Calculate l.
-5, -1, 2
Let u(b) = b**2 + 5*b + 3. Let x be u(-5). Find s such that 4*s**3 - 2*s**2 - 9*s**3 + 0*s**2 + 3*s**x = 0.
-1, 0
Let t(a) be the first derivative of -5 + 0*a**2 + 1/2*a**6 - 9/4*a**4 - 2*a**3 + 0*a + 0*a**5. Determine y so that t(y) = 0.
-1, 0, 2
Let p be (16/240)/(1*(-2)/(-18)). Factor -1/5*n**3 - p*n**2 + 0*n + 4/5.
-(n - 1)*(n + 2)**2/5
Let o = 38 + -36. Let f(j) be the second derivative of 0*j**3 + 0*j**o - 1/45*j**6 + j + 0*j**4 + 0 + 0*j**5. Factor f(a).
-2*a**4/3
Suppose -i = i. Suppose 3*r + i = 9. Solve 4*f**3 + 3*f**5 + f**2 - f**4 + f**2 - 10*f**r + 3*f - 1 = 0 for f.
-1, 1/3, 1
Factor -3*q**2 + 96*q - 72*q - 48 + 0*q**2.
-3*(q - 4)**2
Let i(p) be the third derivative of -p**5/60 + p**4/3 - 4*p**3/3 + 4*p**2. Let k be i(6). Factor m + m**2 + k - 4.
m*(m + 1)
Factor -104*d**4 + 2*d + 4*d**2 - 8*d**5 + 100*d**4 + 6*d**5.
-2*d*(d - 1)*(d + 1)**3
Suppose 0 = -4*d + 8*d + 16. Let k be (-1)/(d/(-6))*-2. Find s such that 0*s - 1/3*s**k + 2/3*s**2 + 0 = 0.
0, 2
Let v(d) be the second derivative of -10*d + 0 + 128*d**2 + 32*d**3 + 4*d**4 + 1/5*d**5. Suppose v(w) = 0. Calculate w.
-4
Let f(g) be the third derivative of g**8/40320 - g**7/10080 - g**6/720 + g**5/20 + 2*g**2. Let s(n) be the third derivative of f(n). Factor s(v).
(v - 2)*(v + 1)/2
Let n(j) be the second derivative of j**5/10 + 5*j**4/9 + 4*j**3/9 - 8*j**2/3 - 13*j. Factor n(q).
2*(q + 2)**2*(3*q - 2)/3
Let l(h) be the second derivative of -h**6/60 - h**5/8 - h**4/3 - h**3/3 + 32*h. Factor l(g).
-g*(g + 1)*(g + 2)**2/2
Let j(k) = -3*k + 42. Let x be j(13). What is q in 0 - 1/4*q**5 + 1/4*q**4 - 1/4*q**2 + 0*q + 1/4*q**x = 0?
-1, 0, 1
Let v = 22 - 16. Let a(h) = -v*h + 7*h - 2*h**2 - 9 + 0*h**2 + 14*h. Let s(t) = t**2 - 7*t + 4. Let k(b) = 6*a(b) + 13*s(b). Suppose k(d) = 0. What is d?
-1, 2
Let k(d) be the second derivative of -5*d + 0*d**3 + 1/42*d**7 + 1/12*d**4 + 0*d**2 + 0 + 3/20*d**5 + 1/10*d**6. Factor k(q).
q**2*(q + 1)**3
Let i(k) be the third derivative of k**7/30 - 37*k**6/120 - 8*k**5/15 + k**4/2 - 24*k**2. Factor i(j).
j*(j - 6)*(j + 1)*(7*j - 2)
Let a(l) be the second derivative of -l**4/12 + l**3/4 - l**2/4 - 2*l. Factor a(b).
-(b - 1)*(2*b - 1)/2
Let d(u) be the first derivative of -4*u**3/3 + 12*u**2 - 20*u - 12. Factor d(k).
-4*(k - 5)*(k - 1)
Let n(f) be the first derivative of 2 - 1/3*f**3 - 1/40*f**5 + 1/360*f**6 + 0*f + 0*f**2 + 1/12*f**4. Let m(u) be the third derivative of n(u). Factor m(q).
(q - 2)*(q - 1)
Let k(d) = d**2 - 7*d - 5. Let x be k(13). Let b = -509/7 + x. Solve -4/7*a**4 + 0 + b*a**5 + 0*a**2 + 2/7*a**3 + 0*a = 0.
0, 1
Suppose -2*a + 4 = -10. Suppose 4*p = a + 5. Let s + 4*s**2 + p*s + 3*s**3 - 2*s**3 = 0. Calculate s.
-2, 0
Let p = 995/2 + -497. Factor -p + 1/2*d**3 + 3/2*d - 3/2*d**2.
