et r(o) = o**3 - 9*o**2 + 9*o - 4. Let j be r(8). Factor 5*h**3 - 2*h**3 - h**3 - h**2 - h**j.
-h**2*(h - 1)**2
Let x be (-8)/16*(0 + -10) + -3. Factor -3/4*z - 3/4*z**x + 3/4*z**3 + 3/4.
3*(z - 1)**2*(z + 1)/4
Find n, given that 17*n - 5*n**4 + 2*n**2 + n**4 - n**5 - 12*n - 4*n**3 + 2 = 0.
-2, -1, 1
Suppose 6*q = 4*q + 6, y = 2*q. Factor 10*z + 2/3*z**3 + y + 14/3*z**2.
2*(z + 1)*(z + 3)**2/3
Factor 32/5*v**4 + 0*v - 8/5*v**3 + 0*v**2 + 0 - 14/5*v**5.
-2*v**3*(v - 2)*(7*v - 2)/5
Let j(w) be the second derivative of 3*w**5/10 + w**4/30 - 2*w**3/15 - 11*w. Let j(q) = 0. What is q?
-2/5, 0, 1/3
Let k(t) be the third derivative of 0*t + 0*t**3 + 1/90*t**5 + 0 - 1/180*t**6 + 0*t**4 + 7*t**2. Solve k(d) = 0 for d.
0, 1
Let a(t) be the second derivative of -t**4/48 + t**3/12 - t**2/8 + 18*t. Suppose a(n) = 0. Calculate n.
1
Let l(m) be the first derivative of m**5/10 - m**4 + 3*m**3 - 27*m/2 - 1. Solve l(x) = 0.
-1, 3
Factor l**4 + 6*l**3 - l + l - 4*l**3.
l**3*(l + 2)
Let s = -1 + 3. Suppose g = s*g + 1, 0 = -4*r + 4*g + 12. Factor -8 + 3 + 12*t - 13 - 2*t**r.
-2*(t - 3)**2
Let c(u) be the second derivative of -7*u**6/10 - 12*u**5/5 - u**4 - 7*u. Find v, given that c(v) = 0.
-2, -2/7, 0
Let z = -1460 + 83218/57. Let s = z + 67/285. Factor 0 + s*f + 0*f**3 - 2/5*f**4 + 2/5*f**2 - 1/5*f**5.
-f*(f - 1)*(f + 1)**3/5
Let y(f) = -f**2 - f + 2. Let n(d) = d**2 + d - 1. Let u(z) = -z**2 + 4. Let l(h) = 3*n(h) - u(h). Let p(s) = -4*l(s) - 14*y(s). Suppose p(r) = 0. Calculate r.
0, 1
Suppose -4*b = -3*b. Suppose -3 + b = 3*z. Let q(j) = -3*j**3 + 3*j**2 + 3*j - 1. Let r(p) = p**3 - p**2 - p. Let u(t) = z*q(t) - 2*r(t). What is o in u(o) = 0?
-1, 1
Suppose -3*z = 15, 5*y = z - 0*z + 20. Let g be -2 + (8 - 3) + 0. Factor u**4 + 0*u**y + 0*u**4 - 2*u**g + 3*u**3 - u**2 - u.
u*(u - 1)*(u + 1)**2
Let x(w) = -6*w**4 - 2*w**3 + 2*w**2. Let n(g) = -g**5 + 13*g**4 + 5*g**3 - 3*g**2 + g. Let k(v) = 2*n(v) + 5*x(v). Let k(y) = 0. Calculate y.
-1, 0, 1
Let r(s) be the first derivative of -3*s**4/4 - 3*s**3 - 2. Factor r(f).
-3*f**2*(f + 3)
Suppose 0 = -3*s + u + 1, u + 3 = 2*s + 2. Suppose s*j + 0 + 2/11*j**2 = 0. Calculate j.
0
Let s(w) be the second derivative of -w**8/672 + w**7/60 - 3*w**6/40 + w**5/6 - w**4/6 + w**2 + 7*w. Let x(v) be the first derivative of s(v). Factor x(t).
-t*(t - 2)**3*(t - 1)/2
Let k(n) be the first derivative of -2*n**6/3 - 8*n**5/5 + 2*n**4 + 16*n**3/3 - 2*n**2 - 8*n + 11. Let k(d) = 0. What is d?
-2, -1, 1
Let t = 7672 - 138041/18. Let b = -14/9 + t. Let 1/2*i**5 + i**2 + 1/2 + i**3 - 3/2*i - b*i**4 = 0. What is i?
-1, 1
Let i(h) be the third derivative of h**7/1680 - h**6/720 - h**5/120 - 5*h**3/3 - 7*h**2. Let a(r) be the first derivative of i(r). Let a(f) = 0. What is f?
