Let o(d) be the second derivative of d**7/1260 + d**6/180 + d**4/4 + d. Let w(x) be the third derivative of o(x). Determine h so that w(h) = 0.
-2, 0
Suppose 2*t = -3*t - 45. Let h(p) = -2*p - 10. Let b be h(t). What is n in 2*n**2 + 2*n - 4*n**2 - 7*n**2 + 4*n**3 + b*n**3 - 5*n**4 = 0?
0, 2/5, 1
Factor -12*z - 149*z**4 + 20*z**2 - 4*z**3 + 145*z**4 + 0*z**3.
-4*z*(z - 1)**2*(z + 3)
Suppose 5*h + 10 = -25. Let p = h - -9. Factor 3/4*z - 1/4*z**p - 1/2.
-(z - 2)*(z - 1)/4
What is m in 2/9 - 2/9*m**2 - 2/9*m + 2/9*m**3 = 0?
-1, 1
Suppose 3*f - k - 5 = 5*f, 5*f + 3*k + 14 = 0. Let j be (-1)/((-3)/(-9))*f. Let -4*l**3 - 7*l - j*l**4 + 9*l**2 + 19*l - 2*l**3 - 12 = 0. What is l?
-2, 1
Let l(o) be the third derivative of 0 - 1/66*o**5 - 4/33*o**3 - 1/660*o**6 + 2*o**2 + 0*o - 2/33*o**4. Let l(f) = 0. What is f?
-2, -1
Let a(x) be the third derivative of -x**6/8 - 5*x**5/12 - 5*x**4/24 + 5*x**3/6 + 20*x**2. Determine m so that a(m) = 0.
-1, 1/3
Let c = 22 - 64/3. Factor 0 + 2/3*w**5 - 4/3*w**3 + 0*w**4 + 0*w**2 + c*w.
2*w*(w - 1)**2*(w + 1)**2/3
Let x(s) be the second derivative of 0*s**2 + 0 + 1/24*s**4 - 2*s + 1/40*s**5 + 0*s**3. Factor x(t).
t**2*(t + 1)/2
Factor 0*n + 3/8*n**3 + 1/4*n**4 + 0 + 1/8*n**2.
n**2*(n + 1)*(2*n + 1)/8
Let l(m) be the first derivative of m**5/10 - m**3/3 + m/2 + 7. Find t such that l(t) = 0.
-1, 1
Let x be (-18)/(-4) + 21/14 + -2. Factor 2*j**3 - 4/7*j**2 + 0*j - 16/7*j**x + 6/7*j**5 + 0.
2*j**2*(j - 1)**2*(3*j - 2)/7
Suppose -3*r - 3*s = -5 - 10, 0 = r - 2*s + 10. Find w such that -6/5*w**3 + r - 9/5*w**2 - 3/5*w = 0.
-1, -1/2, 0
Suppose -18 = -h + 3*h. Let l(k) = -7*k**4 + 13*k**2 + 2*k. Let p(x) = -15*x**4 + 27*x**2 + 3*x. Let r(c) = h*l(c) + 4*p(c). Factor r(u).
3*u*(u - 2)*(u + 1)**2
Factor 9*u**4 - 7*u**2 - 7*u**4 - 4*u**3 + 9*u**2.
2*u**2*(u - 1)**2
Let n(t) be the third derivative of -t**2 + 0*t + 0 - 2/27*t**3 + 1/270*t**5 - 1/108*t**4. Let n(x) = 0. Calculate x.
-1, 2
Let q be (-18)/(-45) - (-2)/(-30). Suppose -4*b + 1 = -19. Suppose 0*f + 1/3*f**2 + f**4 + 0 + f**3 + q*f**b = 0. Calculate f.
-1, 0
Let b(c) = 12*c**3 - 39*c**2 + 6*c. Let t(p) = -p**2. Let w(o) = b(o) - 12*t(o). Factor w(m).
3*m*(m - 2)*(4*m - 1)
Factor -4*f**3 + f**3 + 0*f**3 - 2*f**3.
-5*f**3
Let h(q) be the first derivative of -4*q**3/9 + 2*q**2/3 + 8*q/3 - 4. Factor h(l).
-4*(l - 2)*(l + 1)/3
Let o(y) be the second derivative of 0 - 1/12*y**4 + 0*y**3 + 2*y + 1/2*y**2. Solve o(c) = 0 for c.
-1, 1
Let m(r) = -r**2 - 1. Let y be -3*(-1)/(-15)*-5. Let a(v) = 3*v**3 - 6*v**2 - 3*v - 6. Let t(o) = y*a(o) - 6*m(o). Suppose t(i) = 0. What is i?
-1, 0, 1
Let x = -17 - -18. Suppose -1 + 2*p**5 - p**4 + 2*p**2 + 4 - x + 2*p - 3 - 4*p**3 = 0. Calculate p.
