e the second derivative of 3/10*s**6 + 0 - 4/5*s**5 + 1/2*s**2 - 2*s - 1/21*s**7 - s**3 + 7/6*s**4. Factor y(w).
-(w - 1)**4*(2*w - 1)
Let a be -4*3*((-424)/(-108) + -4). Factor 2/9 + 2/9*d**4 + 4/3*d**2 + 8/9*d + a*d**3.
2*(d + 1)**4/9
Factor 5/2*a + 1/2*a**5 + 5*a**2 + 5*a**3 + 1/2 + 5/2*a**4.
(a + 1)**5/2
Let m(a) be the first derivative of -15/4*a**4 - 2 + 7*a**3 + 0*a - 12/5*a**5 + 3*a**2. Suppose m(p) = 0. Calculate p.
-2, -1/4, 0, 1
Let s(j) be the first derivative of -j**5/15 - j**4/6 + j**2/3 + j/3 + 7. Factor s(r).
-(r - 1)*(r + 1)**3/3
Let i(f) be the second derivative of 1/10*f**2 - 3*f - 1/15*f**3 + 0 + 1/60*f**4. Find t such that i(t) = 0.
1
Let t(i) be the second derivative of i**7/70 + i**6/40 + 2*i**2 + 2*i. Let q(n) be the first derivative of t(n). Determine h, given that q(h) = 0.
-1, 0
Let q(r) = -8*r + 14. Let x(w) = w - 1. Let i(z) = -q(z) - 6*x(z). Let s be i(5). Factor 0 + 3*k - 9/2*k**s + 3/2*k**3.
3*k*(k - 2)*(k - 1)/2
Let u(w) be the second derivative of 0*w**3 + 0 - 1/11*w**2 - 1/165*w**6 + 3*w + 0*w**5 + 1/33*w**4. Find b such that u(b) = 0.
-1, 1
Let p(m) be the third derivative of m**7/630 - m**6/72 + m**5/20 - 7*m**4/72 + m**3/9 - 8*m**2 + 2. What is z in p(z) = 0?
1, 2
Suppose 5*g = -o + 27, 0 = -10*o + 7*o - g + 11. Factor -2/9*t**5 + 2/9*t**3 + 0*t - 2/9*t**4 + 0 + 2/9*t**o.
-2*t**2*(t - 1)*(t + 1)**2/9
Let p(k) be the second derivative of -k**7/56 + k**6/15 + 3*k**5/16 + k**4/12 + 5*k. Let p(r) = 0. Calculate r.
-1, -1/3, 0, 4
Let q be 14/(-12)*(-18)/126. Factor 1/2*j**2 + 1/2*j + 1/6 + q*j**3.
(j + 1)**3/6
Factor 3*u**3 + 43*u - 4*u**3 - 34*u.
-u*(u - 3)*(u + 3)
Let f(i) = 10*i**4 - 24*i**3 + 59*i**2 - 79*i + 20. Let n(a) = -3*a**4 + 8*a**3 - 20*a**2 + 26*a - 7. Let m(s) = 2*f(s) + 7*n(s). Factor m(y).
-(y - 3)**2*(y - 1)**2
Suppose -2*v - 2 = 2*u, v + 3*u = -0*v - 9. Let i(h) be the first derivative of -h + 1 + h**2 - 1/3*h**v. Factor i(d).
-(d - 1)**2
Let k(b) be the first derivative of 2*b**3/15 - b**2 - 12*b/5 - 33. Factor k(w).
2*(w - 6)*(w + 1)/5
Suppose -5*r**5 - 16/5*r - 24/5*r**3 + 0 + 16*r**4 - 64/5*r**2 = 0. What is r?
-2/5, 0, 2
Let l = -427/195 - -34/15. Let p = 11/26 + l. Determine s, given that s**2 - 1/2*s**5 + s**3 - 1/2*s**4 - p*s - 1/2 = 0.
-1, 1
Let c(t) be the third derivative of -1/28*t**8 - 3/70*t**7 + 1/40*t**6 + 0*t**5 - 3*t**2 + 0 + 0*t + 0*t**4 + 0*t**3. Let c(i) = 0. What is i?
-1, 0, 1/4
Let f(n) be the second derivative of -n**9/1008 + n**8/280 - n**7/280 + n**3/6 + n. Let b(h) be the second derivative of f(h). Factor b(w).
-3*w**3*(w - 1)**2
Let q be -3*(-4)/(-18) + (-21 - -22). Factor 2/3 + q*m**4 + 3*m**2 + 7/3*m + 5/3*m**3.
(m + 1)**3*(m + 2)/3
Let q(i) = -9*i**2 + 12*i - 3. Let w(r) be the second derivative of -3*r**4/2 + 4*r**3 - 3*r**2 - 2*r. Let m(n) = -13*q(n) + 6*w(n). Factor m(k).