-1, 0, 2
Let n(t) be the second derivative of -3*t + 17/6*t**4 - 21/20*t**5 + t**2 + 0 - 5/2*t**3. Find i, given that n(i) = 0.
2/7, 1/3, 1
Factor -12*o + 71*o**3 - 36*o**3 + 36*o**2 + 3*o**4 - 14*o**3 - 48.
3*(o - 1)*(o + 2)**2*(o + 4)
Let o be (-6)/33*15/(-15). Factor -o*m**4 + 0 + 0*m + 6/11*m**2 + 4/11*m**3.
-2*m**2*(m - 3)*(m + 1)/11
Let j(q) = -q**3 + 18*q**2 + q - 2. Let c be j(18). Suppose 4*w + m = -4*m + 5, 2*m = 2*w - c. Solve d**3 + d**2 + 1/2*d**w + 1/2 - 3/2*d**4 - 3/2*d = 0 for d.
-1, 1
Suppose 0 = -x - 0 + 12. Suppose 0 = 4*g - x. Factor -g*s**2 + s + 2*s**2 - 3*s + 0 - 1.
-(s + 1)**2
Let a be 3 - (-3 - 0 - -1). Let k(v) be the first derivative of 10/27*v**3 - 2/9*v**a - 2 + 0*v + 1/9*v**2 - 4/27*v**6 + 1/6*v**4. Solve k(g) = 0 for g.
-1, -1/4, 0, 1
Factor -31*j**3 - 4*j**5 + 10*j**3 + 40*j**2 + 9*j**5 - 10*j**4 + j**3.
5*j**2*(j - 2)**2*(j + 2)
Let m(c) be the third derivative of c**6/120 + c**5/60 + c**4/24 - 2*c**2. Let a(t) = -t. Let j(b) = a(b) + m(b). Solve j(g) = 0.
-1, 0
Let j = -12 - -16. Suppose -8 = -j*r - 0. Factor 0*u + 0*u**r - 4/9*u**3 + 0 + 10/9*u**5 - 2/3*u**4.
2*u**3*(u - 1)*(5*u + 2)/9
Let z(i) be the third derivative of i**9/181440 - i**8/60480 - i**7/15120 + i**6/2160 + i**5/15 - 2*i**2. Let w(m) be the third derivative of z(m). Factor w(g).
(g - 1)**2*(g + 1)/3
Let t(q) be the second derivative of q**8/1680 + q**7/840 - q**3/6 + 3*q. Let n(l) be the second derivative of t(l). Suppose n(m) = 0. Calculate m.
-1, 0
Suppose 2 - 4 = 4*x + i, -10 = 2*x + 5*i. What is w in x + 1/2*w**2 - 1/4*w - 1/4*w**3 = 0?
0, 1
Let q(l) = -l - 4. Let x(b) = b + 5. Let c(f) = -6*q(f) - 5*x(f). Let w(d) = -2*d**2 - 4*d + 6. Let z(o) = -2*c(o) - w(o). Factor z(k).
2*(k - 1)*(k + 2)
Let t(h) = 3*h**5 - h**4 - 2*h**3 + 5. Let q(b) = 4*b**5 - b**4 - 3*b**3 + 8. Let m(a) = -5*q(a) + 8*t(a). Determine s, given that m(s) = 0.
-1/4, 0, 1
Suppose 0 = -2*o - 2, -2*f - 1 + 3 = 2*o. Factor 0 - 2/11*j**f - 2/11*j.
-2*j*(j + 1)/11
Suppose 8 = 3*a - 4*x - 8, a - 3*x - 12 = 0. Factor 2/3*v**4 + 0*v**2 + 0 - 1/3*v**3 - 1/3*v**5 + a*v.
-v**3*(v - 1)**2/3
Let y be 1/(-2)*1*2. Let l(m) = m**2 - 1. Let v be l(y). What is p in v*p + 2/7*p**2 - 2/7 = 0?
-1, 1
Let d = 751/15 - 50. Let v(z) be the first derivative of d*z**3 + 0*z - 1 + 19/25*z**5 + 1/5*z**2 - 7/30*z**6 - 3/4*z**4. Suppose v(y) = 0. What is y?
-2/7, 0, 1
Let d(w) be the first derivative of w**9/1008 - w**8/280 + w**6/60 - w**5/40 + 7*w**3/3 - 3. Let q(t) be the third derivative of d(t). Solve q(k) = 0 for k.
-1, 0, 1
Let h(p) be the third derivative of -1/30*p**5 + 0 + 0*p - p**2 + 1/60*p**6 + 0*p**4 + 0*p**3. Factor h(g).
2*g**2*(g - 1)
Let l(u) be the second derivative of -u**4/12 - 2*u**3/3 - 3*u**2/2 - u - 48. Factor l(s).
