 - 29/12*k**4 - 1/2*k**3. Find y such that u(y) = 0.
-1, -2/7, 1/4, 1
Let b(n) = -12*n**2 + 4*n + 2. Let l(m) = 61*m**2 - 19*m - 9. Let y(o) = -11*b(o) - 2*l(o). Factor y(c).
2*(c - 1)*(5*c + 2)
Let z(c) be the third derivative of -c**7/1680 + c**5/240 - c**3/48 - 4*c**2. Suppose z(g) = 0. Calculate g.
-1, 1
Let q(a) = a**3 + 9*a**2 + a + 11. Let c be q(-9). Factor 2*y**c + 4/3*y**3 + 0 + 2/3*y.
2*y*(y + 1)*(2*y + 1)/3
Let f(j) be the third derivative of j**5/45 - 2*j**4/9 + 2*j**3/3 - 3*j**2. Determine l, given that f(l) = 0.
1, 3
Factor -98*d**4 - 60*d**3 + 5*d - 28*d**5 + 22*d**4 - 4*d**2 + 3*d.
-4*d*(d + 1)**3*(7*d - 2)
Factor 0*a**2 + 0*a + 0 - 3/2*a**3 + 6*a**4 - 6*a**5.
-3*a**3*(2*a - 1)**2/2
Let l = 7 + -2. Suppose 3*h = 2*h + l. Factor -3*t**3 + h*t**4 + 5*t**3 - 4*t**4.
t**3*(t + 2)
Let f(a) be the second derivative of -a**5/150 - a**4/10 - 3*a**3/5 + 3*a**2 - 9*a. Let h(z) be the first derivative of f(z). Suppose h(q) = 0. Calculate q.
-3
Factor -4*a + 8 - 8*a + 19 + 4*a**2 - 19.
4*(a - 2)*(a - 1)
Solve 0 - 1/5*m**3 - 2/5*m**2 + 8/5*m = 0.
-4, 0, 2
Let a(f) be the second derivative of -f**6/6 - f**5 + 5*f**4/4 + 15*f**3 + 29*f. Factor a(b).
-5*b*(b - 2)*(b + 3)**2
Let d(k) be the first derivative of 2*k**2 + 2 - 2*k - 2/3*k**3. Factor d(u).
-2*(u - 1)**2
Suppose -6*g + 8 = -40. Suppose -2*i = 4*j + g, -3*i + 4*i = j + 8. Let -9/2*r**3 - 3/2*r**5 + 0 - 3/2*r**2 + 0*r - 9/2*r**i = 0. What is r?
-1, 0
Suppose 4*g - 6 - 10 = 0. Suppose -3*y + g = -5. Solve 1/3*c - 1/3*c**y + 0*c**2 + 0 = 0.
-1, 0, 1
Factor 16*s**5 + 18*s**4 + s - 5*s**3 + 6*s**3 + 6*s**4 - 6*s**2.
s*(s + 1)**2*(4*s - 1)**2
Let y(r) be the first derivative of r**6/4 - 6*r**5/5 + 3*r**4/2 + 12. Factor y(i).
3*i**3*(i - 2)**2/2
Let u(j) be the third derivative of 1/270*j**6 + 0*j + 0 - 1/54*j**4 - 1/945*j**7 + 1/27*j**3 + 0*j**5 - 3*j**2. Solve u(l) = 0.
-1, 1
Let t(q) = q - 1. Let p be t(6). Suppose 2*f + 2*f = 2*d - 12, 5*f + p = 0. Factor 2/9*m**d - 8/9*m**3 + 2/9 + 4/3*m**2 - 8/9*m.
2*(m - 1)**4/9
Let z(m) be the second derivative of -m**6/1080 + m**5/180 - m**3/3 - m. Let s(o) be the second derivative of z(o). Factor s(v).
-v*(v - 2)/3
Let r(u) = 11*u**5 + 16*u**4 + 14*u**3 - u**2 - 5*u + 5. Let y(v) = -17*v**5 - 24*v**4 - 21*v**3 + 2*v**2 + 8*v - 8. Let s(o) = -8*r(o) - 5*y(o). Factor s(g).
-g**2*(g + 1)**2*(3*g + 2)
Let n(g) be the third derivative of -1/30*g**5 + 0*g**3 + 0 - 1/96*g**4 + 1/84*g**8 - 1/32*g**6 + 1/105*g**7 + 0*g + 5*g**2. Suppose n(x) = 0. Calculate x.
-1, -1/4, 0, 1
Suppose 3 + 3 = u. Suppose -4*k + u*q - 2*q = 0, -2*q + 6 = k. Factor -3*m**5 + m**3 + m**5 + m**5 - k*m**3 - 2*m**4.
-m**3*(m + 1)**2
Factor 33/5*u + 9/5*u**2 + 18/5.
