4/5*o**4 = 0. Calculate o.
-2, 0, 1/4
Let r(y) be the first derivative of y**4/4 - y**3 + 3*y**2/2 - 4*y - 6. Let k(j) be the first derivative of r(j). Factor k(z).
3*(z - 1)**2
Let o(j) = -2*j + 18. Let g be o(8). Let h(r) be the first derivative of 1/4*r**4 + 0*r**3 - 1/5*r**5 - g + 0*r**2 + 0*r. Factor h(z).
-z**3*(z - 1)
Let k(f) = -4*f**2 - f + 3. Suppose -4*x + 3 = -5*x + 5*n, 5*x - n = 9. Let d(p) = -10*p**x + 5 - 2*p + p**2 + 2*p**2. Let u(h) = -3*d(h) + 5*k(h). Factor u(r).
r*(r + 1)
What is t in 8*t**5 - 5*t**3 - 3*t**3 - 27*t**2 - 9*t**5 - 9*t**4 - 19*t**3 = 0?
-3, 0
Let g(v) = v**3 + v**2 + v + 3. Let d be g(0). Suppose -x + 12 = d*x. Solve 4*p**x - 4*p**3 + 2*p**3 = 0 for p.
0
Let k(m) = 3*m**2 - m - 2. Let j be k(-1). Let 5 - 5 + 2*z**4 - j*z**3 = 0. What is z?
0, 1
Factor 0*q**4 + 0*q + 0*q**2 + 0 - 3/4*q**5 + 0*q**3.
-3*q**5/4
Let h = -2212 - -13307/6. Let y = 397/66 - h. Factor -2/11*x - 2/11*x**4 + 2/11*x**3 + 0 + y*x**2.
-2*x*(x - 1)**2*(x + 1)/11
Let y be ((-20)/(-4) - 6) + 2*2. Find s such that 0 - 1/5*s**y - 1/5*s - 2/5*s**2 = 0.
-1, 0
Let r(w) be the first derivative of 3/16*w**4 - 2 + 0*w + 0*w**3 + 3/20*w**5 + 0*w**2. Factor r(i).
3*i**3*(i + 1)/4
Let q(i) = i**3 - 8*i**2 + i - 2. Let p be q(8). Suppose 20 = 2*l + 5*x + 1, 3*x - 13 = -2*l. Factor 2 - p*r + 0*r + 2 + 2*r**l.
2*(r - 2)*(r - 1)
Let j(i) be the first derivative of 2*i**3/3 + 3*i**2 - 13. Factor j(v).
2*v*(v + 3)
Let m(h) be the third derivative of -h**6/60 - h**5/30 + h**4/12 + h**3/3 - h**2. Factor m(l).
-2*(l - 1)*(l + 1)**2
Factor 2*z - 22*z - 7*z**3 - 15 + 5*z**4 - 38*z**3 + 10*z**2 + 65*z**3.
5*(z - 1)*(z + 1)**2*(z + 3)
Suppose 2*y - 13 = -5*n, 2*y = 5*y + 3. Factor 8*b**4 + 2*b**n - 2*b**4 - 4*b**4 - b**3 + b**5.
b**3*(b + 1)**2
Factor 6*z**4 - 18*z**3 - 203*z**5 + 6*z**4 + 201*z**5.
-2*z**3*(z - 3)**2
Let l(z) = -z**2 + 7*z - 3. Let t be l(6). Suppose t*o**2 - o**2 + o**5 - o**2 - o**4 - o**3 = 0. What is o?
-1, 0, 1
Let h(x) be the third derivative of -x**5/180 + 5*x**4/36 - 25*x**3/18 - 10*x**2. Let h(m) = 0. Calculate m.
5
Let n = 387/5 + -77. Let w(z) be the first derivative of n*z**4 + 1 + 0*z + 2/25*z**5 + 2/3*z**3 + 2/5*z**2. Find g, given that w(g) = 0.
-2, -1, 0
Suppose -2*g = -3*g + 2*g. Let i(h) be the first derivative of 0*h + g*h**2 + 2/5*h**5 - 1/2*h**4 - 4 + 1/6*h**3. Determine s, given that i(s) = 0.
0, 1/2
Let c(i) be the first derivative of 0*i + 2*i**3 + i**2 - 3 + 3/2*i**4 + 2/5*i**5. Find q such that c(q) = 0.
-1, 0
Let n(m) be the third derivative of 0*m + 1/20*m**5 + 0*m**3 + m**2 + 0 - 1/70*m**7 + 0*m**6 + 0*m**4. Factor n(g).
-3*g**2*(g - 1)*(g + 1)
Let p = -3 - -13. Let i be 0 + -1 + p/8. Let 1/2*a**3 - i*a**2 - 1/4*a**4 + 0 + 0*a = 0. What is a?