-1, 1/2, 1
Let o(s) be the first derivative of -3*s**5/35 + 3*s**4/28 - 19. Factor o(l).
-3*l**3*(l - 1)/7
Let z(n) = -n**2 + 5. Let t(s) = -3. Let o(v) = -5*t(v) - 3*z(v). Factor o(f).
3*f**2
Let a(y) be the third derivative of y**7/105 - y**6/60 - y**5/30 + y**4/12 - 36*y**2. Factor a(c).
2*c*(c - 1)**2*(c + 1)
Let r(y) = -y**3 - 9*y**2 - 8*y + 2. Let l be r(-8). Factor -l*w**2 - 2*w + 1 - 2*w + 0*w**2 - 3.
-2*(w + 1)**2
Let v = 65 - 449/7. Suppose -24/7*i**3 + 4/7*i + v*i**2 + 0 + 2*i**4 = 0. What is i?
-2/7, 0, 1
Determine i, given that 36/11*i - 6/11*i**2 + 42/11 = 0.
-1, 7
Solve 12*t + 77*t**3 + 13*t - 16*t**2 - 8 - 73*t**3 - 5*t = 0 for t.
1, 2
Let f(l) = -2*l + 12 - 4*l - 4 - 4*l**2. Let z(v) = 9*v**2 + 13*v - 17. Let q(r) = 5*f(r) + 2*z(r). What is a in q(a) = 0?
-3, 1
Let x(v) be the first derivative of 1/3*v**3 - 1/4*v**4 + 0*v + 3 - 1/6*v**2 + 1/15*v**5. Let x(c) = 0. What is c?
0, 1
Determine d so that 3/4*d**2 + 3/2 - 9/4*d = 0.
1, 2
Suppose -7*p = -3*p - 20. Factor -6*d**3 - 2*d + 7*d**3 - 2*d**p + 3*d**3.
-2*d*(d - 1)**2*(d + 1)**2
Suppose 39 = 3*w - 3. Let x be (4/w)/(25/35). Factor 2/5 - 2/5*h + 2/5*h**3 - x*h**2.
2*(h - 1)**2*(h + 1)/5
Let m = 6/89 - -35/801. Let s(l) be the first derivative of 1 + m*l**4 - 2/27*l**3 + 0*l**2 + 0*l - 2/45*l**5. Let s(c) = 0. What is c?
0, 1
Let g(f) be the third derivative of 3*f**2 + 2/165*f**6 - 3/55*f**5 + 0*f**4 - 1/1155*f**7 + 0 + 0*f + 9/11*f**3. Find z such that g(z) = 0.
-1, 3
Determine n, given that 33/4*n**2 - 27/4*n**4 + 3*n - 3 - 9/2*n**3 = 0.
-1, 2/3
Let c(u) = 2*u**3 - 18*u**2 + 32*u + 52. Let n(r) = -8*r**3 + 72*r**2 - 129*r - 209. Let s(k) = 9*c(k) + 2*n(k). Factor s(a).
2*(a - 5)**2*(a + 1)
Let k(y) be the first derivative of -1/4*y**4 - 1/10*y**5 + 0*y**2 + 2 + 0*y**3 + 0*y + 1/4*y**6. Determine x, given that k(x) = 0.
-2/3, 0, 1
Suppose -3*r - 12 = -0*d - 3*d, -20 = -r - 5*d. Solve r*b + 8/3 - 2/3*b**2 = 0.
-2, 2
Factor -76*r**4 - 10*r**2 - 2*r**3 + 96*r**4 + 15*r**5 - 3*r**3.
5*r**2*(r + 1)**2*(3*r - 2)
Let t(g) be the first derivative of -28*g**5/5 + 12*g**4 - 4*g**3 - 4*g**2 - 12. Find p, given that t(p) = 0.
-2/7, 0, 1
Let h be (2/(-6))/((-5)/15). Let n(d) = d**3 + d. Let b(j) = 6*j**2 + 11*j + 8. Let t(q) = h*b(q) + n(q). Factor t(m).
(m + 2)**3
Let n(y) = y**5 + y**4 - y**2. Let c(j) = -19*j**5 + 26*j**4 - 5*j**3 - j**2. Let h(a) = -c(a) + n(a). Factor h(m).
5*m**3*(m - 1)*(4*m - 1)
Let z(o) be the second derivative of o**7/168 - o**6/40 + 3*o**5/80 - o**4/48 - 4*o. Factor z(q).
q**2*(q - 1)**3/4
Let v(w) be the second derivative of 3*w**5/20 - w**4/4 - w**3/2 + 3*w**2/2 - 3*w. Find i, given that v(i) = 0.
-1, 1
Let j be 11 - 7 - (-14)/(-4). Factor -j*l**3 + 1/2*l - 1/2*l**2 + 1/2.
