- a - 2/3*a**2 + a**3.
-(a - 5)*(a - 1)**2*(a + 1)/6
Let s(k) be the second derivative of 1/12*k**4 - 5/2*k**2 - k + 2/3*k**3 + 0. Let q(l) = -2*l + 2. Let x(f) = -5*q(f) - 2*s(f). Factor x(h).
-2*h*(h - 1)
Let h(w) be the third derivative of -w**8/560 - 9*w**7/350 - 3*w**6/100 + 4*w**5/25 - 248*w**2. What is u in h(u) = 0?
-8, -2, 0, 1
Let s(l) be the second derivative of l**4/36 - 14*l**3/3 + 294*l**2 - 63*l. Suppose s(o) = 0. Calculate o.
42
Let n(k) be the first derivative of k**5/5 - k**4/4 - k**3/3 - k**2/2 + 12. Let j(f) = 7*f**4 + 3*f**3 - 7*f**2 - 7*f. Let a(p) = j(p) - 2*n(p). Factor a(x).
5*x*(x - 1)*(x + 1)**2
Solve 87/4*p**3 - 3/2*p**4 - 48*p**2 - 9 + 147/4*p = 0 for p.
1/2, 1, 12
Let u = 12 - 16. Let j(m) = -15*m**2 - 54*m - 81. Let v(p) = 3*p**2 + 11*p + 16. Let s(k) = u*j(k) - 21*v(k). Let s(a) = 0. What is a?
-4, -1
Let q be (-2)/4 + 14/4. Suppose 0*w + 5 = w. Determine o so that -2*o - 13*o - 17*o**2 + w*o**2 - q = 0.
-1, -1/4
Let p(f) be the second derivative of 14*f + 0*f**3 + 0*f**2 + 0*f**4 - 1/5*f**5 + 0. Solve p(n) = 0.
0
Let l(r) be the second derivative of -r**8/7560 + r**7/945 - r**6/324 + r**5/270 - r**3/3 + 3*r. Let s(y) be the second derivative of l(y). Factor s(a).
-2*a*(a - 2)*(a - 1)**2/9
Let s = 0 + 4. Suppose 2*p = -8, -3*h - s*p + 3 = -2. Let -q**2 + 8 + h + 3*q**2 - 7 - 8*q = 0. Calculate q.
2
Suppose -2/7*n**4 + 48/7*n + 52/7*n**3 + 0 - 14*n**2 = 0. Calculate n.
0, 1, 24
Solve -8*t**4 - 13*t + 3*t**5 + 14*t**4 + 12*t - 2*t - 6*t**2 = 0.
-1, 0, 1
Let k = 47 + -45. Factor 22*p**4 - 6*p**4 - 6*p**3 + 4*p**5 + 4*p**4 + 18*p**3 - 36*p**k.
4*p**2*(p - 1)*(p + 3)**2
Let i = 897/1340 + 27/335. Factor -3 - i*b**2 - 9/4*b**3 + 6*b.
-3*(b - 1)*(b + 2)*(3*b - 2)/4
Let i = 50798/9 + -5644. Factor 20/9*o + 50/9 + i*o**2.
2*(o + 5)**2/9
Let q(n) be the first derivative of n**5/100 + 9*n**4/20 + 81*n**3/10 + 729*n**2/10 + 46*n + 22. Let s(i) be the first derivative of q(i). Factor s(a).
(a + 9)**3/5
Let r be 34/51 - (49/(-30))/(-7). Let n(v) be the third derivative of 0 + 0*v - r*v**5 + 6*v**2 - 1/105*v**7 - 4/3*v**3 + v**4 + 1/10*v**6. Factor n(s).
-2*(s - 2)**2*(s - 1)**2
Suppose 5*n + 40 = 55. Let l(j) be the third derivative of -8*j**2 - 4/3*j**n + 0 - 1/30*j**5 - 1/40*j**6 + 1/210*j**7 + 1/2*j**4 + 0*j. Factor l(y).
(y - 2)**2*(y - 1)*(y + 2)
Let r(y) be the second derivative of -y**4/36 + 154*y**3/9 - 11858*y**2/3 - 25*y + 12. Determine c so that r(c) = 0.
154
Suppose 4*p - 25*p = -3529 + 967. Factor -144*n - p*n**2 - 32 + 90*n**3 - 25/2*n**4.
-(n - 4)**2*(5*n + 2)**2/2
Let z = 1664 - 1661. Suppose z + 3/2*w**2 - 9/2*w = 0. Calculate w.
1, 2
Let x(t) be the third derivative of -t**8/560 + t**7/280 + t**6/120 - t**5/40 - 37*t**3/6 + 32*t**2. Let k(w) be the first derivative of x(w). Factor k(p).