0, 1
Factor -1/3*l + 0 - 1/2*l**2 - 1/6*l**3.
-l*(l + 1)*(l + 2)/6
Factor 0 - 32/3*i**2 + 8/3*i - 6*i**3.
-2*i*(i + 2)*(9*i - 2)/3
Let v(z) be the third derivative of z**7/70 + 3*z**6/40 + z**5/20 - 3*z**4/8 - z**3 - 16*z**2. Determine b so that v(b) = 0.
-2, -1, 1
Let v be (-4 - -7)/(6/16). Let s = v - 5. Factor 1/4 - 1/2*z**s - 1/4*z**4 + 1/2*z + 0*z**2.
-(z - 1)*(z + 1)**3/4
Suppose -10 = -p - p. Let b(j) be the second derivative of 0 + 1/12*j**4 + 7/20*j**6 + 0*j**2 + j + 0*j**3 - 13/40*j**p. Solve b(z) = 0.
0, 2/7, 1/3
What is u in -9*u - 3*u**4 - 497*u**3 + u**2 + 6 + 506*u**3 - 4*u**2 = 0?
-1, 1, 2
Let w(d) be the first derivative of -1/3*d - 1/6*d**2 + 1/9*d**3 + 8 + 1/12*d**4. Factor w(y).
(y - 1)*(y + 1)**2/3
Let g(l) be the first derivative of l**6/30 + l**5/5 + 7*l**4/20 + l**3/5 + 34. Find j such that g(j) = 0.
-3, -1, 0
Let p(f) be the second derivative of -f**4/36 - 2*f**3/9 + 17*f. Suppose p(o) = 0. Calculate o.
-4, 0
Let t = -169 + 173. Find i such that -1/3*i**4 - 4/3 - 2*i**3 - t*i - 13/3*i**2 = 0.
-2, -1
Let s be (1/4 + (-264)/96)/(-20). Factor s*w**4 - 3/8*w**2 + 1/8*w**3 + 1/4 - 1/8*w.
(w - 1)**2*(w + 1)*(w + 2)/8
Let z be ((-6)/(-20))/(3/4). Factor 4/5 + z*f**2 - 6/5*f.
2*(f - 2)*(f - 1)/5
Suppose -5*u = -u. Suppose -2*a + u*a = -4*w + 2, 3*w = -2*a + 19. Find z such that z + 4*z**2 + w*z**3 - z**2 + 0*z + z**4 = 0.
-1, 0
Let a(b) be the first derivative of -7*b**3/3 + 6*b - 3. Let p(z) = 20*z**2 - 17. Let m(f) = -17*a(f) - 6*p(f). Find c such that m(c) = 0.
0
Let k be 16/(-64) + (-9)/(-4). Let p(f) be the first derivative of -4 - 2/15*f**3 - 1/5*f**k + 0*f. Determine m, given that p(m) = 0.
-1, 0
Factor -4/11*n**3 + 4/11 + 16/11*n**2 - 14/11*n - 4/11*n**4 + 2/11*n**5.
2*(n - 1)**4*(n + 2)/11
Let n(w) be the first derivative of -4*w**5/5 + 2*w**4 - 4*w**3/3 + 9. Factor n(x).
-4*x**2*(x - 1)**2
Let f(z) be the second derivative of -z**6/90 + z**5/20 - z**4/12 + z**3/18 + 6*z. Factor f(i).
-i*(i - 1)**3/3
Solve 32/9*y - 2/3*y**5 + 10/9*y**4 - 8/9 - 14/3*y**2 + 14/9*y**3 = 0 for y.
-2, 2/3, 1
Let x(v) be the third derivative of -2*v**7/105 - v**6/40 + v**5/60 - 6*v**2. Factor x(w).
-w**2*(w + 1)*(4*w - 1)
Let c(k) = k**2 + k - 1. Let r(n) = 0*n + 5 + 3*n**2 - 4*n**2 - 4*n. Suppose 11*o = 6*o + 25. Let d(t) = o*c(t) + r(t). What is x in d(x) = 0?
-1/4, 0
Let v(j) = j**2 + 7*j - 12. Let y be v(-11). Determine t, given that -32/5 - 128/5*t - 10*t**4 + y*t**3 - 48/5*t**2 = 0.
-2/5, 2
Factor -2*s**3 + 8*s**2 - 5*s**3 + 3*s**3.
-4*s**2*(s - 2)
Let b(h) be the second derivative of 0*h**3 + 0 - 1/5*h**5 + 0*h**2 - 1/12*h**4 + 3*h. Solve b(m) = 0 for m.
-1/4, 0
Let h(u) = -6*u - 1. Let x(f) = f - 1. Let b(c) = -h(c) - 5*x(c). Let k be b(-6). Find y such that -3*y**3 + k*y - 4*y**3 + y + 6*y**3 = 0.
