m(n) be the second derivative of -n**5/420 + n**3/42 + 2*n**2 - 3*n. Let u(q) be the first derivative of m(q). Solve u(r) = 0.
-1, 1
Let f = -6 + 9. Factor -13*k + 12*k + 0*k**3 + 2*k**2 - k**f.
-k*(k - 1)**2
Let m = 1 + 3. Find p such that 0 + 3*p**2 + 2 + m*p - p**2 = 0.
-1
Let n be ((-2)/20)/((-3)/4). Let t(f) be the third derivative of 5/12*f**4 - 2*f**2 + 0*f + 0 - 1/3*f**3 - n*f**5. Find u such that t(u) = 0.
1/4, 1
Let q(f) = 4*f**5 - 4*f**4 + 2*f**3 + 7*f**2 + 3. Let v(s) = -3*s**5 + 4*s**4 - 2*s**3 - 6*s**2 + s - 2. Let n(w) = 2*q(w) + 3*v(w). Factor n(g).
-g*(g - 3)*(g - 1)**2*(g + 1)
Let u be (3340/16)/(7/(-4)). Let i = -119 - u. Factor -i + 4/7*v - 2/7*v**2.
-2*(v - 1)**2/7
Let h be ((15/(-10))/(-3))/1. Let i(j) be the first derivative of h*j**3 + 0*j**2 + 0*j - 1/4*j**6 + 3/8*j**4 + 1 - 3/10*j**5. Solve i(z) = 0.
-1, 0, 1
Solve -3 + 63*o**2 - 60*o**2 + 3*o**3 - o - 2*o = 0 for o.
-1, 1
Let i(y) be the third derivative of y**5/15 - 2*y**2. What is t in i(t) = 0?
0
Let d(y) be the third derivative of y**8/672 - y**7/210 + y**5/60 - y**4/48 - 7*y**2. Find f, given that d(f) = 0.
-1, 0, 1
Suppose 12 = 4*k, 2*h + 0*k - 9 = -3*k. Factor 1/2*t**3 + 0*t + h - 3/2*t**2.
t**2*(t - 3)/2
Factor 2/7*b**2 - 2/7*b - 4/7.
2*(b - 2)*(b + 1)/7
Let y(a) be the first derivative of -5*a**5 - 5*a**4/2 + 175*a**3/3 - 40*a**2 - 60*a - 20. Determine n so that y(n) = 0.
-3, -2/5, 1, 2
Let w(n) = 2*n**3 + 6*n**2 + 2*n - 1. Let u be w(-4). Let h = u + 89. Find l such that -44*l**2 - 84*l**3 + h*l - 49/2*l**4 - 8 = 0.
-2, 2/7
Suppose -r + 8 = 5. Factor 0 - 2*m**r - 2/3*m - 2*m**2 - 2/3*m**4.
-2*m*(m + 1)**3/3
Let s = 13 - 5. Suppose -3*d = d - s. Suppose z**2 + 0*z**d + 6*z**5 - 5*z**3 - 3*z**3 + 2*z - z**4 = 0. Calculate z.
-1, -1/2, 0, 2/3, 1
Let o be (3 - 4)/(3/6). Let r be 5/2 + o/(-4). What is p in 7*p - 4*p + 6*p**2 - r*p + 3*p**3 = 0?
-2, 0
Suppose 3*l = -0*l + 240. Let 34*d**2 + d**4 + 12*d**4 + 17*d**4 - 4*d + 2*d**4 - l*d**3 = 0. What is d?
0, 1/4, 2
Let g = 2 + 0. Determine h so that -8*h**4 + 3*h**2 - 6*h + 12*h**2 - 7*h**4 + 0*h**g - 21*h**5 + 27*h**3 = 0.
-1, 0, 2/7, 1
Let n(f) be the first derivative of -f**4/5 - 2*f**3/15 + f**2/5 - 5. Factor n(v).
-2*v*(v + 1)*(2*v - 1)/5
Let k(z) be the first derivative of z**4/8 + 3. What is v in k(v) = 0?
0
Let -16/3*g**2 + 0*g + 32/3 + 2/3*g**4 + 0*g**3 = 0. What is g?
-2, 2
Let z(m) be the third derivative of -m**8/30240 + m**7/3780 - m**6/1080 + m**5/60 - 3*m**2. Let b(o) be the third derivative of z(o). Factor b(a).
-2*(a - 1)**2/3
Determine h, given that -2/3*h**3 + 2/3*h - 1/3 + 0*h**2 + 1/3*h**4 = 0.
-1, 1
Let r = 8 + -16. Let l be r*2*(-1)/10. Factor 8/5*z - 2/5*z**2 - l.
