4. Let y be 2*(-4 - -3 - g). Factor -3*j**4 + 0*j**2 + 4*j**4 - j**5 + j + y*j**2 - 3*j**4.
-j*(j - 1)*(j + 1)**3
Suppose -8*d**4 + 6*d**3 - 3 - 12*d**5 + 3*d + 3*d**5 + 18*d**2 - 7*d**4 = 0. Calculate d.
-1, 1/3, 1
Let r = -8 + 8. Suppose 4*i - i = r. Factor -2 - 2*z**3 - 6*z**2 + 0*z + i - 6*z.
-2*(z + 1)**3
Let u(p) be the second derivative of p**6/540 - p**5/30 + p**4/4 - 2*p**3/3 - 5*p. Let t(x) be the second derivative of u(x). Solve t(h) = 0 for h.
3
Let k(f) = -f**3 + f**2 + f + 2. Let r be k(2). Suppose 0 = -r*x - 3*x. Find o, given that x + 1/2*o + 1/2*o**2 = 0.
-1, 0
Let t(s) be the third derivative of -s**6/200 - 3*s**5/100 - s**4/20 - 2*s**2. Factor t(x).
-3*x*(x + 1)*(x + 2)/5
Solve 4*x**2 - 4*x - 12*x**2 - x**4 + 0*x**2 - 5*x**3 = 0 for x.
-2, -1, 0
Let u = 11 + -8. Suppose -5*l = -u*l - 8. Factor 2*m**2 - 4*m**3 - l*m**2 + 2*m + 0*m.
-2*m*(m + 1)*(2*m - 1)
Let m(z) be the third derivative of 0*z + 0 - 5*z**2 - 1/3*z**3 - 1/30*z**5 - 1/6*z**4. Solve m(j) = 0.
-1
Let s(x) be the first derivative of x**5/90 - x**4/12 + 2*x**3/9 - x**2 - 1. Let r(o) be the second derivative of s(o). Solve r(w) = 0.
1, 2
Let g(q) be the third derivative of q**8/280 + q**7/75 + q**6/150 - q**5/25 - q**4/12 - q**3/15 + 22*q**2. Find n, given that g(n) = 0.
-1, -1/3, 1
Factor -5/4 + 25/4*l**2 - 5*l.
5*(l - 1)*(5*l + 1)/4
Find h, given that 0 + 1/2*h**3 + 1/2*h**5 + 0*h**2 + 0*h + h**4 = 0.
-1, 0
Factor -3/5*l**2 + 0 + 2/5*l**3 + 1/5*l.
l*(l - 1)*(2*l - 1)/5
Let p be (-3)/((27/(-2))/1). Let z(i) = -i**3 - 22*i**2 - 20*i + 24. Let s be z(-21). Suppose 0*b**s + 0*b + 0 + p*b**2 - 2/9*b**4 = 0. What is b?
-1, 0, 1
Let y = -9 - -29/3. Let p(l) = l - 4. Let j be p(6). Solve 0 - 2*g**3 + y*g**4 - 2/3*g + j*g**2 = 0.
0, 1
Let y(a) = a**2 + 20*a + 4. Let v(b) = -2*b**2 - 21*b - 4. Let u(o) = -5*v(o) - 6*y(o). Factor u(s).
(s - 4)*(4*s + 1)
Factor -3*g**4 + 2*g**4 + 3*g**2 - 3*g**4 + 0*g**2 + 11*g**3.
-g**2*(g - 3)*(4*g + 1)
Factor 6*q**2 + 2*q**4 + 2*q**2 + 8*q**3 + 0*q**3.
2*q**2*(q + 2)**2
Let k(l) = l**4 - 6*l**3 + 4*l**2 - 4*l - 5. Let f(j) = -j**3 + j**2 - j - 1. Let a(x) = 10*f(x) - 2*k(x). Suppose a(t) = 0. Calculate t.
-1, 0, 1
Let z(b) be the third derivative of 2*b**5/75 + b**4/60 - 9*b**2. Factor z(j).
2*j*(4*j + 1)/5
Let h(t) = -3*t - 16. Let b be h(-4). Let q be (-36)/81*(b - 2). Suppose -4/3 - q*p - 5/3*p**2 - 1/3*p**3 = 0. Calculate p.
-2, -1
Let d be 2/(45/12 - (2 + 1)). Find o such that d*o + 2/3*o**2 + 8/3 = 0.
-2
Factor 17*k**2 - 23*k**2 - k**3 + 24 + 4*k**3 - 12*k.
3*(k - 2)**2*(k + 2)
Let q be 2 + -2*(-10)/(-18). Let -q*s**2 - 4/9*s**3 + 2/9*s + 4/9*s**4 + 2/9*s**5 + 4/9 = 0. What is s?
