/6 + 7*t**2. Let u(n) be the second derivative of s(n). What is i in u(i) = 0?
0, 2
Let f(j) = 7*j**4 + j**3 - 25*j**2 + 16*j + 1. Let g(d) = -d**5 + d**4 - d**2 + 1. Let i(v) = f(v) - g(v). Solve i(y) = 0.
-4, 0, 1
Let d(t) be the third derivative of t**8/504 - 2*t**7/315 + t**6/180 + 14*t**2. Factor d(b).
2*b**3*(b - 1)**2/3
Factor 8*k - 12*k - 3*k**3 + 7*k**3.
4*k*(k - 1)*(k + 1)
Let o(s) be the second derivative of -s**4/102 + 9*s**2/17 + 6*s - 2. Suppose o(w) = 0. What is w?
-3, 3
Let c(g) be the first derivative of 25*g**7/84 - 5*g**6/6 + g**5 - 2*g**4/3 - g**3 + 3. Let x(k) be the third derivative of c(k). Factor x(s).
2*(5*s - 2)**3
Let d(r) = -4*r**3 - 8*r**2 + 13*r + 17. Let w(z) = z**3 + 2*z**2 - 3*z - 4. Let a(c) = -2*d(c) - 9*w(c). Factor a(v).
-(v - 1)*(v + 1)*(v + 2)
Let c(y) be the third derivative of -y**7/840 + y**6/480 + y**5/240 - y**4/96 + 3*y**2. Factor c(t).
-t*(t - 1)**2*(t + 1)/4
Suppose -h = -2*w - 2*w + 9, -5*w - 2*h + 21 = 0. Suppose 0 = -w*k + k. Factor k + 0*g**2 - 1/2*g**3 + 1/2*g.
-g*(g - 1)*(g + 1)/2
Let o(d) = 3*d**4 + 3*d**2 + 6. Let f(u) = -u**4 + u**3 - u**2 - 1. Let y(l) = -6*f(l) - o(l). Factor y(j).
3*j**2*(j - 1)**2
Suppose -336/5*k**4 - 274/5*k**3 - 98/5*k**5 + 52/5*k**2 + 72/5*k - 16/5 = 0. Calculate k.
-2, -1, 2/7
Let n(g) be the first derivative of 0*g**4 - 1/9*g**3 + 1 + g**2 + 0*g + 1/90*g**5. Let x(f) be the second derivative of n(f). Factor x(l).
2*(l - 1)*(l + 1)/3
Let c = 247/605 - 1/121. Let g(m) be the first derivative of 0*m - 4/3*m**3 + 0*m**2 + 3/2*m**4 + 2 - c*m**5. Let g(j) = 0. Calculate j.
0, 1, 2
Suppose 3*w = -4*l + 3, 2*l + w + 1 = 2. Let 2/7*t**3 + l + 0*t + 0*t**2 + 2/7*t**5 + 4/7*t**4 = 0. Calculate t.
-1, 0
Let n(s) be the first derivative of -s**9/3024 - s**8/1680 + s**7/840 + s**6/360 - 4*s**3/3 - 9. Let u(k) be the third derivative of n(k). Solve u(t) = 0 for t.
-1, 0, 1
Find h, given that -7*h + 5*h**2 - 9*h - 4*h + 9 + 6 = 0.
1, 3
Factor -2*z**3 - 3*z**2 + 5*z**3 + 0*z + z - 7*z.
3*z*(z - 2)*(z + 1)
Let d(x) be the third derivative of x**8/1512 - 17*x**7/945 + 4*x**6/27 - 32*x**5/135 + 16*x**2. Determine a, given that d(a) = 0.
0, 1, 8
Let b = -1/6 + 5/12. Factor 3/4 + b*m**2 - m.
(m - 3)*(m - 1)/4
Let s(d) be the third derivative of -d**9/4032 + d**8/1120 - d**6/240 + d**5/160 - d**3 + 4*d**2. Let w(m) be the first derivative of s(m). Factor w(n).
-3*n*(n - 1)**3*(n + 1)/4
Let d = 744/7 + -106. Factor 0 + 2/7*r**5 + 0*r**2 + d*r**3 + 0*r - 4/7*r**4.
2*r**3*(r - 1)**2/7
Let v(d) be the third derivative of -d**8/336 - d**7/210 - 13*d**2. Factor v(y).
-y**4*(y + 1)
Suppose 12*g - 14*g = -4. Find n, given that -n - n**3 + 3*n**3 + g - n - 2*n**2 = 0.
-1, 1
Suppose 5*y = 3*k - 23, 0*k = k - 3*y - 9. Factor 2*z**2 + k + 2*z**3 - 6 + 0*z**3.
2*z**2*(z + 1)
Let q = -2/75 + 79/150. Factor q*w**3 + 0 - 1/2*w + 0*w**2.
w*(w - 1)*(w + 1)/2
Let k be 2/8 - (-6 + 250/40). Factor -18/11*l**2 + k + 4/11*l.