-(l - 1)*(l + 1)**2/2
Let x(r) = 4*r**5 - 5*r**4 + 7*r**3 + r**2 + 5*r - 5. Let f(k) = -k**5 + k**4 + k**2 - k + 1. Let q(t) = -15*f(t) - 3*x(t). Solve q(i) = 0.
-2, -1, 0, 3
Factor 2*a - 44/13*a**2 - 6/13 + 2/13*a**5 + 36/13*a**3 - 14/13*a**4.
2*(a - 3)*(a - 1)**4/13
Let m(l) be the second derivative of -1/10*l**5 - 2*l + 0*l**2 + 1/3*l**3 + 1/6*l**4 - 1/15*l**6 + 0. Factor m(i).
-2*i*(i - 1)*(i + 1)**2
Factor 6/7*k + 6/7*k**2 + 2/7 + 2/7*k**3.
2*(k + 1)**3/7
Let u(b) be the second derivative of -b**7/98 - b**6/10 - 9*b**5/28 - 9*b**4/28 - 13*b. Find p, given that u(p) = 0.
-3, -1, 0
Factor 2/7*g**3 + 0*g - 4/7*g**2 + 0.
2*g**2*(g - 2)/7
Suppose 2*s - 26 = -5*v, 2*s - 4 + 2 = v. Let d(m) be the third derivative of -1/300*m**5 + 0*m - 1/15*m**3 - 1/40*m**v + m**2 + 0. Factor d(p).
-(p + 1)*(p + 2)/5
Let d(p) be the third derivative of -p**9/1512 - p**8/420 + p**6/90 + p**5/60 - p**3/2 + 4*p**2. Let j(u) be the first derivative of d(u). Factor j(g).
-2*g*(g - 1)*(g + 1)**3
Let a(z) be the third derivative of -z**8/84 + 2*z**7/105 + z**6/15 - 2*z**5/15 - z**4/6 + 2*z**3/3 - 15*z**2. Determine i so that a(i) = 0.
-1, 1
Suppose 2*b = -y - 7, 3*b + b = -4*y - 8. Let 6*x**y + 3*x**4 - x**5 - 8*x**3 - 6*x**4 = 0. What is x?
-2, -1, 0
What is l in -2/5*l**2 + 1/5 + 1/5*l**4 - 1/10*l - 1/10*l**5 + 1/5*l**3 = 0?
-1, 1, 2
Let g(v) = 15*v**3 - 105*v**2 + 114*v + 27. Let c(s) = -8*s**3 + 53*s**2 - 57*s - 14. Let t(p) = 9*c(p) + 4*g(p). Suppose t(y) = 0. Calculate y.
-1/4, 2, 3
Let u = -1/195005 - -41536786/140598605. Let j = -1/103 + u. Let 0*v - j*v**4 + 2/7*v**2 + 0*v**3 + 0 = 0. Calculate v.
-1, 0, 1
Factor 45 - 7*v**2 + 5*v**3 + 106*v - 31*v + 42*v**2.
5*(v + 1)*(v + 3)**2
Let q be -16 + -3 + 2 + 1. Let t be (-1 + 2)*(-2 - q). Let h + 9*h**3 - 24*h**4 + 13*h**3 - 18*h**2 + 2*h + t*h**3 = 0. Calculate h.
0, 1/2
Let z(h) be the second derivative of h**8/960 - h**7/1260 - 7*h**6/720 + h**5/60 - h**4/4 + h. Let s(d) be the third derivative of z(d). Factor s(y).
(y - 1)*(y + 1)*(7*y - 2)
Let i = 3 + 2. Find l, given that 0*l - 1 - 2*l + i - 5 - l**2 = 0.
-1
Factor 2 + 0 + 7*l**2 + 16*l - 7*l.
(l + 1)*(7*l + 2)
Let a(o) = o**2 + 7*o. Let f(x) = -x. Let z(j) = -a(j) - 6*f(j). Let h(w) = 4*w - 2. Let l(s) = 2*h(s) + 2*z(s). Factor l(q).
-2*(q - 2)*(q - 1)
Let k(s) be the third derivative of 1/15*s**5 - 2/105*s**7 + 0*s**6 + 0*s**3 + 0*s + 0 - 1/12*s**4 + 1/168*s**8 - 3*s**2. Determine w so that k(w) = 0.
-1, 0, 1
Let k(z) be the first derivative of -3 - z + 1/6*z**3 - 1/4*z**2. Factor k(r).
(r - 2)*(r + 1)/2
Let f be (-2 - 0)/(-2)*3. Solve -a + a**2 + 2*a**f + 3*a - 5*a**2 = 0.
0, 1
Let c = 4 + -7. Let g be ((-6)/(-4))/(c/(-4)). Solve 0 - 1/2*b**3 + 0*b - 1/2*b**g = 0.
-1, 0
Let j(v) be the second derivative of v**6/180 - v**5/30 - v**4/4 - 5*v**3/6 + 5*v. Le