-2*(z - 2)**2/5
Let f(x) be the first derivative of -x**6/3 + 2*x**5/5 - 5. Let f(w) = 0. What is w?
0, 1
Suppose 4*a + 2*v = -5 + 27, 5*v - 19 = 2*a. Find z, given that -12*z**4 + 8*z**2 + 12*z + z**5 - 8*z**3 + 1 + a - 5*z**5 = 0.
-1, 1
Let x = -78 + 82. Let d(b) be the second derivative of 0 + 2*b**2 + 5/3*b**3 - b + 1/10*b**5 + 2/3*b**x. Determine v so that d(v) = 0.
-2, -1
Factor 4/3*t**3 + 4/3*t - 1/3 - 1/3*t**4 - 2*t**2.
-(t - 1)**4/3
Let q(y) = y**2 + y + 7. Let i(f) = f**2 + 8. Let v = 7 - 11. Let n(p) = v*q(p) + 3*i(p). Factor n(a).
-(a + 2)**2
Let t(y) be the first derivative of -y**6/33 - 8*y**5/55 + y**4/11 + 8*y**3/11 - 9*y**2/11 + 9. Factor t(b).
-2*b*(b - 1)**2*(b + 3)**2/11
What is a in 22/3*a**2 + 2/3 + 14/3*a**3 - 8*a**4 - 14/3*a = 0?
-1, 1/4, 1/3, 1
Let d = 9 + -2. Suppose 8*y - d*y = 3. Let 1/3*p**y - 1/3*p**2 - 1/3*p + 1/3 = 0. Calculate p.
-1, 1
Factor 0*y**3 + y**3 - 1228*y**2 + 1222*y**2.
y**2*(y - 6)
Let s(v) = -12*v**3 + 3*v**2 + 9*v + 9. Let g(x) = x**3 - x - 1. Let u(c) = 9*g(c) + s(c). Factor u(a).
-3*a**2*(a - 1)
Let b(n) = -n**3 + 4*n**2 - 4. Let d be b(3). Factor -3 + 5*q**5 - 2*q**3 + 2*q**4 - 2*q**2 + 3 - 3*q**d.
2*q**2*(q - 1)*(q + 1)**2
Let f(i) be the first derivative of i**4/16 - i**2/8 + 13. Factor f(n).
n*(n - 1)*(n + 1)/4
Factor 4/11*w**3 + 0*w + 0 + 0*w**2 + 10/11*w**4.
2*w**3*(5*w + 2)/11
Let j(f) be the third derivative of -11/8*f**4 + 4/5*f**5 - 7/40*f**6 + 0*f - 2*f**2 + 0 + f**3. Factor j(n).
-3*(n - 1)**2*(7*n - 2)
Let w(m) be the second derivative of 3*m**7/14 + m**6 + 21*m**5/20 - m**4 - 2*m**3 + 10*m. Solve w(o) = 0.
-2, -1, 0, 2/3
Let n = -789 - -7123/9. Determine l, given that 2*l**2 - n*l + 4/9 = 0.
2/9, 1
Let t(w) be the first derivative of -9/2*w**4 + 3/5*w**5 - 18*w**2 + 12*w + 8 + 13*w**3. Determine u so that t(u) = 0.
1, 2
Let j = -1 - -3. Let u(p) be the second derivative of 1/33*p**3 + 0*p**2 - j*p - 1/231*p**7 - 2/165*p**6 + 1/33*p**4 + 0 + 0*p**5. Factor u(b).
-2*b*(b - 1)*(b + 1)**3/11
Let w = -4 + 4. Suppose w = 2*b - 4. Find s such that -1/5*s**3 + 0*s + 1/5*s**b + 0 = 0.
0, 1
Let t(w) be the first derivative of w**6/600 + w**5/300 - w**4/120 - w**3/30 + 3*w**2/2 + 2. Let n(y) be the second derivative of t(y). Factor n(u).
(u - 1)*(u + 1)**2/5
Let c(q) be the second derivative of -q**5/360 - q**4/72 - q**3/36 + 2*q**2 + q. Let z(g) be the first derivative of c(g). Factor z(i).
-(i + 1)**2/6
Let p be 4 + (-4 + 7)*4/(-6). Let g(d) be the first derivative of 0*d**3 - 1/12*d**4 + 1/15*d**5 + 0*d**p + 0*d + 2. Factor g(u).
u**3*(u - 1)/3
Let f = 96 + -478/5. Let j(s) be the second derivative of -5/12*s**4 + 0 + 3*s + 27/50*s**6 - 1/6*s**7 + 2/5*s**2 - 37/100*s**5 + f*s**3. Solve j(o) = 0.