-2*l*(9*l - 2)/11
Factor -4 - 8*t**2 - 5*t**2 + 16*t - 7*t**2 + 8*t**3.
4*(t - 1)**2*(2*t - 1)
Suppose -8*h + 17*h = 27. Factor -2/3*b**5 + 0*b**2 + 0*b - 4/3*b**4 - 2/3*b**h + 0.
-2*b**3*(b + 1)**2/3
Let w(o) = o**3 - o**2 + 1. Let g(j) = -30*j**3 - 55*j**2 - 21*j - 7. Let n(f) = g(f) + 5*w(f). Factor n(t).
-(t + 2)*(5*t + 1)**2
Solve 2*b**5 + 4*b**2 + 11*b - 13*b**4 + b**4 + 3*b + 8*b**2 - 16*b**3 = 0.
-1, 0, 1, 7
Let j(g) be the second derivative of 1/84*g**4 + 8*g + 4/21*g**3 + 8/7*g**2 + 0. Determine c so that j(c) = 0.
-4
Let i(r) = 2*r**5 - 7*r**4 + 8*r**3 + 3*r. Let t(h) = 5*h**5 - 15*h**4 + 15*h**3 + 5*h. Let k(v) = -5*i(v) + 3*t(v). Factor k(x).
5*x**3*(x - 1)**2
Let h be ((-18)/(-4))/(5/(50/15)). Find y, given that 0 + 1/4*y**h - 1/2*y**2 + 1/4*y = 0.
0, 1
Let r be 14/6 + (-2)/6. Factor 25*f**4 + 8*f**r - 2*f**2 + 21*f**3 + 10*f**4 - 11*f**4 + 9*f**5.
3*f**2*(f + 1)**2*(3*f + 2)
Let m(j) be the second derivative of j**4/36 + j**3/9 + j**2/6 - 3*j. Factor m(t).
(t + 1)**2/3
Let b(q) = -12*q**2 - 39*q - 7. Let h be b(-3). Factor 10/13*a**h - 14/13*a + 4/13.
2*(a - 1)*(5*a - 2)/13
Let m(r) be the third derivative of 1/60*r**5 + 0*r + 0*r**4 + 2*r**2 + 0 - 1/12*r**3 - 1/420*r**7 + 0*r**6. Find u, given that m(u) = 0.
-1, 1
Let t(d) = -d**2 + 4*d - 3. Let y(h) = -2*h**2 + 8*h - 6. Let o(j) = -10*t(j) + 6*y(j). Factor o(g).
-2*(g - 3)*(g - 1)
Let b = 28 - 26. What is w in -7*w**4 + 0 + 6*w**4 + w**2 - 1 + w**b = 0?
-1, 1
Let a(x) be the third derivative of x**7/10080 - x**6/1440 + x**4/6 - 2*x**2. Let z(n) be the second derivative of a(n). Solve z(k) = 0.
0, 2
Let f(z) be the first derivative of z**6/16 + 3*z**5/20 - z**3/4 - 3*z**2/16 + 13. Suppose f(h) = 0. Calculate h.
-1, 0, 1
Suppose -2*u = 5*u - 6*u. Solve -3/2*r**3 - 3/2*r**4 + 3/2*r**2 + 3/2*r + u = 0 for r.
-1, 0, 1
Suppose -j + 1 = 3*u, 0 = 5*u + 2*j + 2*j - 4. Factor 0*z + 2/7*z**2 + u.
2*z**2/7
Factor 0 - 1/4*l**4 + 0*l - l**2 - l**3.
-l**2*(l + 2)**2/4
Let r be (-20)/(-8) + 1/2. Let y(x) be the first derivative of 2/3*x**r + 0*x**4 + 0*x**2 - 1/5*x**5 - x - 1. Factor y(a).
-(a - 1)**2*(a + 1)**2
Let j be (8/(-12))/(2/6). Let k be (11 - 5)*j/(-18). Factor 2/3*i + 0 - 2/3*i**2 + k*i**4 - 2/3*i**3.
2*i*(i - 1)**2*(i + 1)/3
Determine r so that 2/13*r**5 + 0 - 4/13*r**2 + 0*r**3 + 4/13*r**4 - 2/13*r = 0.
-1, 0, 1
Suppose 8 = 5*s - 3*s. Let n(m) be the second derivative of 1/3*m**3 + m + 0 - 1/20*m**5 + 1/12*m**s + 0*m**2. Factor n(h).
-h*(h - 2)*(h + 1)
Let f = -193 + 195. Factor 0*m**f + 0 + 0*m - 2/3*m**4 - 2/3*m**3.
-2*m**3*(m + 1)/3
Let j be 2/12*(0 + -3). Let r = j - -5/6. Factor 5/3*v**2 - 8/3*v + 4/3 - r*v**3.