-2, -1, 1
Let o(m) be the second derivative of 0 + 0*m**2 - 2*m + 1/360*m**6 - 1/2*m**3 + 0*m**4 + 1/60*m**5. Let b(k) be the second derivative of o(k). Factor b(u).
u*(u + 2)
Let p(l) be the first derivative of l**6/2 + 3*l**5 + 15*l**4/2 + 10*l**3 + 15*l**2/2 + 3*l - 10. Factor p(j).
3*(j + 1)**5
Let v(z) be the third derivative of z**9/12096 - z**8/2240 + z**7/1120 - z**6/1440 + z**3/6 + z**2. Let t(h) be the first derivative of v(h). Factor t(d).
d**2*(d - 1)**3/4
Factor -2*c**3 + 29*c**2 + 4*c**3 - 27*c**2.
2*c**2*(c + 1)
Let b = -233 - -3033/13. Let k be 1 + 0 + 2/(-1) - -3. Factor 10/13*t**3 + 0 - b*t**k + 0*t.
2*t**2*(5*t - 2)/13
Suppose 0*s + 5*s = 25. Factor -5*d + 5 + 3*d - s + d**2.
d*(d - 2)
Let f(c) be the second derivative of c**5/40 - c**4/12 + c**3/12 + 7*c. Factor f(p).
p*(p - 1)**2/2
Solve 4/3 - 4/3*z**2 - 2/3*z**3 + 2/3*z = 0 for z.
-2, -1, 1
Let c = -19 - -22. Suppose -c*s + 5 = -2*s. Determine u, given that 10/11*u**3 + 2/11*u**4 - 6/11*u**s + 0 - 4/11*u - 2/11*u**2 = 0.
-1, -2/3, 0, 1
Let p = -93 - -281/3. Let n(j) be the first derivative of 3 - p*j**3 - 6/5*j**5 - 2*j**4 + 0*j + 0*j**2. Factor n(a).
-2*a**2*(a + 1)*(3*a + 1)
Let z = -59/224 - -13/32. Factor 1/7*k + 0 + z*k**2.
k*(k + 1)/7
Suppose 60 = 3*b + 54. Factor 1/5*d**3 - 2/5*d + 0 - 1/5*d**b.
d*(d - 2)*(d + 1)/5
Let c be (-81)/36 - -5 - 2/(-8). Factor 18/7*u**4 + 0 + 0*u + 18/7*u**c + 4/7*u**2.
2*u**2*(3*u + 1)*(3*u + 2)/7
Let i(q) = q - 1. Suppose 15 = -4*t - 1. Let f be i(t). Let x(c) = 2*c**2 + 7*c + 5. Let r(s) = -3*s**2 - 11*s - 8. Let d(p) = f*r(p) - 8*x(p). Factor d(w).
-w*(w + 1)
Suppose 0 = -0*o + 4*o. Let u(i) be the third derivative of 1/90*i**5 + 2*i**2 + o*i**3 + 1/18*i**4 + 0*i + 0. Find z such that u(z) = 0.
-2, 0
Let o = -2 + 5. Let k be (-1 - 2)*(2 - o). Factor -2*f**2 - f**2 - 60*f**4 - 39*f**k + 0*f**2 - 3*f**2.
-3*f**2*(4*f + 1)*(5*f + 2)
Factor 3/4 + 1/2*a**3 - 2*a + 3/4*a**2.
(a - 1)*(a + 3)*(2*a - 1)/4
Factor -2/3*p**5 + 0 + 2*p**4 + 0*p + 2/3*p**2 - 2*p**3.
-2*p**2*(p - 1)**3/3
Let t(v) be the first derivative of v**3/3 - v**2/2 - 13. Factor t(z).
z*(z - 1)
Determine o so that 0*o - 2 + 3 + o + 2*o**2 - 4 = 0.
-3/2, 1
Let g(f) be the second derivative of 0 + 0*f**2 + 1/150*f**5 + 1/1800*f**6 + 1/30*f**4 + 1/6*f**3 - 2*f. Let l(u) be the second derivative of g(u). Factor l(b).
(b + 2)**2/5
Let l = -1726/3 - -576. Determine t, given that 0*t - 2/3*t**4 - l*t**2 + 0 - 4/3*t**3 = 0.
-1, 0
Let v = -689/40 - -141/8. Solve -v*y**3 - 2/5*y**2 + 0 + 0*y = 0.
-1, 0
Let n(p) = 2*p + 5. Let o(w) = w + 4. Let b(g) = -5*n(g) + 6*o(g). Let j be b(-1). Factor -2 + c**2 + 0 - j*c + 4.
(c - 2)*(c - 1)
Let l(b) be the third derivative of -b**6/480 - 7*b**5/240 - 5*b**4/32 - 3*b**3/8 + 2*b**2. Determine t, given that l(t) = 0.
-3, -1
Determine u, given that -1/4 + 1/2*u**2 + 0*u - 1/4*u**4 + 0*u**3 = 0.