-1, 0, 1
Let q(g) be the second derivative of -g**5/20 + 2*g**4/3 - 11*g**3/6 - g**2 - 3*g. Let s be q(6). Factor 0 + 0*l + 6/7*l**s - 6/7*l**3 + 2/7*l**2 - 2/7*l**5.
-2*l**2*(l - 1)**3/7
Let v = -28 - -31. Let f(z) be the second derivative of 0*z**2 + 0 - 3/20*z**5 - 1/6*z**4 - 3*z + 1/6*z**6 + 0*z**v. Factor f(w).
w**2*(w - 1)*(5*w + 2)
Suppose -v + 1 = -1. Let l = 102 + -99. Solve -4/5*f**l - 2/5*f**4 + 2/5 + 0*f**v + 4/5*f = 0 for f.
-1, 1
Let v(g) be the second derivative of g**6/10 - 3*g**5/5 + g**4/2 + 2*g**3 - 9*g**2/2 - 25*g. Factor v(m).
3*(m - 3)*(m - 1)**2*(m + 1)
Let n = 7 - 9. Let h be (-4 - 2)/3*n. Factor 3*a**4 + a**3 - a**h - 3*a**4.
-a**3*(a - 1)
Let l(h) be the third derivative of 0 + 2/9*h**3 + 0*h - 13/90*h**5 - 5/36*h**4 + 1/126*h**8 + 1/180*h**6 + 11/315*h**7 - 5*h**2. What is b in l(b) = 0?
-2, -1, 1/4, 1
Let b(v) be the second derivative of -v**4 + 5*v**3/3 - v**2 + 7*v - 5. Solve b(x) = 0.
1/3, 1/2
Let x = -19 - -15. Let m(h) = -6*h**2 + 27*h - 21. Let v(o) = o**2 - 4*o + 3. Let y(b) = x*m(b) - 27*v(b). Factor y(q).
-3*(q - 1)*(q + 1)
Let a = -14 - -16. Suppose 2*u + 18 = 3*q, q + 24 = 5*q - u. What is g in 6*g**3 - q*g**4 - 2*g**2 - 21*g + a*g**5 + 0*g**2 + 21*g = 0?
0, 1
Let l(k) be the first derivative of 5*k**6/6 + 5*k**5 + 45*k**4/4 + 35*k**3/3 + 5*k**2 - 7. Solve l(o) = 0.
-2, -1, 0
Let w be ((-4)/(-8)*0)/1. Solve 1/6*i**3 + w*i**2 - 1/3 - 1/2*i = 0 for i.
-1, 2
Let y be 3 + (40/(-12) - -3). Let h = y - 13/6. Factor -h*w + w**2 + 0 + 1/2*w**5 - w**4 + 0*w**3.
w*(w - 1)**3*(w + 1)/2
Suppose 14 = 5*p - 6. Suppose 8 = 3*y - p. Solve 19/4*c**y + 7/4*c**5 + 0 + 15/4*c**3 + 1/4*c**2 - 1/2*c = 0 for c.
-1, 0, 2/7
Let u(s) be the third derivative of -s**8/16800 + s**7/1050 - s**6/150 + 2*s**5/75 - s**4/6 - 9*s**2. Let p(v) be the second derivative of u(v). Factor p(c).
-2*(c - 2)**3/5
Let a(o) = 3*o**3 + 21*o**2 - 5*o. Let w(f) = -2*f**3 - 10*f**2 + 2*f. Let u(s) = -2*a(s) - 5*w(s). Find l, given that u(l) = 0.
-2, 0
Find t, given that 5*t**2 - 40 + 165 + 21*t + 29*t = 0.
-5
Find x such that -24 - 5*x**3 + 11 + 13 = 0.
0
Let a(w) be the second derivative of w**9/6048 - w**3/2 + 4*w. Let j(l) be the second derivative of a(l). Factor j(v).
v**5/2
Let d(j) = -j - 6. Let x be d(-8). Suppose x*r - 3 - 1 = 0. Factor 4/3 - 2/3*p**3 + 0*p**2 + r*p.
-2*(p - 2)*(p + 1)**2/3
Let x = -2 + 2. Suppose x = u + u. Suppose 2*k**3 + 2/3*k - 2*k**2 + u - 2/3*k**4 = 0. Calculate k.
0, 1
Let r(d) = d**3 + 4*d**3 + 11*d**2 - 4*d**3 + 9*d + 4. Let i be r(-10). Factor 6 + i*o - 1 - 1 + 17*o**2 - 7*o**2.
2*(o + 1)*(5*o + 2)
Factor -1 - 1/2*y**2 + 3/2*y.
-(y - 2)*(y - 1)/2
Let p be (-1)/(12/15) + 2. Factor k**4 + 5/4*k**3 - 1/4 - p*k**2 - 5/4*k.
(k - 1)*(k + 1)**2*(4*k + 1