**3 + 0*r. Let u(v) = 0. Calculate v.
-3, 0
Let g(a) = -2*a**4 - 6*a**3 + 13*a**2 + 21*a - 13. Let t(n) = n**4 + 3*n**3 - 6*n**2 - 10*n + 6. Let s(b) = 6*g(b) + 13*t(b). Let s(l) = 0. Calculate l.
-2, 0, 1
Factor 0*p**2 + 0 - 2/7*p**3 + 8/7*p.
-2*p*(p - 2)*(p + 2)/7
Let g(q) be the second derivative of -1/14*q**7 + 1/7*q**3 - 29*q - 9/28*q**5 + 1/28*q**4 + 0 + 0*q**2 + 19/70*q**6. Let g(l) = 0. What is l?
-2/7, 0, 1
Factor -21/4 + 6*l - 3/4*l**2.
-3*(l - 7)*(l - 1)/4
Let w = 33 - 31. Solve g - 6*g**3 - 6*g**2 - 4*g**w - 5*g = 0.
-1, -2/3, 0
Factor 18/7*n + 8/7*n**2 + 0.
2*n*(4*n + 9)/7
Solve 6/5*a**2 - 1/5*a**4 - 8/5 - 1/5*a**3 + 4/5*a = 0 for a.
-2, 1, 2
Determine c, given that -3*c**4 - c**4 + 24*c - 29*c**2 + 24*c**3 - 19*c**2 + 4*c**2 = 0.
0, 1, 2, 3
Let c(t) be the second derivative of -t**6/90 - 3*t**5/10 - 17*t**4/36 + 23*t + 2. Let c(b) = 0. What is b?
-17, -1, 0
Let b = -1745786/5 - -267090038/765. Let c = -178/9 - b. Factor c*z**2 - 4/17*z + 2/17.
2*(z - 1)**2/17
Suppose 24/7 + 78*a**4 + 726/7*a**2 - 974/7*a**3 - 32*a - 14*a**5 = 0. What is a?
2/7, 1, 3
Let h(y) = 7*y**2 - 15*y + 14*y**2 + 18*y - 9. Let u(o) = -2 + 6*o**2 - o**2 + o + 0*o**2. Let j(n) = 2*h(n) - 9*u(n). Let j(x) = 0. Calculate x.
-1, 0
Let j(s) be the third derivative of s**6/960 - s**5/80 - 7*s**3/3 + 13*s**2. Let p(x) be the first derivative of j(x). Factor p(h).
3*h*(h - 4)/8
Let g(o) = -98*o**3 - 278*o**2 - 12*o - 12. Let t(s) = s**3 - s**2 - 2*s + 2. Let p(a) = g(a) + 6*t(a). Let p(f) = 0. Calculate f.
-3, -2/23, 0
Let q be (3/6)/((-4)/8) - -1. Let f(r) be the second derivative of 0*r**3 + 8*r - 1/8*r**2 + q + 1/48*r**4. Factor f(t).
(t - 1)*(t + 1)/4
Let n(l) be the second derivative of 5*l**4/66 + 2*l**3/11 + l**2/11 - 125*l. Determine p so that n(p) = 0.
-1, -1/5
Let b be ((-80)/(-155))/((-5)/((-10)/(-4))). Let c = b - -55/93. Factor -c + l**2 - 2/3*l.
(l - 1)*(3*l + 1)/3
Let i be ((-40)/12)/((-4)/6). Suppose 37 = i*j - 3. Factor 1 + 6*d**5 - 4*d**3 - 2*d**4 - 1 - 2*d + 12*d**2 - j*d**4 - 2.
2*(d - 1)**3*(d + 1)*(3*d + 1)
Let h(q) = -5*q + 123. Let u be h(24). Let f(r) be the first derivative of 0*r - 3/4*r**6 + 0*r**2 - 3/5*r**5 + 0*r**u + 3/8*r**4 - 7. Factor f(v).
-3*v**3*(v + 1)*(3*v - 1)/2
Let y(h) = -11*h**4 + 16*h**3 - 27*h**2 + 20*h - 10. Let q(m) = 10*m**4 - 17*m**3 + 28*m**2 - 20*m + 9. Let d(g) = 6*q(g) + 5*y(g). Let d(k) = 0. What is k?
2/5, 1, 2
Let m(t) be the first derivative of -t**6/12 - t**5/2 - t**4 - 2*t**3/3 + 8. Factor m(a).
-a**2*(a + 1)*(a + 2)**2/2
Let a(u) = u**3 - 3*u**2 + u + 2. Let o be a(2). Suppose o = 2*k, -3*k - 7 = -5*s + 8. Factor 2*d**s + 14*d - 6*d + 8*d**2 - 16*d**2.