-1, 1
Let b(m) be the first derivative of -1/3*m + 1/9*m**3 - 1 + 0*m**2. Let b(o) = 0. What is o?
-1, 1
Let d(f) be the third derivative of -f**8/1680 + f**7/350 - f**6/600 - f**5/100 + f**4/60 + 2*f**2. Solve d(a) = 0.
-1, 0, 1, 2
Let p = 15 + -10. Suppose -p = -5*w - 2*q + 12, 2*w - 4*q = 2. Let 0 + 0*t + 2/5*t**2 + 7/5*t**w = 0. Calculate t.
-2/7, 0
Let g(x) = x**2 - x. Let q(u) = -8*u**2 + 12*u - 4. Let r(i) = 10*g(i) + q(i). Factor r(h).
2*(h - 1)*(h + 2)
Factor -3/5*u**2 - 27/5*u**5 - 21/5*u**3 + 0*u - 9*u**4 + 0.
-3*u**2*(u + 1)*(3*u + 1)**2/5
Factor -1/6*r**3 + 1/6*r + 2/3*r**2 - 2/3*r**4 + 0.
-r*(r - 1)*(r + 1)*(4*r + 1)/6
Let i(n) be the first derivative of -n**3/6 + n**2 + 23. What is x in i(x) = 0?
0, 4
Let p(k) = -k**2 + 7*k - 7. Let a be p(3). Factor 1/3*u**a - 2/3*u**4 + 0 + 0*u + 0*u**2 + 1/3*u**3.
u**3*(u - 1)**2/3
Let n = -1527/5 - -306. Solve 1/5 - 3/5*w - 1/5*w**3 + n*w**2 = 0.
1
Let w = 10 - 3. Factor 3 + 0*f**2 + w*f**2 + 2*f**2 - 15 + 3*f**3.
3*(f - 1)*(f + 2)**2
Let o = 1/1417 - -1237/255060. Let y(j) be the third derivative of 1/12*j**4 + 0*j - o*j**6 - 3*j**2 + 0*j**5 + 0 - 2/9*j**3. Factor y(m).
-2*(m - 1)**2*(m + 2)/3
Suppose -4*t = -2*t. Suppose -g + 4*g**3 - 2*g**2 + t*g**3 - 5*g**3 = 0. What is g?
-1, 0
Suppose 4*z = y - 7, -4*z - 16 = 5*y - 27. Factor 30/7*q - 2*q**2 - 18/7 + 2/7*q**y.
2*(q - 3)**2*(q - 1)/7
Let v = 50 + -46. Let x(i) be the third derivative of 0*i - 2*i**2 + 0 + 1/6*i**3 + 1/60*i**5 - 1/12*i**v. Factor x(y).
(y - 1)**2
Let s(k) = k**3 - 5*k**2 - 3*k + 7. Let y be s(5). Let i be ((-4)/10)/(y/10). Let -i*j**2 + 1/2*j**3 + 0*j + 1/2*j**4 - 1/2*j**5 + 0 = 0. Calculate j.
-1, 0, 1
Let n(g) be the third derivative of g**10/45360 - g**9/9072 + g**8/5040 - g**7/7560 + g**4/24 + 4*g**2. Let b(k) be the second derivative of n(k). Factor b(y).
y**2*(y - 1)**2*(2*y - 1)/3
Let r(s) be the first derivative of 1/2*s**6 + 1/12*s**4 + 3 + 0*s - 1/3*s**2 - 7/9*s**3 + s**5. Solve r(v) = 0 for v.
-1, -1/3, 0, 2/3
Let u be ((-2)/(-6))/(2/18). Factor 2*w - 6*w**2 + 0*w**2 + w**2 + u*w**2.
-2*w*(w - 1)
Let x = -6 - -8. Determine s so that 35*s + x*s**2 - 35*s = 0.
0
Let s(g) be the first derivative of 2*g**3/9 + g**2 + 10. Factor s(w).
2*w*(w + 3)/3
Suppose -3*f = -2*f - 4. Suppose -z = z - f. Factor -2/5*u**z + 0*u + 0.
-2*u**2/5
Suppose -4*z = -3*v + 12, -4*v - 5 + 2 = z. Determine c so that 0*c + 2/7*c**2 + v - 2/7*c**4 - 8/7*c**5 + 8/7*c**3 = 0.
-1, -1/4, 0, 1
Let x(n) be the first derivative of n**4/20 - 3*n**2/10 + 2*n/5 + 6. Factor x(z).
(z - 1)**2*(z + 2)/5
Suppose -f + 45 = 2*f. Solve 5*b**4 - 4 + f*b - b - 20*b**3 + 6*b**5 - b**4 = 0.
-2, -1, 1/3, 1
Let q be (-4)/(-22) - (2 + 732/(-330)). Factor -32/5*a**4 + 0 + 14/5*a**2 + q*a + 1