3*(u + 3)*(3*u + 2)/5
Let w(r) be the second derivative of 0 + 1/4*r**4 - 1/20*r**5 - 1/2*r**3 + 1/2*r**2 - 5*r. What is d in w(d) = 0?
1
Let f(c) be the first derivative of c**4 - 4*c**3 + 6*c**2 - 4*c - 3. Factor f(k).
4*(k - 1)**3
Let s(g) = -g**3 + 2*g**2 + 5*g + 2. Let r(j) = -2*j**3 + 4*j**2 + 11*j + 5. Let h(x) = 4*r(x) - 9*s(x). Determine z so that h(z) = 0.
-1, 1, 2
Let n(v) be the second derivative of 2*v**6/15 - 3*v**5/5 + v**4/3 + 2*v**3 - 4*v**2 + v - 9. Determine q, given that n(q) = 0.
-1, 1, 2
Let q(t) be the second derivative of -3*t**7/70 - t**6/10 - t**5/20 - 5*t**2/2 - 4*t. Let c(n) be the first derivative of q(n). Factor c(j).
-3*j**2*(j + 1)*(3*j + 1)
Let t(w) be the first derivative of 2*w**5/35 + 3*w**4/14 + 2*w**3/21 - 3*w**2/7 - 4*w/7 - 8. Find i, given that t(i) = 0.
-2, -1, 1
Let g(x) be the second derivative of -x**7/168 - x**6/120 + 11*x. Find i such that g(i) = 0.
-1, 0
Let p(m) = m**2. Suppose 0 = -q + 2*n + 3 - 8, -3*q - n - 15 = 0. Let w(a) = -6*a**2. Let c(u) = q*p(u) - w(u). Factor c(x).
x**2
Suppose -13*j - 6 = -15*j. What is m in 9 - 3*m**j + 2*m**2 - 9 + m**2 = 0?
0, 1
Suppose 0 = 3*c - 17*c + 42. Suppose -1/6*n**c + 0*n + 0*n**2 + 0 = 0. Calculate n.
0
Let k be (-40)/2*(-6)/15. Find o such that 4*o**3 + 2*o**4 - 6*o**2 + 0*o**2 + 8 - k*o + 0 + 0 = 0.
-2, 1
Factor 2*h**4 - 24/7*h**3 + 4/7*h + 0 + 6/7*h**2.
2*h*(h - 1)**2*(7*h + 2)/7
Factor -24*x**2 + 3/4*x**5 - 6*x**4 + 0 + 18*x**3 + 12*x.
3*x*(x - 2)**4/4
Let 0*h - 4*h**2 + 16*h**4 - 24*h**3 + 64*h**5 + 4*h + 0*h - 32*h**5 = 0. What is h?
-1, -1/2, 0, 1/2
Let h(w) be the third derivative of w**6/660 + w**5/165 - 4*w**2. Factor h(i).
2*i**2*(i + 2)/11
Let c(f) be the second derivative of -f**7/11340 + f**6/1620 + f**4/4 - 3*f. Let r(p) be the third derivative of c(p). Determine x, given that r(x) = 0.
0, 2
Let z = -8 - -10. What is g in -2*g - 83 + g**4 - 4*g**3 + 83 + 5*g**z = 0?
0, 1, 2
Suppose -3*n - 3*v + 12 = 2*v, 3*n - 2*v - 12 = 0. Factor 2*h**3 - n*h**3 + 4*h**3 - 4*h**2 - 4*h**3.
-2*h**2*(h + 2)
Let w(r) be the first derivative of 2*r**3/3 - 3*r**2 + 4*r + 2. Find s such that w(s) = 0.
1, 2
Let g(j) = 21*j**3 - 51*j**2 + 19*j. Let b(t) = 4*t**3 - 10*t**2 + 4*t. Let k(n) = -11*b(n) + 2*g(n). Factor k(o).
-2*o*(o - 3)*(o - 1)
Let p = -2/5 - -3/5. Suppose -6/5*w**2 + 16/5*w**5 + 1/5*w + 24/5*w**4 + p*w**3 + 0 = 0. Calculate w.
-1, 0, 1/4
Suppose 4*t + x = 17, -t + 15 = 2*x + 2. Factor -8*k**t + 6*k + 4*k**4 + 7*k - 13*k.
4*k**3*(k - 2)
Let f be (-5)/6*(-6)/90. Let c(k) be the second derivative of 1/12*k**4 - 1/20*k**5 + 1/90*k**6 - f*k**3 + 0 + 0*k**2 - 3*k. Factor c(n).
n*(n - 1)**3/3
Let l(f) = f**3 - 4*f**2 + 2*f. Let b be l(4). Suppose 0 = -r - r + b. Determine u so that -5/2*u**r + 1/2*u - 9/2*u**2 + 1 - 13/2*u**3 = 0.