2*d*(d - 2)**2
Let q(j) be the first derivative of j**3/18 - 7*j**2/3 + 98*j/3 + 77. Suppose q(l) = 0. Calculate l.
14
Let o be (4/(-9))/((-18)/81). Factor -4*v**2 - v - 5*v + 3*v**o - 8 + 3*v**2.
2*(v - 4)*(v + 1)
Let j(u) be the third derivative of u**6/360 + u**5/30 - 5*u**4/24 + 5*u**3/3 - 11*u**2. Let o(v) be the first derivative of j(v). Find m such that o(m) = 0.
-5, 1
Let h(r) be the first derivative of -r**5/12 + 5*r**3/6 - 13*r**2/2 - 14. Let l(f) be the second derivative of h(f). Factor l(q).
-5*(q - 1)*(q + 1)
Let w(t) = 3*t**2 - 7*t - 94. Let y be w(7). Let o(z) be the first derivative of 0*z**y + 0*z - z**3 + 3/5*z**5 + 1 + 0*z**2. Factor o(g).
3*g**2*(g - 1)*(g + 1)
Factor g + 3*g - 3*g**3 - g + 0*g**3.
-3*g*(g - 1)*(g + 1)
Let w be (-3)/(-9) + (-484)/(-132). Let h(v) be the first derivative of 16/3*v**3 + 10*v**2 + 4*v + w. Suppose h(l) = 0. What is l?
-1, -1/4
Let r be 4/6 - 16/3*(-7)/28. Factor 0 + 0*f + 0*f**r + 2/9*f**3 - 4/9*f**5 + 2/9*f**4.
-2*f**3*(f - 1)*(2*f + 1)/9
Factor -p**2 + 0 - 4/5*p - 1/5*p**3.
-p*(p + 1)*(p + 4)/5
Let c(u) be the second derivative of -10*u + 1/105*u**6 + 0*u**2 + 0*u**3 - 1/42*u**4 + 0*u**5 + 0. Factor c(v).
2*v**2*(v - 1)*(v + 1)/7
Suppose 14 = 178*x - 171*x. Let n(o) be the first derivative of 2*o + 1 - 1/3*o**3 + 1/2*o**x. Find w such that n(w) = 0.
-1, 2
Let j(c) be the first derivative of -c**6/9 - 2*c**5/15 + 13*c**4/6 + 50*c**3/9 + 4*c**2 + 292. What is k in j(k) = 0?
-3, -1, 0, 4
Suppose 742 = -5*n - 2*m, -4*m + 320 = -2*n + m. Let f be (-4)/n*5*6. Factor -49/5*w**5 + f + 16/5*w - 23/5*w**2 - 67/5*w**3 + 119/5*w**4.
-(w - 1)**3*(7*w + 2)**2/5
Let t(s) be the third derivative of s**9/15120 - s**8/4480 - s**7/1680 + s**6/720 + 5*s**4/12 + 15*s**2. Let k(p) be the second derivative of t(p). Factor k(b).
b*(b - 2)*(b + 1)*(2*b - 1)/2
Let t(f) = -4*f - 13. Let u be (-1)/2 - 7/2. Let y be t(u). Factor 20*w + 23*w**2 + 4 + y*w**3 - w**3 + 5*w**3.
(w + 1)*(w + 2)*(7*w + 2)
Let 2/3*n**3 - 34/3*n**2 + 62/3*n - 10 = 0. Calculate n.
1, 15
Factor -18*g + 4*g**3 + 290*g**2 - 289*g**2 + 4*g.
g*(g + 2)*(4*g - 7)
Factor -56/11 - 2/11*q**2 + 32/11*q.
-2*(q - 14)*(q - 2)/11
Let r(x) be the first derivative of 5/2*x**4 - 45/4*x - 55/6*x**3 + 15*x**2 - 1/4*x**5 - 22. Factor r(s).
-5*(s - 3)**2*(s - 1)**2/4
Let u(h) be the first derivative of -h**5/170 + h**4/34 - 17*h - 6. Let o(d) be the first derivative of u(d). Factor o(i).
-2*i**2*(i - 3)/17
Suppose 335*k = 344*k - 36. Factor 0 + 1/7*d**2 - 2/7*d**3 - 1/7*d**k + 2/7*d.
-d*(d - 1)*(d + 1)*(d + 2)/7
Let i(c) be the third derivative of c**5/12 - 5*c**4/6 - 20*c**2. Let i(j) = 0. What is j?
0, 4
Let i be (5/30)/(7/((-252)/(-20))). Factor -i*t + 1/10*t**2 + 0.
t*(t - 3)/10
Let f = 10103 - 10100. Factor -8/5*w**2 - 2/5*w + 4/5 + 6/5*w**f.
2*(w - 1)**2*(3*w + 2)/5
Let h be (-36)/(-126)*(-112)/(-40). Find n, given that -4/5 - 2/5*n**3 + h*n**2 + 2/5*n = 0.
