 + 3/5*k**2 + c = 0.
0, 1
Let y(z) be the first derivative of -8*z + 6*z - z - 13*z + 25*z**4 - 60*z**3 - 3 + 48*z**2. Factor y(h).
4*(h - 1)*(5*h - 2)**2
Let h(t) = t**2 + 5*t - 2. Suppose -p = 5 + 1. Let g be h(p). What is w in -3*w**5 - w**4 - 2*w**3 + 4*w**g + 9*w**3 - w**3 = 0?
-1, 0, 2
Let h(u) be the third derivative of u**6/120 - u**5/30 - 5*u**4/24 + u**3 - 20*u**2. Factor h(w).
(w - 3)*(w - 1)*(w + 2)
Factor 0*j - 10*j**4 + 0 + 0*j**2 + 5/2*j**5 + 10*j**3.
5*j**3*(j - 2)**2/2
Let u(p) be the third derivative of p**6/30 + 4*p**5/15 + 5*p**4/6 + 4*p**3/3 + 4*p**2. Determine c so that u(c) = 0.
-2, -1
Let y(d) = d**2. Let v(x) = 12*x**2 + 33*x - 6. Let a(c) = -v(c) - 6*y(c). Find u such that a(u) = 0.
-2, 1/6
Suppose -3*i = -5*i + 6. Suppose -3 = -4*d + i*d. Factor 2*q**4 + 4*q**2 - 3*q**3 - 2*q**2 - q**d.
2*q**2*(q - 1)**2
Let z be 9/(2 + 1) + -1. Suppose 0*h**2 - 2*h**z + 5*h**2 + 2*h**3 + 2*h + h**2 = 0. What is h?
-1, 0
Let n(a) be the first derivative of 7*a**4/22 + 6*a**3/11 + 2*a**2/11 + 5. Factor n(o).
2*o*(o + 1)*(7*o + 2)/11
Let a(y) be the first derivative of y**5/55 - y**4/11 - 37. Factor a(o).
o**3*(o - 4)/11
Find i such that -1/3*i**4 - 1/3 - 2*i**2 - 4/3*i - 4/3*i**3 = 0.
-1
Factor -m**4 - 2*m**4 + 36*m**2 + 54*m**3 - 54*m**3 - 48*m.
-3*m*(m - 2)**2*(m + 4)
Let s(w) be the third derivative of w**8/13440 + w**7/2520 + w**6/1440 - w**4/6 + 8*w**2. Let y(j) be the second derivative of s(j). Let y(n) = 0. What is n?
-1, 0
Suppose -4*d + 4 = f - 5*d, 0 = 5*f + 5*d - 30. Suppose 21*g = 22*g. Factor 2*v**3 + g + 1/3*v**f - 4/3*v**2 + 1/3*v - 4/3*v**4.
v*(v - 1)**4/3
Let a(g) = -g**2 + 5*g + 16. Let b be a(7). Let o be ((-48)/(-30))/(b/5). Factor 1 - 5/2*n**3 - o*n**2 - 1/2*n.
-(n + 1)**2*(5*n - 2)/2
Suppose -2*a + 0*a = -18. Let i be -3*(-6)/a - -1. What is u in -46*u**3 - 40*u + 20*u**i - 34*u**3 - 13*u**4 - 74*u**2 - 5*u**4 - 8 = 0?
-1, -2/3
Let t be (-3)/2*20/(-6). Suppose -l + t*c = -16 - 9, -4*c = 2*l + 20. Factor -6/5*h**5 + 0 + l*h**2 + 0*h + 2/5*h**3 + 4/5*h**4.
-2*h**3*(h - 1)*(3*h + 1)/5
Let g(p) = -6*p + 22*p + 6 + 18 - 3 + 6*p**2. Let z(n) = n**2 + 3*n + 4. Let v = 6 + -8. Let h(l) = v*g(l) + 11*z(l). Factor h(q).
-(q - 2)*(q + 1)
Let l be 1/2 - (-9 + 9). Let m(w) be the first derivative of -1/6*w**3 + l*w + 0*w**2 - 2. Factor m(r).
-(r - 1)*(r + 1)/2
Let q(j) be the first derivative of 2*j**3/3 + 2*j**2 - 4. Factor q(s).
2*s*(s + 2)
Find i, given that 4*i**4 - 4*i**3 - 12*i**2 + 7*i**2 - 3*i**2 + 2 + 2*i + 2*i**5 + 2 = 0.
-2, -1, 1
Let n(p) be the third derivative of p**6/90 - p**5/10 + p**4/3 + 2*p**3/3 - 8*p**2. Let y(z) be the first derivative of n(z). Determine i, given that y(i) = 0.
1, 2
Suppose f + 21 = 2*y + 4*f, -3*y = 3*f - 24. Let -3*w**4 + 7*w**y - 19*w**2 + 5*w**3 + 7*w**2 = 0. What is w?
