- 2*u + u**4 + 3*u**n - k*u.
u*(u + 1)**3
Let z(d) be the second derivative of 1/45*d**6 + 0*d**4 - 2*d + 2/9*d**3 - 1/15*d**5 + 0 - 1/3*d**2. Factor z(k).
2*(k - 1)**3*(k + 1)/3
Let v(j) be the first derivative of j**6/27 - 4*j**5/45 + 4*j**3/27 - j**2/9 - 1. Solve v(o) = 0.
-1, 0, 1
Suppose y + y + 134 = 5*o, -o - 110 = 2*y. Let l = -169/3 - y. Factor 0*c**4 + 0 + l*c**5 - 2/3*c**3 + 0*c**2 + 0*c.
2*c**3*(c - 1)*(c + 1)/3
Let s(h) be the first derivative of h**6/6 + 2*h**5/5 + 37. Factor s(b).
b**4*(b + 2)
Suppose 7*j = 34*j - 81. Let 4/3*r**j + 2/9*r - 8/9*r**2 - 8/9*r**4 + 2/9*r**5 + 0 = 0. What is r?
0, 1
Let d(g) be the first derivative of -2*g**5/5 + 2*g**4 - 4*g**3 + 4*g**2 - 2*g + 11. Factor d(m).
-2*(m - 1)**4
Let a = 47/6 - 151/30. Factor a*h**2 - 12/5 - 38/5*h.
2*(h - 3)*(7*h + 2)/5
Suppose -2 = -5*l + 3*b - 5*b, 5*l + 3*b = -2. Find k, given that -2*k**4 + 2*k**2 - k**4 - 6*k - 3 + 10*k**3 + 2*k**3 - 6*k**5 + 4*k**l = 0.
-1, -1/2, 1
Let q(y) be the second derivative of 1/6*y**4 - y + 0*y**3 + 0 + 0*y**2 + 1/10*y**5. Factor q(g).
2*g**2*(g + 1)
Let n(c) be the first derivative of -1/9*c**3 - 1/2*c**2 - 2/3*c - 3. Find p such that n(p) = 0.
-2, -1
Let z(a) be the third derivative of -a**9/272160 + a**8/90720 + a**5/20 - 8*a**2. Let h(f) be the third derivative of z(f). Find w, given that h(w) = 0.
0, 1
Let d(i) be the second derivative of i**6/45 - i**5/20 + i**3/18 - 5*i. Factor d(j).
j*(j - 1)**2*(2*j + 1)/3
Factor 5 - d**2 - 10 - 2*d + 4*d + 4*d.
-(d - 5)*(d - 1)
Determine b, given that -14/5*b**2 - 16/5*b - 2/5*b**3 + 32/5 = 0.
-4, 1
Let i(p) be the first derivative of 49*p**4/2 + 238*p**3/3 - 80*p**2 + 24*p + 7. Factor i(s).
2*(s + 3)*(7*s - 2)**2
Let w(t) be the second derivative of -t**5/5 - t**4/3 + 4*t**3/3 - 7*t. Factor w(y).
-4*y*(y - 1)*(y + 2)
Let o(q) be the first derivative of 22/9*q**3 - 8/3*q - 10/3*q**5 - 4*q**2 - 5 + 5*q**4. Factor o(d).
-2*(d - 1)**2*(5*d + 2)**2/3
Let k(a) = -a + 1. Let i(q) = 0 + 12*q - 3*q - 6 + 3*q**2. Let f be 1*-7*8/(-56). Let n(y) = f*i(y) + 6*k(y). Factor n(o).
3*o*(o + 1)
Suppose 0 = 3*j + 2*j - q - 26, -4*j + 32 = 2*q. Determine c so that -3/2*c**2 + 0 + 3/4*c**3 + 15/4*c**5 + j*c**4 + 0*c = 0.
-1, 0, 2/5
Let v = -68 - -206/3. Let q(p) be the first derivative of -4/7*p + v*p**3 + 2 - 5/7*p**2. Factor q(y).
2*(y - 1)*(7*y + 2)/7
Factor 0 - 1/8*y**2 - 1/4*y.
-y*(y + 2)/8
Let 3/2*x**4 - 9/2*x**3 + 3/2*x**2 + 9/2*x - 3 = 0. Calculate x.
-1, 1, 2
Let b(o) = 11*o**2 + 13*o - 5. Let u(z) = -6*z**2 - 6*z + 3. Let f(k) = 3*b(k) + 5*u(k). Find v, given that f(v) = 0.
-3, 0
Let g(l) be the second derivative of 0*l**3 - 2*l + 0*l**2 - 1/24*l**4 - 1/40*l**5 + 0. Factor g(v).
-v**2*(v + 1)/2
Suppose i - 1 = 0, i = -18*t + 19*t - 2. Factor z - 1/4*z**t - 1 + 1/4*z**2.