3*(k - 1)*(3*k - 1)
Let c be 1/1*(29 - -5). Let u = 137/4 - c. Suppose 1/4*g - u*g**2 + 1/4*g**4 - 1/4*g**3 + 0 = 0. Calculate g.
-1, 0, 1
Let a(l) = -6*l - 6. Let z be a(-7). Let s be (-4)/14 - z/(-77). Factor -s - 4/11*o - 2/11*o**2.
-2*(o + 1)**2/11
Let q(n) be the second derivative of n**5/50 - n**4/10 + 2*n**3/15 - 3*n. Factor q(x).
2*x*(x - 2)*(x - 1)/5
Let d(o) = 2*o**2 + 2*o - 1. Let a be d(1). Let j = 1 - -1. Solve -4*r**3 + r - j*r**3 + 5*r**a = 0 for r.
-1, 0, 1
Let x(v) be the third derivative of v**6/180 + v**5/90 - v**4/36 - v**3/9 + 7*v**2. Determine n so that x(n) = 0.
-1, 1
Let a(l) be the first derivative of 5*l**4/4 + 10*l**3/3 - 5*l**2/2 - 10*l - 2. Factor a(v).
5*(v - 1)*(v + 1)*(v + 2)
Let s = -8 + 4. Let j be 3 - ((s - -3) + 1). Factor 2 - j + 4*p - p**2 - 3.
-(p - 2)**2
Suppose -2 - 34 = -3*m. Solve 6*j**2 - 6*j**4 + 3*j - 6*j + 0*j**2 + m*j**3 - 3*j**5 - 6*j**5 = 0.
-1, 0, 1/3, 1
Let g = 1026/3419 - -2/263. Solve -g*u + 6/13*u**3 - 14/13*u**4 + 0 + 6/13*u**5 + 6/13*u**2 = 0.
-2/3, 0, 1
Let p(o) be the third derivative of -5*o**8/336 + o**6/6 - 15*o**2. Factor p(h).
-5*h**3*(h - 2)*(h + 2)
Let p = -246 - -7381/30. Let m(v) be the third derivative of 0 - p*v**5 + 0*v**3 + 0*v**4 + 0*v + v**2. Factor m(y).
-2*y**2
Let i be (0 - 0)/((-8)/8). Suppose 2*s = 3*u - i*u - 1, -u = -s + 1. Factor -7/5*c + 8/5*c**s - 6/5*c**2 - 2/5 + 4/5*c**3 + 3/5*c**5.
(c - 1)*(c + 1)**3*(3*c + 2)/5
Let c = -23 - -23. Suppose 2/5*r**4 - 2/5*r**3 - 2/5*r**2 + 2/5*r + c = 0. Calculate r.
-1, 0, 1
Suppose -20 = 2*j - 7*j. Suppose -j*l + 11 = 3. Solve -2/9*n**l + 2/9*n + 0 = 0 for n.
0, 1
Let h = 5 + 16. Let n = h + -19. Find w, given that 0 - 2/9*w**4 + 0*w**n + 2/9*w**3 + 0*w = 0.
0, 1
Factor -1/7*p**2 + 1/7*p + 0.
-p*(p - 1)/7
Let o(c) be the third derivative of c**5/360 - c**3/36 + 8*c**2. Factor o(n).
(n - 1)*(n + 1)/6
Let u(a) be the second derivative of 0*a**2 + 8/105*a**6 + 1/7*a**4 + 2*a - 1/21*a**3 + 0 - 6/35*a**5. Factor u(k).
2*k*(2*k - 1)**3/7
Let f(t) be the third derivative of t**8/20160 - t**7/1680 - t**5/10 - 11*t**2. Let l(v) be the third derivative of f(v). Factor l(b).
b*(b - 3)
Let g(l) be the first derivative of l**4/24 + l**3/4 + l**2/2 - l + 3. Let j(z) be the first derivative of g(z). Let j(h) = 0. What is h?
-2, -1
Let z(h) be the first derivative of -h**5/90 + 3*h + 1. Let s(u) be the first derivative of z(u). Suppose s(q) = 0. What is q?
0
Suppose 9*l = 6*l + 18. Let h(q) be the third derivative of 1/420*q**l + 2*q**2 + 0*q**5 + 0 - 1/84*q**4 + 0*q + 0*q**3. Factor h(m).
2*m*(m - 1)*(m + 1)/7
Let z = 0 - -1. Let y = z + 2. Solve 5*v**2 + 1 + v**4 + 7*v**y + v**2 - 3*v**3 + 4*v = 0 for v.
-1
Solve -1 + 1 + 4 - n + 2*n**2 - 5 = 0.