-(v - 2)**2*(v - 1)/3
Let h(n) be the third derivative of n**5/20 + 3*n**4/2 + 18*n**3 + 4*n**2. Suppose h(b) = 0. Calculate b.
-6
Factor -8/5 - 14/5*b - 4/5*b**2 + 2/5*b**3.
2*(b - 4)*(b + 1)**2/5
Suppose -15 = -3*d - 2*d. Suppose 0*a + 6 = d*a. Find v such that 2 + 4*v**4 - 2*v**5 - 4*v**a + 0*v**5 + 2*v - 2 = 0.
-1, 0, 1
Suppose 1 - 7 = -3*d. Let w(r) be the first derivative of r**d - 1/3*r**3 + 2 - r. Factor w(x).
-(x - 1)**2
Let c(n) be the second derivative of 0*n**2 + 3*n + 0*n**3 - 1/48*n**4 - 1/80*n**5 + 0. Suppose c(f) = 0. What is f?
-1, 0
Let r(l) be the first derivative of 2*l**3/15 + 2*l**2/5 - 7. Factor r(n).
2*n*(n + 2)/5
Factor 4 - 8*c**3 - 8*c**4 + 4*c**4 + 2*c + 6*c.
-4*(c - 1)*(c + 1)**3
Let a(c) be the third derivative of -c**6/120 + c**5/30 - c**4/24 - 8*c**2. Factor a(b).
-b*(b - 1)**2
Suppose 0 = w + 2 - 5. Suppose -6*o = -w*o - 12. Factor -3/5*p**o + 3/5*p**2 + 0 - 3/5*p**3 + 3/5*p.
-3*p*(p - 1)*(p + 1)**2/5
Solve -96 - 44 - 53 - 7 + 40*b - 2*b**2 = 0 for b.
10
What is b in -3 + 3*b - 3/4*b**4 + 9/4*b**2 - 3/2*b**3 = 0?
-2, 1
Let p(i) be the second derivative of 1/15*i**4 - i + 1/15*i**3 + 0 + 0*i**2 + 1/50*i**5. Factor p(k).
2*k*(k + 1)**2/5
Let l(a) = a**2 + a + 1. Let w(t) be the second derivative of -t**4/4 + t**3/6 - 2*t**2 - t. Let c(b) = 2*l(b) + w(b). Let c(f) = 0. Calculate f.
1, 2
Let l be 0/(-5)*(-1)/2. Suppose q - 3*d + 1 = -l, 0 = -5*q - d + 11. Factor 4*j**3 - 4*j**q + 5*j**3 + j**3.
2*j**2*(5*j - 2)
Let v = -20 - -41/2. Let y = -180 - -184. Factor -1/6*s**y - 1/2*s**2 - 1/6*s + 0 - v*s**3.
-s*(s + 1)**3/6
Let f(o) be the second derivative of -5*o**4/18 - 25*o**3/18 + 5*o**2/2 - 5*o. Suppose f(a) = 0. What is a?
-3, 1/2
Let o be -2 + 5 + -2 + -1. Let u(p) be the first derivative of o*p - 1/24*p**6 + 1/16*p**4 + 1 - 1/12*p**3 + 1/20*p**5 + 0*p**2. Suppose u(w) = 0. Calculate w.
-1, 0, 1
Suppose 0 = 5*b - 2*b - 36. Suppose 4*i = 8*i - b. Factor 13/3*y**i + 5*y**2 + 4/3*y**4 + 1/3 + 7/3*y.
(y + 1)**3*(4*y + 1)/3
Let t(b) be the third derivative of b**8/84 - 4*b**7/35 + 2*b**6/15 + 2*b**5/5 - 5*b**4/6 - b**2 - 2*b. Factor t(x).
4*x*(x - 5)*(x - 1)**2*(x + 1)
Suppose f + 17 = -5*s, 5 = 4*s + 21. Factor -6*w - w**2 + w**2 + 8*w**f + 2.
2*(w + 1)*(2*w - 1)**2
Let f(w) = 2*w**2 - 2. Let r be f(1). Suppose r*l = 3*o + 2*l - 14, 5*o - 3*l = -2. Solve 2/5*j**5 + 0 - 2/5*j + 4/5*j**4 - 4/5*j**o + 0*j**3 = 0.
-1, 0, 1
Factor -35 - 7*c**3 + c**3 + 2*c**5 - 14*c - 4*c**4 + 2*c**3 + 16*c**2 + 39.
2*(c - 1)**4*(c + 2)
Let g = 0 - -4. Suppose 0 = -f + g - 2. Factor 0*c + f*c**2 - 1 - c**4 + 0*c.
-(c - 1)**2*(c + 1)**2
Let h = -132817/30 - -13156/3. Let u = h - -572/5. Factor 49/2*c**5 