - 9*f**4 + 8*f**3 + 413. Factor v(u).
-3*u**2*(u - 4)**2*(u - 1)/2
Let t(b) be the third derivative of -b**6/60 + b**5/3 - 17*b**4/12 + 8*b**3/3 - 41*b**2. Solve t(f) = 0.
1, 8
Let p(s) = -s + 1. Let j be (-2)/((-25)/10 + 2). Let r(a) = -a**2 - 13*a - 50. Let o(w) = j*p(w) + 4*r(w). Let o(l) = 0. Calculate l.
-7
Let a(d) be the third derivative of -d**8/672 - d**7/210 + d**6/80 + d**5/30 - d**4/12 + 200*d**2. Suppose a(s) = 0. Calculate s.
-2, 0, 1
Let a be (1442/927)/((-10)/(-18)). Factor -32/5*l - 8/5 + a*l**3 - 2*l**2.
2*(l - 2)*(l + 1)*(7*l + 2)/5
Find y such that 0*y + 0 - 2/15*y**3 + 4/15*y**2 = 0.
0, 2
Let q(n) be the third derivative of -n**7/420 + n**6/60 - 3*n**3/2 - 6*n**2. Let t(j) be the first derivative of q(j). Suppose t(d) = 0. Calculate d.
0, 3
Let w(j) be the first derivative of -15*j**5/4 - 45*j**4/4 - 12*j**3 - 6*j**2 + j - 3. Let h(t) be the first derivative of w(t). Find n such that h(n) = 0.
-1, -2/5
Let b(v) = -v + 1. Let q be b(-7). Factor q*h**2 - 8*h**4 + 2*h + 2*h**5 + 2*h**4 - 2*h.
2*h**2*(h - 2)**2*(h + 1)
Let k(x) be the second derivative of -x**5/70 + x**4/7 - 5*x**3/21 + 49*x. Solve k(s) = 0.
0, 1, 5
Let m be 0*((-6)/9 + (-4)/(-12)). Suppose -2*q - q + 12*q = m. Let q*g**2 + 0*g - 2/5*g**4 - 2/5*g**3 + 0 = 0. What is g?
-1, 0
Let l(q) be the second derivative of -1/54*q**4 - 169/9*q**2 - 38*q + 0 - 26/27*q**3. Let l(c) = 0. Calculate c.
-13
Suppose 3*o = x, -4*x - 3*o + 0 = -15. Let s(d) = 2*d**3 + 4*d**2 + 2*d. Let b(r) = 3*r**3 + 5*r**2 + 2*r. Let l(k) = x*b(k) - 4*s(k). Solve l(m) = 0.
-1, 0, 2
Suppose -89*y - 24 = -93*y. Let f(h) be the second derivative of -1/10*h**4 + 0 + 0*h**2 + 1/75*h**y - 2/15*h**3 + 0*h**5 - 3*h. Factor f(d).
2*d*(d - 2)*(d + 1)**2/5
Let a(c) = 14*c**3 + 28*c**2 + 8*c - 28. Let l(q) = -2*q**3 - 4*q**2 - q + 4. Let f(y) = 6*a(y) + 44*l(y). Solve f(n) = 0.
-2, -1, 1
Let z = 80 + -68. Suppose -7*y**3 + 11*y**3 + 16*y**4 - 8 - z*y**2 - 20*y - 12*y**4 = 0. Calculate y.
-1, 2
Let g be (6 - 8)/((-2)/3) + 9. Let s be (-36)/2*((-16)/4)/g. Factor 4/3 + 14/3*n**2 - s*n.
2*(n - 1)*(7*n - 2)/3
Let g = 0 + 10. Let j = -10 + g. Factor j + 0 - 4 - 2*y + 0*y + 2*y**2.
2*(y - 2)*(y + 1)
Suppose 26*r + 16 = 15*r + 19*r. Factor 3/4*z**3 - 3/2 - 3*z**r + 15/4*z.
3*(z - 2)*(z - 1)**2/4
Let r(w) be the second derivative of w**5/130 + 32*w**4/39 - w - 62. Factor r(l).
2*l**2*(l + 64)/13
Let o(d) be the second derivative of d**4/22 + 20*d**3/11 + 123*d. Let o(u) = 0. What is u?
-20, 0
Let g(r) = -30*r - 508. Let b be g(-17). Factor 0*u + 0 + 1/3*u**5 - 1/3*u**b 