t**3 - 86 = 0.
-3, -2
Let l(f) be the second derivative of -f**5/390 - f**4/78 - f**3/39 - f**2/2 + 33*f. Let r(z) be the first derivative of l(z). Factor r(n).
-2*(n + 1)**2/13
Let m = -1136/329 - -216/47. Suppose -8/7 + m*y**2 + 30/7*y = 0. Calculate y.
-4, 1/4
Factor 8424 - 72*r + 2/13*r**2.
2*(r - 234)**2/13
Let t(l) = -7*l + 3*l**2 + 4*l**2 - 3*l**2 - 3*l**2. Let z(n) = -n**2 + 6*n + 1. Let j(x) = -5*t(x) - 6*z(x). Factor j(m).
(m - 3)*(m + 2)
Let w(h) be the second derivative of -h**6/180 + h**4/12 - 2*h**3/9 - 2*h**2 + 13*h. Let f(r) be the first derivative of w(r). Factor f(m).
-2*(m - 1)**2*(m + 2)/3
What is x in 4/3 - 4*x - 7/3*x**2 = 0?
-2, 2/7
Solve 1175*k + k**3 - 586*k - 591*k - 10 + k**3 + 10*k**2 = 0.
-5, -1, 1
Let i(u) be the first derivative of 27*u**4/4 + 15*u**3 + 21*u**2/2 + 3*u - 107. Let i(g) = 0. What is g?
-1, -1/3
Let a be (-6 - 0)/(6/(-4)) - 0/(-187). Factor -3/11*u**2 + 1/11*u**a - 2/11 - 5/11*u + 1/11*u**3.
(u - 2)*(u + 1)**3/11
Let z(v) = -4*v**4 - 11*v**3 + 7*v**2 + 11*v - 3. Let x(a) = -a**3 + a**2 + a - 1. Let l(d) = -3*x(d) + z(d). Factor l(p).
-4*p*(p - 1)*(p + 1)*(p + 2)
Let h(s) be the first derivative of -4*s**3/3 + 4*s**2 + 32*s + 91. Let h(d) = 0. What is d?
-2, 4
Let s(h) be the second derivative of 1/21*h**7 + 0*h**6 + 0*h**4 + 0 - 1/10*h**5 - 3*h + 0*h**2 + 0*h**3. What is a in s(a) = 0?
-1, 0, 1
Determine c so that -3/8*c**2 - 3/2*c**5 + 0 + 21/8*c**3 - 9/8*c + 3/8*c**4 = 0.
-1, -3/4, 0, 1
Let c(q) = q**3 + q**2 - 2. Let p(z) = -3*z**3 + 3*z + 4. Let i(s) = 2*c(s) + p(s). Let i(j) = 0. Calculate j.
-1, 0, 3
Suppose -111 = 5*g - 141. Let p(z) be the second derivative of 1/9*z**3 + 0*z**2 - g*z + 1/36*z**4 + 0. Factor p(a).
a*(a + 2)/3
Let j(r) be the second derivative of -3/10*r**5 + 0*r**2 - 16*r - 7/6*r**4 + 2*r**3 + 0. Factor j(n).
-2*n*(n + 3)*(3*n - 2)
Suppose -4*b = 4*p + 316, 3*b - p = 4*p - 245. Let r = -75 - b. Factor 0*w - 3*w**r + 0 + 0*w**2 - 1/3*w**3 + 2*w**4.
-w**3*(3*w - 1)**2/3
Let 56/3*q + 192/5*q**2 - 54/5*q**3 + 32/15 = 0. Calculate q.
-2/9, 4
Let r(m) be the second derivative of m**4/4 + 179*m**3/2 - 270*m**2 - 2*m + 3. Let r(i) = 0. What is i?
-180, 1
Let q(l) be the first derivative of l**3/3 + 7*l**2/2 - 294. Find n, given that q(n) = 0.
-7, 0
Let j(g) = 4*g**2 - 9*g + 9. Let b(h) = -9*h**2 + 18*h - 15. Let c(v) = -3*b(v) - 7*j(v). Factor c(f).
-(f - 6)*(f - 3)
Let g(y) be the second derivative of y**7/630 - y**6/36 + 2*y**5/15 + y**4 + 16*y. Let k(r) be the third derivative of g(r). Factor k(w).
4*(w - 4)*(w - 1)
Let y(d) be the first derivative of 4*d**3/3 + 4*d**2 - 12*d - 5. Let o(i) = -i + 1. Let u(x) = -16*o(x) - y(x). Factor u(w).
-4*(w - 1)**2
What is f in 172*f + 79*f + 1140 - 41*f + 1065 + 5*f**2 = 0?