0, 2
Let k = 5/1322 - 1241383/6610. Let y = -187 - k. Solve -2/5 - 2/5*w**2 + y*w = 0 for w.
1
Let n be ((-7)/(-2) - 4)*-12. Let j be (n/84)/(2/7). Determine d so that -j*d**5 + 0 + 3/2*d**4 + 3*d**2 - 13/4*d**3 - d = 0.
0, 1, 2
Let k be (1 - 0) + 0 + -2. Let y be 1 - k/(-14)*-2. Determine g so that y + 8/7*g + 2/7*g**2 = 0.
-2
Let h be (-1)/((3/1)/(-3)). Factor -43*n**2 - 44*n**3 + 23*n**5 + 117*n**3 + 11*n - 7*n**5 - 56*n**4 - h.
(n - 1)**3*(4*n - 1)**2
Let i(a) = -2*a + 4*a**4 + 2*a**2 + 3*a - 7*a + 4*a**3 - 2. Let w(r) = -9*r**4 - 8*r**3 - 5*r**2 + 13*r + 4. Let k(d) = 5*i(d) + 2*w(d). What is t in k(t) = 0?
-1, 1
Let a be -2 - -4 - (-6)/(-9). Factor 2/3*m + 0 + 5/3*m**2 + 1/3*m**4 + a*m**3.
m*(m + 1)**2*(m + 2)/3
Factor 0 + 2/3*w + 2/3*w**3 + 4/3*w**2.
2*w*(w + 1)**2/3
Let t(x) = -x**3 + 3*x**2 + x - 1. Let g be t(3). Let q be (-5 - -3)/(g + -6). Find k, given that -q*k**2 - 1/2 - k = 0.
-1
Suppose 2 = 5*g - 13. Determine n, given that -4*n**3 + 0*n**3 + n**3 + n**g + 2*n**2 = 0.
0, 1
Suppose -6*x**2 - 49*x**3 + 19*x**3 + 21*x + 6 + 9*x**3 = 0. What is x?
-1, -2/7, 1
Let r be 2 + 2 + (-12)/(-4). Find m, given that -r*m**5 - 4*m - 16*m**4 - 16*m**3 + 2*m**5 - 16*m**2 - 8*m**3 + m**5 = 0.
-1, 0
Let b = 3 - -1. Let c(r) = 2*r**3 - 2*r**4 + 0*r**b + 0*r**4 - 4*r. Let k(y) = y**5 - y**4 - y**3 - y. Let v(m) = -c(m) + 2*k(m). Factor v(o).
2*o*(o - 1)**2*(o + 1)**2
Let b(n) be the second derivative of -n - 1/12*n**3 + 0 + 0*n**2 - 1/12*n**4 + 0*n**5 + 1/84*n**7 + 1/30*n**6. Find i, given that b(i) = 0.
-1, 0, 1
Let p = -198 - -198. Factor 0 - 1/2*u**2 + p*u + 1/2*u**3.
u**2*(u - 1)/2
Let a(p) be the first derivative of p**4/6 - 4*p**3/9 - 4*p**2/3 + 16*p/3 + 7. Suppose a(w) = 0. What is w?
-2, 2
Let k(p) = -13*p - p**3 - 4 - p**3 + 6*p**2 + 5*p. Let m be -4 + (2 - 4) + 3. Let i(d) = 2*d**3 - 6*d**2 + 7*d + 3. Let a(l) = m*k(l) - 4*i(l). Factor a(o).
-2*o*(o - 2)*(o - 1)
Suppose 4*r = 3*m + 39, -m + 6*m = -2*r + 39. Suppose -2*n = 2*n - r. Factor 3*o**5 + n*o**5 - 2*o**4 - o**5 - 3*o**5.
2*o**4*(o - 1)
Let w(j) = -3*j**5 + 18*j**4 - 33*j**3 + 27*j**2 - 18*j + 3. Let v(o) = o**4 - o**3 - o**2 - o. Let y(i) = -3*v(i) + w(i). Factor y(u).
-3*(u - 1)**5
Let u(q) = q**4 - 9*q**3 + 18*q**2 - 8*q - 3. Let c(p) = 4*p**4 - 37*p**3 + 74*p**2 - 32*p - 13. Let j(v) = -6*c(v) + 26*u(v). Solve j(b) = 0 for b.
0, 2
Let 4/15*l**3 + 0 + 6/5*l**4 + 8/15*l**5 + 0*l**2 + 0*l = 0. What is l?
-2, -1/4, 0
Suppose -6*r = -2*r. Let j(c) be the second derivative of 0 - 1/3*c**3 + r*c**2 - 1/6*c**4 - 2*c. Factor j(w).
-2*w*(w + 1)
Suppose 0 = -0*m - 2*m. Let d(u) be the third derivative of m*u**4 + 0*u**5 + 1/60*u**6 + 1/168*u**8 + 0 + u**2 + 0*u**3 + 2/105*u**7 + 0*u. Factor d(s).