-1/2, 1
Suppose -h - 4*b = 2*h - 12, 5*h = -3*b + 9. Let v = -1 + 3. What is w in -w - 5*w**2 + 6*w**v + h*w**2 = 0?
0, 1
Let a(v) be the third derivative of -v**6/120 + v**5/60 - v**4/24 + v**3/2 + v**2. Let p be a(0). Factor 0*k - k**p + 1/3*k**2 + 0 - 1/3*k**5 + k**4.
-k**2*(k - 1)**3/3
Let t = 1049/12 - 1231/14. Let o = 5/21 - t. Solve o*u**4 - 2*u**3 + 0*u + 3/2*u**2 - 1/4 = 0.
-1/3, 1
Let -3/4*h**2 + 0 + 9/4*h = 0. Calculate h.
0, 3
Factor 24/5*r**2 + 8/5*r**3 + 32/5*r + 1/5*r**4 + 16/5.
(r + 2)**4/5
Let c = 16 + -14. Suppose 0 = -0*m + c*m. Let m + 1/2*f + 1/2*f**2 = 0. Calculate f.
-1, 0
Let u(j) be the first derivative of j**6/12 + j**5/2 + 9*j**4/8 + 7*j**3/6 + j**2/2 - 20. Factor u(n).
n*(n + 1)**3*(n + 2)/2
Factor 0 - 1/5*u**2 - 1/5*u.
-u*(u + 1)/5
Let d = -381 + 3431/9. What is u in -2/9*u + 0 - d*u**2 = 0?
-1, 0
What is a in -5*a**2 - 5*a**3 + 5*a - 16 + 11 + 10 = 0?
-1, 1
Suppose 4*o**2 - o**2 + 541*o - 538*o = 0. Calculate o.
-1, 0
Let c = 12 + -6. Find s, given that -5*s**4 + 3*s**2 - 4*s**4 + c*s**2 - s**5 - 3*s**3 + 6*s - 2*s**5 = 0.
-2, -1, 0, 1
Let s(u) = u**2 - 4*u + 6. Let g be s(2). Factor 2/5*w**4 + 8/5*w**3 + 4/5*w + 2*w**g + 0.
2*w*(w + 1)**2*(w + 2)/5
Factor 280*c**2 - 300*c**2 + 39*c - 14*c - 5*c**3.
-5*c*(c - 1)*(c + 5)
Let o = -112 - -115. Determine a so that -3*a**2 + 3/2*a + 3/2 + 3/2*a**4 + 3/2*a**5 - 3*a**o = 0.
-1, 1
Let v(u) be the first derivative of 3*u**6/10 + 12*u**5/25 - u**4/4 - 4*u**3/5 - 2*u**2/5 - 3. Determine a so that v(a) = 0.
-1, -2/3, 0, 1
Let k(i) = -8*i**2 - 10*i + 4. Let u(z) = -z. Let l(t) = -k(t) + 6*u(t). Determine m, given that l(m) = 0.
-1, 1/2
Solve -10/13*n**2 + 0 - 4/13*n = 0 for n.
-2/5, 0
Let o be (-2 + -8)*1/(-2). What is s in -3*s + 2*s**3 - 2*s + 2*s + 0*s - 3*s**4 + s**o + 2*s**2 + 1 = 0?
-1, 1
Suppose x**2 - 2*x + 2*x**3 + x**4 + 2*x + 0*x**4 = 0. Calculate x.
-1, 0
Let s(i) = 100*i**2 + 45*i - 55. Let l(m) = 11*m**2 + 5*m - 6. Let f(n) = 55*l(n) - 6*s(n). Factor f(o).
5*o*(o + 1)
Let d(a) = -a + 2. Let m be d(-2). Suppose 6 - 26 = -m*k. Factor -3*r + k*r - 2*r**2 + 0*r**2.
-2*r*(r - 1)
Factor 5*v - 7*v - 4*v - 3*v**2.
-3*v*(v + 2)
Suppose -8*y = -12*y. Let v(b) be the first derivative of 1/2*b**4 - 2/3*b**3 + 2/5*b**5 + y*b + 1 - b**2. Solve v(a) = 0 for a.
-1, 0, 1
Suppose i**2 + 5*i**2 - 6*i + 3*i - 3*i**4 + 3*i**3 + 3*i**2 - 6 = 0. Calculate i.
-1, 1, 2
Let o be (-8)/(-3) + (-2)/(-6). Factor -4 - 5*n + 2*n + 4 - o*n**2.
-3*n*(n + 1)
Let o(c) be the second derivative of c**5/390 - c**4/26 + 3*c**3/13 - 3*c**2/2 - 2*c. Let a(j) be the first derivative of o(j). Suppose a(r) = 0. Calculate r.
3
Suppose 12*k - 16*k = 0. Let -1/6*x**2 - 1/3*x + k = 0. Calculate x.
-2, 0
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