-3*p*(p - 1)**2*(p + 1)
Suppose -45*i + 856 = 3*i + 59*i. Factor -18*w**2 - 1/2*w**4 - i*w + 32 - 11/2*w**3.
-(w - 1)*(w + 4)**3/2
Let v = 1816 + -10889/6. Suppose v*c**3 - 17/6*c + 8/3*c**2 - 1 = 0. Calculate c.
-3, -2/7, 1
Let z(w) be the second derivative of -2*w**7/21 - 8*w**6/5 - 51*w**5/5 - 88*w**4/3 - 32*w**3 + 210*w. Solve z(a) = 0 for a.
-4, -3, -1, 0
Factor -z**4 - 22*z**2 + 2*z**4 + 32*z + 13*z**2 + 7*z**2 + 16*z**2 - 17*z**3.
z*(z - 16)*(z - 2)*(z + 1)
Let m(r) = 2*r + 32. Let d be m(-15). Let u(k) be the first derivative of 0*k**d + 3/16*k**4 - 5 + 0*k + 0*k**3. Solve u(z) = 0.
0
Factor 0 + 1/2*o**2 + 21/2*o.
o*(o + 21)/2
Suppose -5*r = -4*q - 5 + 16, 13 = 3*q + r. Find u such that 5*u**3 - 3*u**2 + 12*u**4 + 2*u**2 + 7*u**3 + q*u**2 = 0.
-1/2, 0
Suppose -199*y = -157*y. Let 0*c + 0 + y*c**2 - 5/3*c**4 - 5/3*c**3 = 0. What is c?
-1, 0
Let q(a) be the first derivative of -32*a**5/25 - a**4 + 29*a**3/15 + 2*a**2 + 3*a/5 - 98. Find m, given that q(m) = 0.
-1, -3/8, -1/4, 1
Let w(v) be the second derivative of -v**5/20 - v**4/2 + 2*v**3/3 + 12*v**2 + 208*v - 2. Factor w(t).
-(t - 2)*(t + 2)*(t + 6)
Let c(v) be the second derivative of v**5/70 + v**4/21 - 5*v**3/21 - 6*v**2/7 + 2*v - 35. Factor c(f).
2*(f - 2)*(f + 1)*(f + 3)/7
Suppose -2 + 5 = w. Let -51*y**3 - 42*y**3 + 90*y**w + 9*y - 6*y**2 = 0. What is y?
-3, 0, 1
Let k(v) be the third derivative of -v**8/210 + 3*v**7/140 - v**6/90 + 7*v**3 - 38*v**2. Let c(m) be the first derivative of k(m). Factor c(i).
-2*i**2*(i - 2)*(4*i - 1)
Let 6*s**3 + 20*s**2 + 22*s**2 - 12*s**2 + 10*s**2 + 32*s - 4*s**4 - 2*s**3 = 0. What is s?
-2, -1, 0, 4
Let m = -32627/3 + 10881. Determine n, given that -8/3*n**3 + 4/3*n**4 + 16/3 + m*n - 4*n**2 = 0.
-1, 2
Let n(b) be the second derivative of 2*b**7/21 + 26*b**6/15 + 12*b**5/5 + 58*b. Factor n(r).
4*r**3*(r + 1)*(r + 12)
Let n be 1/1 + 1/(-2). Let w(m) = m**3 + 60*m**2 + 226*m + 112. Let r be w(-56). Let r + 0*l**4 - n*l**5 + 0*l**2 - 1/2*l + l**3 = 0. What is l?
-1, 0, 1
Let k(i) be the first derivative of -4*i**3/3 + 10*i**2 + 81. Let k(t) = 0. Calculate t.
0, 5
Let m(q) be the third derivative of 0*q**4 + 0*q**6 - 1/3*q**3 + 0 + 7*q**2 - 1/420*q**7 + 0*q + 1/24*q**5. Find d, given that m(d) = 0.
-2, -1, 1, 2
Let r(n) be the second derivative of -n**6/180 - n**5/18 - 2*n**4/9 - 4*n**3/9 - 15*n**2 + 44*n. Let f(a) be the first derivative of r(a). Factor f(t).
-2*(t + 1)*(t + 2)**2/3
Let p(v) = 4*v**2 - 130*v + 1159. Let w(r) = -8*r**2 + 258*r - 2319. Let d(n) = 7*p(n) + 3*w(n). Let d(z) = 0. What is z?
17
Factor -18 + 2/7*j**2 + 4/7*j.
2*(j - 7)*(j + 9)/7
Let d be 2/(-3)*3*2. Let v be (-4 + 8 + d)/(-1). Factor -1/6*y**3 + 0 - 1/6*y**2 + v*y.