-1, 2/5
Let z be 1/(-4)*64/(-48). Factor -z*i + 0 - 1/3*i**2.
-i*(i + 1)/3
Let g be -4 + (77/(-12))/(-1). Let c = -7/4 + g. Determine b, given that 0 + b**2 + 1/3*b**3 + c*b = 0.
-2, -1, 0
Let l(g) be the first derivative of g**4/3 + 5. Let l(a) = 0. Calculate a.
0
Suppose -3/4*j**2 + 3/2 - 3/4*j = 0. Calculate j.
-2, 1
Let l = 151/3 - 50. Let r(s) be the first derivative of -s**2 - 3 + 0*s + l*s**3. What is n in r(n) = 0?
0, 2
Let z = 5 - 3. Factor -4*t - 18*t**3 + 2 + 2*t**z + 10*t**4 + 12*t**2 - 2 - 2*t**5.
-2*t*(t - 2)*(t - 1)**3
Let q(p) be the second derivative of 3/2*p**2 + 33/40*p**5 + 0 + 15/8*p**4 + 9/4*p**3 + 3/20*p**6 + p. Let q(f) = 0. Calculate f.
-1, -2/3
Let j(w) = w**3 + w**2 + w + 1. Let q(h) = -3*h**4 + 19*h**3 - 47*h**2 + 25*h - 2. Let f(x) = -2*j(x) - q(x). Factor f(d).
3*d*(d - 3)**2*(d - 1)
Let x be (-896)/(-1320) - 4/30. Suppose 8/11*f + x*f**3 + 0 + 16/11*f**2 = 0. What is f?
-2, -2/3, 0
Factor 0 + 0*m - 2/7*m**2 + 2/7*m**3.
2*m**2*(m - 1)/7
Let y(x) be the third derivative of -1/20*x**6 - 1/105*x**7 - 1/12*x**4 + 0 - 5*x**2 + 0*x**3 + 0*x - 1/10*x**5. Factor y(s).
-2*s*(s + 1)**3
Let i(g) = 20*g + 140. Let m be i(-7). Factor 1/2*y - y**2 + m + 1/2*y**3.
y*(y - 1)**2/2
Factor 6 - 3*o - o**2 + 0*o**2 - o**2 + 7*o.
-2*(o - 3)*(o + 1)
Let s(f) be the third derivative of -f**6/420 + 3*f**2. Suppose s(o) = 0. What is o?
0
Suppose 3*t = -k, -3*t = t - 3*k. Let q be 4/(-8) - (-1)/2. Factor t*o + 2/7*o**2 + q.
2*o**2/7
Factor 1475 - 3*z**3 + 12*z**2 + 9*z - 1529 + 0*z**3 + 0*z.
-3*(z - 3)**2*(z + 2)
Suppose m - 6*m + 50 = 0. Factor -2*y**4 - m*y**3 - 4*y**2 + 3*y**4 - 7*y**4.
-2*y**2*(y + 1)*(3*y + 2)
Let y(m) be the second derivative of -m**6/30 + m**5/20 + m**4/12 - m**3/6 - 9*m. Factor y(r).
-r*(r - 1)**2*(r + 1)
Factor 3/5*w**2 + 1/5*w**3 + 2/5*w + 0.
w*(w + 1)*(w + 2)/5
Suppose -15 = 7*m - 12*m. Factor -4*h**5 - 4*h + 16*h**4 - 2*h**3 + 16*h**2 - 2*h**m - 20*h**3.
-4*h*(h - 1)**4
Let n be 7 + -4 + 16/(-6). Factor -2*j**2 + 0 - 3*j**3 - n*j.
-j*(3*j + 1)**2/3
Let z(u) = -u**2 + 7*u + 1. Let f be z(7). Suppose 3*x - 10 = -f. Factor -5*d**2 - 5*d**2 + 8*d**2 - 7*d**x.
-d**2*(7*d + 2)
Let q(p) be the first derivative of -p**4/20 + 3*p**2/10 + 3*p + 1. Let y(n) be the first derivative of q(n). Factor y(t).
-3*(t - 1)*(t + 1)/5
Let x(j) be the first derivative of j**5/120 + j**4/72 - j**3/36 - j**2/12 - 5*j + 5. Let n(c) be the first derivative of x(c). Determine u so that n(u) = 0.
-1, 1
Suppose 3*b = -2*b + 10. Suppose l = -b*l + 57. Find i such that -l*i**3 - 4 + i**3 + 18*i + 6*i**4 + 12*i**4 - 14*i**2 = 0.
-1, 1/3, 2/3, 1
Find y, given that -10*y**2 + 50*y**3 - 67*y**3 + 32*y**3 - 5*y**5 = 0.
-2, 0, 1
Factor -1/3*p**2 - 1/6*p**3 + 0*p + 0.
-p**2*(p + 2)/6
Factor 30*v - 75 + 5*v**2 +