-(z - 2)*(z - 1)*(z + 2)/4
Let q(a) = -5*a**2 - 3*a + 7*a**2 + 0*a - 10*a**3 + 9*a - 6. Let l(m) = 9*m**3 - m**2 - 5*m + 5. Let i(x) = 6*l(x) + 5*q(x). Factor i(d).
4*d**2*(d + 1)
Let a(s) be the second derivative of 0*s**2 + 0 - 1/5*s**5 - 1/15*s**6 + 4*s - 1/6*s**4 + 0*s**3. Find h such that a(h) = 0.
-1, 0
Let t(k) be the first derivative of -k**8/560 + k**7/280 + k**6/60 - 2*k**3/3 - 4. Let w(i) be the third derivative of t(i). Determine d, given that w(d) = 0.
-1, 0, 2
Let p(t) be the first derivative of t**6/80 - t**5/32 + t**4/48 - 5*t - 6. Let o(j) be the first derivative of p(j). Find l, given that o(l) = 0.
0, 2/3, 1
Let g(i) be the first derivative of -i**6/3 - 2*i**5/5 + i**4/2 + 2*i**3/3 + 4. Determine f, given that g(f) = 0.
-1, 0, 1
Let u be ((-21)/(-14))/(2/4). Suppose -f - 7 = -u*h, 5*h - 12 - 3 = 0. Let -4/3*b**f - 2/3*b**5 + 4/3*b**4 + 2/3*b + 0*b**3 + 0 = 0. What is b?
-1, 0, 1
Let v(d) be the first derivative of -d**3/5 - 3*d**2/5 + 9*d/5 - 1. Factor v(h).
-3*(h - 1)*(h + 3)/5
Let g(i) = i - 1. Let f be g(-17). Let q be (20/(-24))/(10/f). Factor -3*h + q + 3/2*h**2.
3*(h - 1)**2/2
Suppose -r = 81 - 90. Find p such that 4 + r*p**2 + 7/2*p**3 + 10*p + 1/2*p**4 = 0.
-2, -1
Let w(u) be the second derivative of 16*u**5 + 20*u**4 + 10*u**3 + 5*u**2/2 + u. Solve w(z) = 0.
-1/4
Let f be (72/4)/(90/96). Factor 2/5 - 18/5*b + 64/5*b**2 + f*b**4 - 112/5*b**3 - 32/5*b**5.
-2*(b - 1)*(2*b - 1)**4/5
Solve -2/7*f**2 + 2/7*f**4 + 0 - 1/7*f**5 + 1/7*f + 0*f**3 = 0.
-1, 0, 1
Let c = -13 - -20. Let j = -3 + c. Factor 2*s**5 + 0*s**5 + 0*s**3 + 6*s**4 + 0*s**5 - 6*s**2 - j*s + 2*s**3.
2*s*(s - 1)*(s + 1)**2*(s + 2)
Let c = 50 - 28. Suppose -4*i = -c + 6. Find m, given that -2*m**3 + m**4 + 0*m**4 + 10*m + m**4 - 6*m**2 - i = 0.
-2, 1
Let y(r) = -12*r**4 - 8*r**3 - 15*r**2 + 2*r + 7. Let h(l) = 11*l**4 + 9*l**3 + 15*l**2 - l - 6. Let v(c) = 7*h(c) + 6*y(c). Factor v(f).
5*f*(f + 1)**3
Let w(x) be the first derivative of 0*x + 2 + 4/25*x**5 + 0*x**4 - 1/15*x**6 + 1/5*x**2 - 4/15*x**3. Factor w(a).
-2*a*(a - 1)**3*(a + 1)/5
Let x = -27 - -96. Let g = 349/5 - x. Let -2/5*d**2 + 0 + g*d = 0. Calculate d.
0, 2
Suppose 2*b = -2 + 10. Suppose -b*u = -0*o - o - 9, -u = -o. Factor 4*v**2 + 2 + 2*v**5 - 3*v**4 + 4*v**3 + 0*v**4 - o*v**4 - 6*v.
2*(v - 1)**4*(v + 1)
Solve -2/3*a**2 - 8*a - 24 = 0.
-6
Suppose -4*z = -4*h + 32, -2*h + 4*z + 21 = z. Factor -5*l**3 + h*l**4 + 4*l**3 + 3*l**2 + 7*l**3.
3*l**2*(l + 1)**2
Let w(o) be the first derivative of 2*o**3/45 - 4*o**2/15 - 2*o/3 - 22. Solve w(t) = 0.
-1, 5
Factor -5*h + 7*h + 2*h**2 + 0*h.
2*h*(h + 1)
Suppose 0*j = j + 3*s + 10, -4*s = 20. Determine d so that 4*d**j + d**4 + 7*d**4 - 8*d**2 - 4*d**3 + 0*d**3 = 0.