(d - 1)**3/2
Let r = 133/3 - 44. Let q(z) be the first derivative of -1/3*z**2 - r*z + 1/6*z**4 + 0*z**3 - 2 + 1/15*z**5. Solve q(f) = 0.
-1, 1
Let w = -817 - -817. Factor 1/3*b**2 + w + 0*b - 2/3*b**3 + 1/3*b**4.
b**2*(b - 1)**2/3
Suppose w - 4 = -2. Let h(y) be the third derivative of 0 + 1/3*y**3 + 1/30*y**5 + 0*y - y**w - 1/6*y**4. Determine k, given that h(k) = 0.
1
Let t(g) be the third derivative of 0 + 4*g**2 + 0*g - 1/9*g**3 - 1/180*g**5 - 1/24*g**4. Find f such that t(f) = 0.
-2, -1
Let x(w) = w**2 + w + 3. Let i be x(0). Suppose 0 = -4*q + i*q + 2. Factor 0 + 2/3*d**5 + 4/3*d**4 - 4/3*d**q + 0*d**3 - 2/3*d.
2*d*(d - 1)*(d + 1)**3/3
Let l(k) be the third derivative of -k**7/735 - k**6/420 + k**5/210 + k**4/84 - 28*k**2. Factor l(p).
-2*p*(p - 1)*(p + 1)**2/7
Let x = -42 - -42. Let s(p) be the third derivative of -1/20*p**6 + x*p**7 + 0*p**3 + 0*p + 0*p**4 - 3*p**2 + 1/168*p**8 + 0 + 1/15*p**5. Factor s(t).
2*t**2*(t - 1)**2*(t + 2)
Let j(t) be the second derivative of -t**5/130 + 5*t**4/78 - 4*t**3/39 + 12*t. Suppose j(c) = 0. What is c?
0, 1, 4
Let n(o) be the first derivative of -8*o - 32/3*o**3 + 2*o**4 - 2/3*o**6 + 14*o**2 - 2 + 8/5*o**5. Suppose n(m) = 0. What is m?
-2, 1
Suppose -5*b + 3*o - 1 = -16, 0 = 2*b + 3*o + 15. Solve -1/6*z**2 + b + 1/6*z = 0 for z.
0, 1
Suppose 0 = -8*i + 6*i. Let x(o) be the third derivative of 4/15*o**3 + 1/150*o**5 - 1/15*o**4 + i - o**2 + 0*o. Find m, given that x(m) = 0.
2
Let j(s) be the first derivative of 15*s**6/7 - 6*s**5/35 - 31*s**4/14 + 10*s**3/7 - 2*s**2/7 - 12. Let j(q) = 0. Calculate q.
-1, 0, 1/3, 2/5
Suppose 4*o = t + 13, 3*t - 3 = 6. Factor -2/5*u**3 - 2/5*u**2 + 0 + 2/5*u**o + 2/5*u.
2*u*(u - 1)**2*(u + 1)/5
Let y(o) be the second derivative of -1/45*o**6 + 3*o + 1/3*o**2 - 2/9*o**3 + 1/15*o**5 + 0 + 0*o**4. Factor y(i).
-2*(i - 1)**3*(i + 1)/3
Find g such that 3*g - 2 - 5*g - 2*g**2 - 2*g + 0*g = 0.
-1
Let g be (-9)/(-2)*20/30. Let k = 3 - g. What is d in k + 10/7*d**2 - 4/7*d = 0?
0, 2/5
Let u(t) = -5*t**2 + 7*t + 2. Let d(n) = 11*n**2 - 15*n - 4. Let a(m) = -2*d(m) - 5*u(m). Factor a(o).
(o - 2)*(3*o + 1)
Factor 0*g - 28/5*g**5 + 0 + 0*g**2 - 8/5*g**3 - 36/5*g**4.
-4*g**3*(g + 1)*(7*g + 2)/5
Suppose 5*o = o - 36. Let x be (o/12)/((-21)/56). What is u in -9/4 - 1/4*u**x + 3/2*u = 0?
3
Let t(d) be the third derivative of -d**5/60 + d**4/8 - d**3/3 - 6*d**2. Factor t(f).
-(f - 2)*(f - 1)
Let m be (-21)/6*4/(-28). Let a(y) be the first derivative of 20*y**3 - m*y**6 + 21/5*y**5 + 0*y - 4 - 12*y**2 - 27/2*y**4. Factor a(o).
-3*o*(o - 2)**3*(o - 1)
Let b(m) be the first derivative of 4*m**5/5 - 4*m**3/3 - 6. What is n in b(n) = 0?
-1, 0, 1
Let m(x) be the third derivative of x**7/140 - x**6/240 - 3*x**5/40 - x**4/16 + x**3/6 + 2*x**2 + 12. Suppose m(i) = 0. What is i?