-y**2*(y + 1)/6
Let z be (-8)/((-3)/5 + 170/(-50)). Determine u so that -11/3*u + 4/3 + 3*u**z - 1/3*u**3 - 1/3*u**4 = 0.
-4, 1
Solve 0 + 2/3*f**4 + 2*f**2 + 2*f**3 + 2/3*f = 0.
-1, 0
Let b = -1321/7 - -189. Let c be (-57)/532*48/(-18). Factor b*m**3 - 4/7*m**2 + 0 + c*m.
2*m*(m - 1)**2/7
Let t(y) be the first derivative of -y**6/1320 + y**5/330 - y**4/264 + 6*y**2 + 15. Let l(o) be the second derivative of t(o). Factor l(u).
-u*(u - 1)**2/11
Suppose 0 = -2*q - 4 - 4. Let h = q - -6. Factor 3*c**2 - 3*c**2 - h*c**3 - 6*c + 4 + 4*c**3.
2*(c - 1)**2*(c + 2)
Let r(u) = 8*u**2 + 6*u - 1. Let h be r(4). Factor 3*v**2 - 3*v + h*v**3 - 72*v**3 - 3 - 76*v**3.
3*(v - 1)*(v + 1)**2
Let b be (-2 - 4 - (-1508)/87) + -10. Determine r so that 0 - 2/3*r**2 - b*r = 0.
-2, 0
Factor 0 + 10/11*i - 2/11*i**2.
-2*i*(i - 5)/11
Let j(f) be the second derivative of f**4/21 + 10*f**3/21 + 8*f**2/7 + 14*f. Solve j(t) = 0 for t.
-4, -1
Suppose -180 + 177 = -o. Let q(f) be the third derivative of 0*f + 0 + 1/12*f**5 + 4*f**2 - 1/8*f**4 - 1/120*f**6 - 3/2*f**o. Solve q(t) = 0 for t.
-1, 3
Let b = -2169 + 2169. Factor b - 3/8*q**4 - 3/8*q**3 + 3/4*q**2 + 0*q.
-3*q**2*(q - 1)*(q + 2)/8
Let d(t) = -4*t**2 + 3*t + 5. Let n(o) = -o**2 + 1. Let u(a) = d(a) + n(a). Let m(f) = -f**2 + f. Let b(k) = -4*m(k) + u(k). Let b(g) = 0. What is g?
-3, 2
Let t(d) be the third derivative of -d**2 + 0 + 0*d**6 + 5/6*d**3 - 1/420*d**7 + 0*d**5 + 0*d + 0*d**4. Let s(r) be the first derivative of t(r). Factor s(m).
-2*m**3
Let q(h) be the third derivative of h**5/30 - h**4/12 - h**3/6 + 8*h**2. Let s be q(-1). Solve 0*g**5 + g**5 + 0*g**5 + s*g**3 + g**2 + 3*g**4 = 0 for g.
-1, 0
Let o(u) = 46*u - 9. Let m be o(7). Factor -619*z**3 + 212*z**3 - 4320*z**2 - 12960*z - m*z**3 - 15552 - 60*z**4 - 2*z**5.
-2*(z + 6)**5
Factor 10*y**3 + 53*y**2 - 63*y**2 - 147*y**2 - 47*y**2 - y**3 + 51*y**4 - 36*y.
3*y*(y - 2)*(y + 2)*(17*y + 3)
Let y(a) be the first derivative of 7*a**3/3 - 13*a**2/2 + 10*a + 1. Let u(d) = -15*d**2 + 25*d - 20. Let p(c) = 2*u(c) + 5*y(c). Factor p(j).
5*(j - 2)*(j - 1)
Let q(h) be the first derivative of h**4/4 + 5*h**3/3 - 300. Find w such that q(w) = 0.
-5, 0
Let s(f) be the second derivative of -1/11*f**2 + 1/66*f**4 - 10*f + 1/33*f**3 + 0 - 1/110*f**5. Suppose s(r) = 0. Calculate r.
-1, 1
Let w(j) be the first derivative of j**4/4 + 35*j**3 - 213*j**2/2 + 107*j + 110. Find t, given that w(t) = 0.
-107, 1
Let m(o) = o**3 + 18*o**2 + 18*o + 20. Let h be m(-17). Suppose 0 = -10*a + h*a. Solve 3/2*p + 3/4*p**2 + a = 0.
-2, 0
Suppose -6*g**2 + 83*g**3 - 18 + 77*g**3 - 145*g**3 - 39*g = 0. What is g?
-1, -3/5, 2
Let q(x) be the second derivative of 36*x + 0 + 1/3*x**4 + 98*x**2 - 28/3*x**3. Factor q(p).
4*(p - 7)**2
Let h(u) be th