-1, 1, 2
Let t(v) be the third derivative of -v**6/600 - 19*v**5/20 - 1805*v**4/8 - 171475*v**3/6 - 31*v**2. Factor t(f).
-(f + 95)**3/5
Let n(w) be the first derivative of w**8/4200 - w**7/700 + w**6/450 + 2*w**3/3 - 20. Let g(v) be the third derivative of n(v). Factor g(t).
2*t**2*(t - 2)*(t - 1)/5
Let n(g) be the third derivative of 43*g**6/260 + 127*g**5/390 - g**4/78 + 6*g**2 + 25*g. Suppose n(k) = 0. What is k?
-1, 0, 2/129
Let n(k) be the first derivative of k**5 + 10*k**4 - 35*k**3 - 20*k**2 + 100*k + 270. Find h such that n(h) = 0.
-10, -1, 1, 2
Suppose -8 = 4*x + 2*o - 22, 3*o = -4*x + 11. Factor -h**x + 14*h**3 + 0*h - 3*h**5 - 4*h**4 - 2*h**3 + 20*h**2 + 8*h.
-4*h*(h - 2)*(h + 1)**3
Suppose -6*v = -22 - 14. Let y be 9/(-27) - (0 + (-2)/v). Factor y*z + 1/4*z**2 + 0 - 1/4*z**3.
-z**2*(z - 1)/4
Let i(c) be the first derivative of -3*c**5/25 + 39*c**4/20 - 9*c**3 - 15*c**2/2 + 150*c - 339. Factor i(u).
-3*(u - 5)**3*(u + 2)/5
Suppose -x - 3*x - 24 = 4*a, 4*x - 2*a + 42 = 0. Let r = x + 12. Suppose 4*h + 2*h - h**r + 4*h**5 - 8*h**2 + 8*h**4 - 2*h - 7*h**5 = 0. Calculate h.
-1, 0, 2/3, 1, 2
Let v(m) = 31*m + 21. Let h be v(3). Let a = h + -1480/13. Factor -6/13*k + 0*k**2 - 4/13 + a*k**3.
2*(k - 2)*(k + 1)**2/13
Suppose s - 2*q - 2 = 0, q = -s + 369 - 367. Factor 21/5*u - 3/5*u**3 + 12/5 + 6/5*u**s.
-3*(u - 4)*(u + 1)**2/5
Let 0 - 2/17*w**3 + 0*w**2 + 6/17*w**4 + 0*w = 0. Calculate w.
0, 1/3
Let r(h) = h**3 + h + 1. Let j(z) be the second derivative of z**5/5 + 7*z**4/6 - 4*z**3 + 12*z**2 - 44*z. Let l(w) = j(w) - 6*r(w). Find t such that l(t) = 0.
1, 3
Let t = 53 + -35. Let z(u) = u**2 - 6*u + 18. Let x(i) = -9. Let r(k) = 5. Let a(v) = 7*r(v) + 4*x(v). Let l(s) = t*a(s) + 2*z(s). Factor l(f).
2*(f - 3)**2
Let l(z) be the first derivative of 3*z**4 + 1/24*z**6 - 9 + 0*z - 16/3*z**3 - 3/5*z**5 + 0*z**2. Factor l(o).
o**2*(o - 4)**3/4
Let k(w) = w**3 - 2*w**2 - 3*w. Let q(z) = 5*z**3 - 11*z**2 - 15*z - 1. Let b(m) = -11*k(m) + 2*q(m). Factor b(u).
-(u - 1)**2*(u + 2)
Let r(x) = -2*x**2 - 6*x + 4. Let i(y) be the third derivative of -y**5/30 - 7*y**4/24 + 5*y**3/6 + 27*y**2. Let s(a) = 4*i(a) - 5*r(a). Factor s(p).
2*p*(p + 1)
Let d = 3071/65 + -609/13. Factor -d*q**2 - 2/5*q + 4/5.
-2*(q - 1)*(q + 2)/5
Suppose -56 = -3*u - 2*x - 2*x, 3*u - 31 = x. Let z be 40/u + 4/(-12). Factor -2*p + 2*p**2 - 5*p + 2*p + z*p**2.
5*p*(p - 1)
Let v(y) = -y**3 - 2*y**2 + 6*y - 5. Let l be v(-4). Let i be l/(-2) - 4/((-280)/135). Solve 6/7*f - i*f**2 - 3/7*f**3 + 0 = 0 for f.
-2, 0, 1
Let x be ((-40)/5)/4*8/(-4). Let c = 12 - 5. Factor 7 - 5*k**2 + 2*k + 4*k**3 - k**x - c.
-k*(k - 2)*(k - 1)**2
Let m(u) be the second derivative of 