-21
Solve 12*c**4 - 4786*c**3 - 8*c**5 + 4738*c**3 + 2*c**5 + 15*c**2 + 27*c**4 = 0 for c.
0, 1/2, 1, 5
Factor 32*l + 2*l**5 - 2*l**4 + 853*l**3 + 2*l**4 - 869*l**3.
2*l*(l - 2)**2*(l + 2)**2
Suppose z - 3*r - 2 = r, -6 = -3*z + 2*r. Let s(q) be the first derivative of -4/9*q + 3 - 2/9*q**4 + q**z - 2/9*q**3. Determine o so that s(o) = 0.
-2, 1/4, 1
Let v(z) be the second derivative of 2/3*z**6 - 8/5*z**5 + 37*z - 2/21*z**7 + 4/3*z**4 + 0*z**2 + 0 + 0*z**3. Factor v(p).
-4*p**2*(p - 2)**2*(p - 1)
Suppose -3*h = 5*q - 19, 18 = 4*q + 4*h - 2. Let l(o) = -39*o**3 - o. Let p be l(-1). Factor p*y**2 - 36 - 21*y**2 - 23*y**q + 24*y.
-4*(y - 3)**2
Let h(f) be the first derivative of -f**6/27 + 4*f**5/15 - 11*f**4/18 + 4*f**3/9 + 769. Determine s so that h(s) = 0.
0, 1, 2, 3
Let h(a) be the third derivative of -1/4*a**4 + 0 - 1/10*a**6 + 0*a - 1/4*a**5 + 0*a**3 - 12*a**2 - 1/70*a**7. Factor h(w).
-3*w*(w + 1)**2*(w + 2)
Let m = 3986 + -11956/3. Let h = 6 - 4. Factor -2*j**3 + 0*j**h + 0 + 8/3*j - m*j**4.
-2*j*(j - 1)*(j + 2)**2/3
Let y(k) be the third derivative of -k**5/300 + 2*k**4/15 + 17*k**3/30 - 514*k**2. Factor y(w).
-(w - 17)*(w + 1)/5
Let r(v) be the second derivative of v**4/30 - 14*v**3 + 2205*v**2 - 34*v + 12. Determine b so that r(b) = 0.
105
Let h(j) be the second derivative of 4/45*j**5 + 16/27*j**3 + 5/9*j**2 - 9*j + 1/135*j**6 + 0 + 1/3*j**4. Factor h(d).
2*(d + 1)**3*(d + 5)/9
Let d(o) be the second derivative of -49*o**7/4 - 147*o**6 - 5481*o**5/8 - 6345*o**4/4 - 2025*o**3 - 1458*o**2 + o + 72. Factor d(t).
-3*(t + 3)**2*(7*t + 6)**3/2
Let m(r) be the third derivative of -r**6/540 - 4*r**5/135 - 7*r**4/36 - 2*r**3/3 + r**2 - 23. Factor m(d).
-2*(d + 2)*(d + 3)**2/9
Let v(a) = a**3 + 4*a**2 - 16*a - 24. Let u be ((-21)/42)/((-1)/(-12)). Let c be v(u). Suppose 3/5*o**3 + 0*o**2 + c*o - 3/5*o**5 + 0*o**4 + 0 = 0. Calculate o.
-1, 0, 1
Suppose -5*q = -3*f + 1717, -3*f - q = 3*q - 1726. Solve -556*i**3 - 80 + 224*i - 264*i**4 - 100*i**5 - f*i**4 + 218*i**4 + 268*i**2 = 0 for i.
-5, -1, 2/5
Let w = -47726/11 - -4339. Solve -1/11*d**2 + 0 + w*d = 0.
0, 3
Let j be 0/(-3 - -4 - 0). Suppose -z + 3*z = j. Factor -1/4*n**2 - 1/4*n**3 + z + 1/2*n.
-n*(n - 1)*(n + 2)/4
Let k(p) be the first derivative of -p**7/3360 - p**6/1440 + p**5/120 + p**4/24 - 11*p**3/3 - 22. Let w(a) be the third derivative of k(a). Factor w(v).
-(v - 2)*(v + 1)*(v + 2)/4
Let p(s) = -19*s + 97. Let g be p(5). Find w such that 4/3*w - 8/3 + 2/3*w**g - 1/3*w**3 = 0.
-2, 2
Solve 6 + 0*g - 6*g**3 + g + 3*g**4 - 27*g**2 + 24 + 5*g - 6 = 0 for g.
-2, -1, 1, 4
Factor 194 + 264 - 169 + 4*u**2 - 68*u.
(2*u - 17)**2
Let k(q) be the second derivative of -1/20*q**4 + 0*q**3 - 1/150*q**5 - 5*q + 0 - 2*q**2. Let t(r) be the first derivative of k(r). Factor t(o).