-1, 1/3, 2
Let z = -5/18 + 61/90. Determine m, given that 0 - 2/5*m**2 + 0*m**3 + z*m**4 + 0*m = 0.
-1, 0, 1
Let v be -1 + 1 - 1*2. Let b = v + 5. Suppose 4*z**4 + 3*z**3 + 2*z**2 - b*z**2 - 6*z**3 = 0. What is z?
-1/4, 0, 1
Find u such that 12/7*u**3 + 3/7*u**4 + 15/7*u**2 + 0 + 6/7*u = 0.
-2, -1, 0
Let g(p) be the first derivative of -p**3 + 12*p - 1. Let g(b) = 0. Calculate b.
-2, 2
Let m(a) = -4*a**2 + 4*a. Let w(c) = -c**2 + c. Let g = -7 + 5. Let t(v) = g*m(v) + 9*w(v). Let t(k) = 0. What is k?
0, 1
Let t(v) be the second derivative of 1/180*v**6 + 2*v - 1/2*v**3 - 1/6*v**4 + 1/60*v**5 + 0*v**2 + 0. Let r(h) be the second derivative of t(h). Factor r(w).
2*(w - 1)*(w + 2)
Let o = 19/7 - 69/28. Suppose o*s - 1/4*s**3 - 1/4 + 1/4*s**2 = 0. What is s?
-1, 1
Let c be 42/(-1224)*(-10 + 2). Let w = c - -1/17. Find y, given that 0*y**2 - 1/3 + 2/3*y**3 - 2/3*y + w*y**4 = 0.
-1, 1
Let i(o) = 4*o**2 + 2*o - 5. Suppose 4*z - 16 = 0, 6*z - 2*z - 11 = 5*s. Let y(n) = n**2 - 1. Let q(g) = s*i(g) - 5*y(g). Determine r so that q(r) = 0.
0, 2
Let b = -35 + 107/3. Factor -1/3*h**3 + b*h + 2/3 + 1/6*h**4 - 1/2*h**2.
(h - 2)**2*(h + 1)**2/6
Determine x, given that 0*x - 1/7*x**3 + 0*x**2 + 0 + 0*x**4 + 1/7*x**5 = 0.
-1, 0, 1
Let p(m) be the third derivative of -m**8/96 + m**7/14 - 43*m**6/240 + m**5/5 - m**4/12 + 19*m**2 + 2*m. Solve p(k) = 0.
0, 2/7, 1, 2
Let v be ((-2)/4)/(4/(-24)). Solve -3*b**4 - 3 + 1 + 3*b**5 + 2 - 3*b**v + 3*b**2 = 0.
-1, 0, 1
Let p = 11 + -23. Let w be (6 - 3)*p/(-198). Determine j, given that -w*j**4 + 20/11*j - 24/11*j**2 - 6/11 + 12/11*j**3 = 0.
1, 3
Let r(o) be the first derivative of o**6/90 - o**4/18 + o**2/6 - 6*o - 5. Let l(m) be the first derivative of r(m). Factor l(z).
(z - 1)**2*(z + 1)**2/3
Suppose 0 + 2*a + 4/3*a**2 - 2/3*a**3 = 0. What is a?
-1, 0, 3
Suppose -5*w = 2*v - 2 - 11, 3*w - 5*v = 14. Suppose 2*f**3 - f**3 + 2*f - w*f**3 = 0. Calculate f.
-1, 0, 1
Suppose 0 = 5*d - 0*d + 5. Let i(r) = -r**3 + r**2 + r + 1. Let j(m) = -8*m**3 - 2*m**2 + 34*m - 6. Let l(k) = d*j(k) + 10*i(k). Let l(o) = 0. Calculate o.
2
Let d(r) be the first derivative of 2*r**3/3 + 10*r**2 - 29. Solve d(c) = 0 for c.
-10, 0
Let y(u) be the second derivative of -u**4/9 - 2*u**3/9 + 4*u**2/3 - 15*u. Suppose y(m) = 0. Calculate m.
-2, 1
Let y(i) be the second derivative of -i**6/6 - 5*i**5/4 + 35*i**4/4 - 115*i**3/6 + 20*i**2 + 3*i + 5. Factor y(w).
-5*(w - 1)**3*(w + 8)
What is w in 5*w**5 + 3*w**4 + 2*w**5 + 34*w**3 - w - 16*w**2 - 10*w**4 + 2 - 19*w**4 = 0?
-2/7, 1
Find x, given that 4/5*x**4 - 6/5*x**2 + 3/5*x**5 - 4/5*x**3 + 1/5*x + 2/5 = 0.
-1, 2/3, 1
Let p(n) be the first derivative of 0*n**5 + 0*n**2 +