-2, -1, 0, 1
Let n(r) be the second derivative of -r**5/50 + r**4/15 - 11*r. Find l such that n(l) = 0.
0, 2
Let w = -865 - -867. Factor 32/5*o**3 + 49/5*o**5 - 4/5*o**w + 0 + 0*o - 77/5*o**4.
o**2*(o - 1)*(7*o - 2)**2/5
Let a be -4*2/(2 + 0). Let r be -1 - (a - (-2 - 0)). Let 2*s + 0*s**2 + r + 4*s**2 + 2*s = 0. What is s?
-1/2
Let r be 1/(-5) - (-91)/130. Factor 0*j**2 - 3/4*j - r + 1/4*j**3.
(j - 2)*(j + 1)**2/4
Let g = -878/333 + -108/37. Let n = 386/63 + g. Solve -2/7*f**3 - n - 10/7*f - 8/7*f**2 = 0 for f.
-2, -1
Let q(m) be the third derivative of -m**5/300 + m**4/120 + m**3/15 + 10*m**2. Factor q(w).
-(w - 2)*(w + 1)/5
Let y be 9/(-27)*1*-2. Let t be 4/30*(6 - -4). Find c such that 2/3*c**2 - t*c + y = 0.
1
Let i(r) be the second derivative of r**5/150 - 3*r**2/2 - 5*r. Let x(a) be the first derivative of i(a). Factor x(f).
2*f**2/5
Suppose 2 = -2*s - 2*l, -s - 62 = 5*l - 49. Find i, given that 2/3 + 44/3*i**s - 19/3*i = 0.
2/11, 1/4
Let h(c) = c**2 - 1. Let w(p) = -20*p**2 - 25*p - 5. Let g(j) = 15*h(j) + w(j). Solve g(b) = 0.
-4, -1
Factor 4*y - 1/2*y**4 + 1/2*y**2 - 5/2*y**3 + 1/2*y**5 + 2.
(y - 2)**2*(y + 1)**3/2
Let j(k) be the third derivative of k**8/32 - 9*k**7/140 - 19*k**6/80 + 41*k**5/40 - 3*k**4/2 + k**3 - 21*k**2. Suppose j(c) = 0. What is c?
-2, 2/7, 1
Solve -2/15*f**2 + 0 + 4/5*f = 0 for f.
0, 6
Let p(f) be the second derivative of 0 + 2/9*f**2 + 2/27*f**4 + 1/3*f**3 + f. Factor p(u).
2*(u + 2)*(4*u + 1)/9
Let c(v) be the second derivative of v**5/90 + v**4/27 + 6*v. Solve c(h) = 0.
-2, 0
Suppose -4*a + 60 = a. Let m = a - 8. Find c such that 2/5*c**3 + 0 + 0*c - 2/5*c**m + 2/5*c**2 - 2/5*c**5 = 0.
-1, 0, 1
Let j(l) = l + 10. Let i be j(14). Let h be 6/i - 2/(-8). Factor -h*b**3 + 0 + 0*b**2 + 0*b - 1/2*b**4.
-b**3*(b + 1)/2
Let n(r) be the first derivative of 4*r**3/3 + 40*r**2 + 400*r + 49. Factor n(x).
4*(x + 10)**2
Find y, given that 15/2*y**3 + 0 - 2*y**2 - 7/4*y**4 + 0*y = 0.
0, 2/7, 4
Let -4/5 + 3/5*p**2 - 1/5*p**3 + 0*p = 0. What is p?
-1, 2
Let o = 81 - 81. Determine y so that -2/9*y**3 - 4/9*y**2 + o - 2/9*y = 0.
-1, 0
Let y(v) be the third derivative of -v**9/120960 - v**5/20 + 4*v**2. Let j(i) be the third derivative of y(i). Factor j(p).
-p**3/2
Let q(y) be the second derivative of y**6/10 - 3*y**5/10 + y**4/4 - 7*y. Let q(d) = 0. What is d?
0, 1
Let c(v) be the third derivative of -v**5/60 + v**4/8 - v**3/3 - v**2 + 4*v. Let c(g) = 0. What is g?
1, 2
Let y(n) be the third derivative of -1/16*n**4 - 1/40*n**5 + 0 + 1/80*n**6 + 0*n + 2*n**2 + 1/140*n**7 + 0*n**3. Factor y(d).
3*d*(d - 1)*(d + 1)**2/2
Let h(s) = -17*s - 2. Let c be h(-4). Let i be (-1 + -11)*(-3)/c. Factor -6/11*f**4 - 2/11*f**2 + 0*f + 0 + i*f**3 + 2/11*f**5.
2*f**2*(f - 1)**3/11
Let