-2*o*(o + 3)/5
Factor 3/4*v**2 - 6 + 3/2*v.
3*(v - 2)*(v + 4)/4
Let y(k) be the second derivative of -5*k**4/12 - 5*k**3 - 45*k**2/2 - 2*k - 69. Find g, given that y(g) = 0.
-3
Let s be 6/(-16) + 133/56. Suppose 6*a**2 - 6*a**s - 4*a**3 - 4*a**5 + 8*a**5 = 0. What is a?
-1, 0, 1
Find w such that -3 + 42 - 8*w**2 + 0*w**2 + 11*w**2 + 78 + 120*w = 0.
-39, -1
Let y(m) = 12*m**2 - 18*m + 9. Let j(h) = -6*h**2 + 7*h + 2*h - 5 + 0*h**2. Let c be 1 - 1 - (-4 - 1). Let r(q) = c*y(q) + 9*j(q). Factor r(p).
3*p*(2*p - 3)
Let r(t) be the first derivative of -6*t**5/25 + 213*t**4/10 + 744*t**3/5 + 1812*t**2/5 + 1824*t/5 - 106. Find g such that r(g) = 0.
-2, -1, 76
Let k(u) = -6*u - 116. Let l be k(-20). Suppose -4*h + 11 + 9 = -5*z, -2*z - 2*h = -10. Factor z + 0*v + 0*v**2 + 3/5*v**l + 3/5*v**3.
3*v**3*(v + 1)/5
Let z = 832 - 440. Factor 90*f + 135*f**2 - 34*f - z - 137*f**2.
-2*(f - 14)**2
Suppose -2*o + 3*b - 265 = 2*b, 0 = o - b + 132. Let y = o + 535/4. Determine w so that 0*w - 1/4*w**5 - 3/4*w**4 - 1/4*w**2 - y*w**3 + 0 = 0.
-1, 0
Let o(l) be the third derivative of -15*l**2 - 1/30*l**6 + 0 + 1/6*l**4 + 0*l + 2/3*l**3 - 1/15*l**5. Let o(c) = 0. Calculate c.
-1, 1
Let w be (3 + 1 + 1)/(-1). Let n = w - -7. Factor -b**n + 8*b**2 - 2 - 6*b**2 - b.
(b - 2)*(b + 1)
Let p be 42/8 - (-2)/(-8). Let k be (-4 - 8/(-4)) + p. Factor -o**2 + 2 + 2*o**3 - o + 0*o**k - o**2 - o**3.
(o - 2)*(o - 1)*(o + 1)
Suppose 7*u - 9*u = -21*u. Let p(s) be the second derivative of -1/15*s**3 + u*s**2 - 1/100*s**5 + 1/20*s**4 - 2*s + 0. Let p(q) = 0. Calculate q.
0, 1, 2
Let j = 4739/5955 - -5/1191. Factor 0*h**4 - 2/5*h - 2/5*h**5 + 0*h**2 + 0 + j*h**3.
-2*h*(h - 1)**2*(h + 1)**2/5
Let k(t) = 77*t - 28*t - t**2 - 23*t - 27*t. Let b(n) = -3*n**3 - 4*n**2 - n. Let o(l) = b(l) + 2*k(l). Let o(r) = 0. Calculate r.
-1, 0
Let s(x) be the third derivative of -x**8/4032 + x**7/504 + 2*x**5/15 - 16*x**2. Let m(y) be the third derivative of s(y). Solve m(q) = 0.
0, 2
Let c(z) = z**3 - 160*z**2 - 729*z - 782. Let s(j) = -80*j**2 - 364*j - 392. Let w(k) = 4*c(k) - 7*s(k). Factor w(b).
4*(b - 24)*(b + 2)**2
Let t(m) be the first derivative of -9/2*m - 1/4*m**3 - 28 + 21/8*m**2. Determine o, given that t(o) = 0.
1, 6
Factor -3/4*m**3 - 21/2 + 21/2*m**2 + 3/4*m.
-3*(m - 14)*(m - 1)*(m + 1)/4
Let t(r) be the third derivative of r**5/270 + 13*r**4/108 - 273*r**2. Solve t(m) = 0.
-13, 0
Let f(x) be the first derivative of -x**5/15 - x**4/9 + 2*x**3/9 + 2*x**2/3 - 8*x + 20. Let d(u) be the first derivative of f(u). Determine p so that d(p) = 0.
-1, 1
Let v(p) be the third derivative of -p**7/1890 + p**6/108 - 2*p**5/45 + p**4/24 + 17*p**2. Let d(o) be the second derivative of v(o). What is t in d(t) = 0