2*s**3*(s + 1)**2
Let k(w) be the third derivative of -w**6/540 - 4*w**5/135 - 13*w**4/108 - 2*w**3/9 + 25*w**2. Determine a so that k(a) = 0.
-6, -1
Let y be (44/264 - 1*3) + 3. Suppose 1/6*t**4 + 0*t - y*t**2 + 0*t**3 + 0 = 0. What is t?
-1, 0, 1
Let w(d) be the third derivative of -d**9/30240 - d**8/13440 - d**4/12 + 4*d**2. Let a(q) be the second derivative of w(q). Factor a(r).
-r**3*(r + 1)/2
Let h(v) be the third derivative of -1/12*v**4 + 0*v**3 + 1/120*v**6 + 0*v + 1/60*v**5 + 0 - 6*v**2. Factor h(o).
o*(o - 1)*(o + 2)
Suppose 3*a - 45 = -33. Factor 0 - 3/2*u**3 + 3/4*u**5 + 0*u**2 + 0*u**a + 3/4*u.
3*u*(u - 1)**2*(u + 1)**2/4
Let r(s) be the third derivative of 0*s**6 + 0*s**5 + 0 - 1/1050*s**7 - 1/1680*s**8 + 0*s**4 + 0*s**3 + 0*s - s**2. Solve r(z) = 0.
-1, 0
Let p(f) be the third derivative of -2/33*f**3 + 0 + 3*f**2 + 1/132*f**4 + 0*f + 1/165*f**5 - 1/660*f**6. Let p(z) = 0. What is z?
-1, 1, 2
Let t(m) = 3*m**5 - 9*m. Let j(g) = -2*g**4 + g**3 + g. Let h(l) = -l**4 + l**3 - l**2. Let w(v) = -h(v) + j(v). Let n(o) = t(o) + 6*w(o). Solve n(y) = 0 for y.
-1, 0, 1
Let x(i) = -15*i - 86. Let k be x(-6). Suppose -25/4*f**k + 21/4*f**2 + 1 + 5*f**3 - 5*f = 0. What is f?
-1, 2/5, 1
Let k be (-8)/42*6/(-4). Let x(t) = t - 1. Let n be x(1). Find f, given that k*f**2 + n*f - 2/7 = 0.
-1, 1
Let n = 159 + -159. Suppose -2/7*d**3 - 4/7*d**4 + n*d**2 + 0 + 0*d - 2/7*d**5 = 0. Calculate d.
-1, 0
Let z(f) be the third derivative of f**5/30 + f**4/4 + f**2. Factor z(m).
2*m*(m + 3)
Let p = -13 - -11. Let m be (-5)/15*p/2. Factor -1/3*w**2 - m - 2/3*w.
-(w + 1)**2/3
Let w = -5 - -7. Factor -4 - 3 - 12*z + 4 - 12*z**w.
-3*(2*z + 1)**2
Let n(h) be the second derivative of h**6/55 - 7*h**5/110 + h**4/33 - 21*h. Let n(c) = 0. What is c?
0, 1/3, 2
Factor 1/3*u**4 - 4/3*u + 1/3 + 2*u**2 - 4/3*u**3.
(u - 1)**4/3
Let l be -2*5/5*(-2)/8. Let w(a) be the second derivative of -l*a**5 - a - 11/20*a**4 + 0*a**3 + 0 + 2/5*a**2 - 7/50*a**6. Solve w(d) = 0 for d.
-1, -2/3, 2/7
Let q(s) = 3*s**4 - 6*s**3 + 3*s**2 - 12*s + 6. Let k(a) = -4*a**4 + 7*a**3 - 2*a**2 + 13*a - 7. Let n(d) = 6*k(d) + 7*q(d). Find u such that n(u) = 0.
-2, 0, 1
Let x(n) be the second derivative of -2*n - 1/12*n**4 + 0*n**3 + 1/30*n**6 - 1/42*n**7 + 0*n**2 + 1/20*n**5 + 0. Factor x(s).
-s**2*(s - 1)**2*(s + 1)
Let u(y) be the first derivative of -4*y**5/5 + y**4 + 4*y**3 - 2*y**2 - 8*y - 17. What is i in u(i) = 0?
-1, 1, 2
Factor 3*c**2 + 135*c - 131*c - 2*c**4 + 3*c**2.
-2*c*(c - 2)*(c + 1)**2
Let m be (-2 + 2)*(2 - (2 + 1)). Let w(q) be the third derivative of m*q**4 + 1/30*q**6 - 1/105*q**7 - 1/30*q**5 + 0 + 2*q**2 + 0*q + 0*q**3. Factor w(r).
-2*r**2*(r - 1)**2
Let f(j) be the third derivative of -j**6/200 + 