-(s + 1)*(s + 3)
Let w be (-40)/(-18) - 8*2/8. Suppose 0 + 0*u + w*u**2 + 2/3*u**3 + 2/9*u**5 + 2/3*u**4 = 0. What is u?
-1, 0
Suppose -2*s - 7 - 25 = 0. Let g be 3/(-12) - 12/s. Determine n so that -n**3 - 5/4*n**2 - 1/4*n**4 + 0 - g*n = 0.
-2, -1, 0
Find b such that 1/3*b**2 + 1/3*b**4 - 2/3*b**3 + 0*b + 0 = 0.
0, 1
Let y(m) be the third derivative of m**7/210 - m**6/120 + 5*m**2. Find r, given that y(r) = 0.
0, 1
Let n(d) be the second derivative of -3/10*d**4 + 11/15*d**3 + 2*d + 0 - 2/5*d**2. Factor n(c).
-2*(c - 1)*(9*c - 2)/5
Let f(s) be the first derivative of -s**6/15 + 6*s**5/25 - 3*s**4/10 + 2*s**3/15 - 17. Factor f(x).
-2*x**2*(x - 1)**3/5
Let f(t) = t**3 + 7*t**2 - 8*t - 2. Let g be f(-8). Let b be 1/g*4/(-7). Determine j so that -b*j**2 + 0*j + 2/7 = 0.
-1, 1
Let i(v) be the third derivative of v**9/211680 + v**5/20 + 3*v**2. Let r(w) be the third derivative of i(w). Let r(b) = 0. Calculate b.
0
Let c = -225 + 4051/18. Let x(o) be the second derivative of 0 + c*o**4 + 0*o**2 + 1/9*o**3 + 2*o. Factor x(l).
2*l*(l + 1)/3
Let a(c) be the first derivative of 5*c**6/12 + 3*c**5/10 - 7*c**4/8 - c**3/2 + c**2/2 - 3. Let a(j) = 0. Calculate j.
-1, 0, 2/5, 1
Let o(n) = -n**2 + 6*n - 3. Let w be o(2). Factor -w*l**2 + 5*l**2 + 2 - 3*l + l**3.
(l - 1)**2*(l + 2)
Let v(w) be the second derivative of 4*w**6/45 - w**5/30 - 2*w**4/9 + w**3/9 - 10*w. Determine r so that v(r) = 0.
-1, 0, 1/4, 1
Let r(b) = -15*b + 5*b**3 + 13*b - b**4 + 3*b**2 - b**3. Let t(u) = u**4 - u**3 - u**2 + u. Let w(c) = -r(c) - 2*t(c). Find m such that w(m) = 0.
-1, 0
Suppose -8*c**3 - c**4 - c - 1 + 2*c**2 - 6*c**3 + c**5 + 2*c + 12*c**3 = 0. What is c?
-1, 1
Suppose -2*a - 8 + 16 = 0. Determine h, given that -a*h**2 + 3*h**3 - 1/2 - 3*h + 9/2*h**4 = 0.
-1, -1/3, 1
Suppose -4*t + 0*t = 0. Factor t*l + 4*l**3 - 6*l + 2*l - 4*l**4 + 4*l**2.
-4*l*(l - 1)**2*(l + 1)
Let i(s) be the first derivative of 1/900*s**6 + 1/60*s**4 - 3 + 0*s + 1/150*s**5 + s**3 + 0*s**2. Let t(o) be the third derivative of i(o). Factor t(f).
2*(f + 1)**2/5
Let -2/7*u**2 - 8/7*u - 8/7 = 0. What is u?
-2
Let c = -49 - -151/3. Determine k so that 2/3*k - c + 2/3*k**2 = 0.
-2, 1
Let a(n) be the first derivative of n**9/378 - 3*n**8/280 + n**7/70 - n**6/180 - n**3 + 1. Let l(i) be the third derivative of a(i). Factor l(h).
2*h**2*(h - 1)**2*(4*h - 1)
Solve 3 + 5*n - 20*n**2 - 17*n + 12*n**3 + 17*n**2 = 0 for n.
-1, 1/4, 1
Let n = 22 + -19. What is z in 0 + 0*z + 2/3*z**n + 4/3*z**2 = 0?
-2, 0
Let y(t) be the first derivative of -3*t**4/4 - 8*t**3/3 + 3*t**2/2 + 9. Suppose y(j) = 0. What is j?
-3, 0, 1/3
Let x = 444 + -2208/5. Solve -x*o**2 + 2/5*o**3 - 16/5 + 24/5*o = 0 for o.
2
Find h, given that 160*h**5 + 153*h**5 + 2*h**3 - 315*h**5 = 0.
-1, 