-2/5, -2/7, 1
Suppose 4*q + k = 5*k - 4, k - 9 = -q. Factor -4*p + 16*p**q - 24*p**3 + 5*p**2 - 4*p**5 + 9*p**2 + 2*p**2.
-4*p*(p - 1)**4
Let g(a) = a - 2. Let n be g(3). Suppose 2*o - y = -4*y + 12, 5*y - n = 3*o. Suppose -4*q**2 - 5 + o*q + 1 + 5 = 0. Calculate q.
-1/4, 1
Factor -3/8*u + 3/4 + 3/8*u**4 + 3/8*u**3 - 9/8*u**2.
3*(u - 1)**2*(u + 1)*(u + 2)/8
Let y(u) be the first derivative of 2*u**3/33 - 6*u**2/11 + 18*u/11 + 5. Let y(s) = 0. Calculate s.
3
Let a(f) be the first derivative of f**5/5 - 3*f**4/4 + f**3 - f**2/2 + 5. Let a(u) = 0. Calculate u.
0, 1
Let r(f) be the second derivative of -7/9*f**3 - 2/3*f**2 + 0 - 1/10*f**5 - f - 4/9*f**4. Factor r(q).
-2*(q + 1)**2*(3*q + 2)/3
Let a(b) be the second derivative of -2*b**6/45 - 7*b**5/60 + b**4/6 + 7*b**3/18 - b**2/3 - 14*b. Let a(w) = 0. Calculate w.
-2, -1, 1/4, 1
Factor 4/21*a - 10/21*a**3 + 0 + 2/7*a**2.
-2*a*(a - 1)*(5*a + 2)/21
Let a(m) = m + 1. Let y(t) = 4*t**2 + 8*t + 4. Let v(w) = 4*a(w) + 2*y(w). Factor v(l).
4*(l + 1)*(2*l + 3)
Suppose 0*u - 42 = -4*u - 2*n, -n - 9 = -u. Let k be (-14)/(-15) + u/25. Factor -k*w**4 + 0*w**3 + 2/3*w**5 + 4/3*w**2 - 2/3*w + 0.
2*w*(w - 1)**3*(w + 1)/3
Let o(i) be the second derivative of 3*i**5/20 + 3*i**4/4 - i**3/2 - 9*i**2/2 + 16*i. Let o(k) = 0. What is k?
-3, -1, 1
Suppose -8*a + 12 = -6*a. Let h(r) be the second derivative of 0 - 2*r + 1/6*r**7 - 4/3*r**4 + r**2 + 17/10*r**5 - 13/15*r**a - 1/6*r**3. Factor h(x).
(x - 1)**4*(7*x + 2)
Let n(a) be the third derivative of 0*a**5 + 0*a**3 + 4*a**2 - 1/240*a**6 + 0*a + 0*a**4 + 0*a**7 + 0 + 1/672*a**8. Let n(b) = 0. Calculate b.
-1, 0, 1
Let r(v) be the second derivative of -5*v**4/12 + 5*v**3/2 - 5*v**2 + 11*v. Factor r(f).
-5*(f - 2)*(f - 1)
Let r(f) be the third derivative of -f**8/35 - 52*f**7/525 - 17*f**6/200 + 4*f**5/75 + 3*f**4/40 - f**3/15 - 14*f**2. Determine d so that r(d) = 0.
-1, -2/3, 1/4
Let i(g) be the second derivative of g**10/136080 - g**9/68040 - g**4/12 - 3*g. Let o(m) be the third derivative of i(m). Suppose o(q) = 0. What is q?
0, 1
Let i = -7 + 7. Let c(p) be the third derivative of 0*p + 1/75*p**6 + 0*p**4 + 1/420*p**8 + 1/105*p**7 + i + 1/150*p**5 + 2*p**2 + 0*p**3. Factor c(j).
2*j**2*(j + 1)**2*(2*j + 1)/5
Let f be 2/(-3) + 91/78. Determine p so that -1/2 - f*p**2 + p = 0.
1
Let f(d) be the third derivative of -d**5/60 + d**3/6 + d**2. Factor f(k).
-(k - 1)*(k + 1)
Factor 0 - 1/4*s + 1/8*s**2.
s*(s - 2)/8
Let x(d) = -2*d**2 + 2. Let f(r) = -2*r**2 - r + 3. Let y(q) = -3*f(q) + 4*x(q). Factor y(p).
-(p - 1)*(2*p - 1)
Let i(j) be the second derivative of j**4/72 - 17*j**3/18 + 289*j**2/12 + j - 1. Let i(h) = 0. Calculate h.
17
Let l(u) be the third derivative of u**8/5040 - u**7/420 + u**6/90 - u**5/12 + u**2. Let k(c) be the third derivative of l(c). Factor k(j).
4*(j - 2)*(j - 1)
Let f(b) be the first