- 1)**2*(w + 1)
Let c(r) be the first derivative of -3*r**4/16 + 2*r**3/3 - 7*r**2/8 + r/2 - 8. Determine i, given that c(i) = 0.
2/3, 1
Factor 8/5 - 7/10*t**4 - 1/10*t**5 - 8/5*t**3 - 4/5*t**2 + 8/5*t.
-(t - 1)*(t + 2)**4/10
Let d(z) = z**2 + 2*z + 4. Let h(a) = 2*a**2 + 2*a + 3. Let i(b) = -3*d(b) + 4*h(b). Factor i(u).
u*(5*u + 2)
Let r = 19/108 + 2/27. Let z(y) be the second derivative of -r*y**2 - y - 1/80*y**5 - 1/120*y**6 + 1/24*y**3 + 0 + 1/16*y**4. Solve z(v) = 0.
-2, -1, 1
Suppose 3*g = -2 - 10. Let c be ((-52)/(-3))/4 + g. Factor -2/3 - c*z**2 - z.
-(z + 1)*(z + 2)/3
Let r(x) = x**3 - 15*x**2 + 4. Let u be r(15). What is p in -28/5*p - u*p**2 - 4/5*p**3 - 12/5 = 0?
-3, -1
Let c(x) be the first derivative of x**6/12 + x**5/10 - x**4/8 - x**3/6 - 27. Factor c(y).
y**2*(y - 1)*(y + 1)**2/2
Let z(l) = 5*l**2 - l + 6. Let g(q) = -5 + q - 4*q**2 + 4*q - 4*q. Let k(v) = 6*g(v) + 5*z(v). Factor k(i).
i*(i + 1)
Let j = -51 - -53. Let 11/2*d - 1 + 8*d**4 - 7*d**2 - 7/2*d**5 - j*d**3 = 0. Calculate d.
-1, 2/7, 1
Let z(t) = -2*t - 8. Let j be z(-6). Let d - 2*d**2 + d**2 - d**2 - 5*d - 72*d**5 + 2*d**j + 76*d**3 = 0. Calculate d.
-1, -2/9, 0, 1/4, 1
Let x(q) = -15*q**5 - 16*q**4 - q**3 - 4*q**2 + 4*q. Let u(s) = 15*s**5 + 15*s**4 + 5*s**2 - 5*s. Let o(p) = -4*u(p) - 5*x(p). Factor o(c).
5*c**3*(c + 1)*(3*c + 1)
Let x(z) = z**3 - 13*z**2 + 17*z - 14. Let q be x(12). Let c = 139/3 - q. What is n in c*n**2 - 2/3*n + 0 = 0?
0, 2
Let t(o) be the third derivative of o**7/70 + 3*o**6/40 + o**5/20 - 3*o**4/8 - o**3 + 7*o**2 + 4. Factor t(q).
3*(q - 1)*(q + 1)**2*(q + 2)
Suppose 0*q - 3*q = -9. Suppose 2 - 2*z + z + 2*z**2 - q*z = 0. What is z?
1
Let w(s) be the third derivative of s**8/168 + s**7/75 + s**6/150 - 7*s**2. Factor w(x).
2*x**3*(x + 1)*(5*x + 2)/5
Let k be (0 - 122/(-3)) + 0. Let l = k - 40. Determine u, given that 1/3*u**2 + l - u = 0.
1, 2
Suppose q + 84 = 5*q. Factor -2 - 5*t**2 - 7*t**4 - q*t**2 + 23*t**3 - t**2 + 13*t.
-(t - 1)**3*(7*t - 2)
Let m(x) = 3*x**3 + x**2 - 11*x + 7. Let f(d) = -5*d**3 - d**2 + 17*d - 11. Let l(h) = 5*f(h) + 8*m(h). Determine q so that l(q) = 0.
1
Suppose -2*p = 2*p - 16. Suppose -14*v**3 + 21*v**2 + 3*v - 7*v**2 - 7*v + p*v**3 = 0. Calculate v.
0, 2/5, 1
Let w be -5*(1 - (-7)/(-5)). Solve 15*h**2 + w*h - h - 17*h**2 = 0.
0, 1/2
Let q be 784/(-504)*(-1 - 3/(-7)). Find g such that q - 8/9*g + 2/9*g**2 = 0.
2
Let f(y) be the third derivative of -y**9/15120 + y**8/1680 - y**7/630 - y**4/6 - 4*y**2. Let s(t) be the second derivative of f(t). Factor s(w).
-w**2*(w - 2)**2
Let j(b) be the second derivative of 0*b**3 - 1/1260*b**7 + 0*b**5 - b + 1/12*b**4 + 0*b**2 + 0*b**6 + 0. Let d(p) be the third derivative of j(p). Factor d(z).
-2*z**2
Let 6/5 - 1/5*m - 1/5*m**2 = 0. Calculate m.
-3, 2
Let y(g) be the first derivative of -g**2 + 0*g**4 - 1/300*g**5 + 1/30*g**3 + 0*g + 2. Let t(o) be the second derivative of y(o). Let t(d) = 0. What is d?
-1, 1
Let i(y) be the third derivative of y**5/15 + y**4/6 - 4*y**3/3 + 15*y**2. Factor i(c).
4*(c - 1)*(c + 2)
Let j(c) = 3*c**3 + 11*c**2 + 7*c - 7. Let v(z) = 2*z**2 - 3*z - 2. Let o be v(3). Let w(q) = q**3 + 5*q**2 + 3*q - 3. Let y(a) = o*w(a) - 3*j(a). Factor y(n).
-2*n**2*(n - 1)
Let s(m) be the second derivative of m**5/240 + m**4/48 + m**3/24 - 5*m**2/2 + 3*m. Let d(x) be the first derivative of s(x). Solve d(h) = 0.
-1
Let y = 13/168 - -5/24. Let i(z) be the second derivative of -1/7*z**3 + y*z**2 + z + 1/42*z**4 + 0. Determine t, given that i(t) = 0.
1, 2
Let t(z) be the third derivative of z**8/112 - z**7/105 - z**6/30 + z**5/30 + z**4/24 - 25*z**2. Determine a so that t(a) = 0.
-1, -1/3, 0, 1
Let p(f) = -4*f + 2. Let z(s) = -s**2 - 9*s + 5. Let w(n) = -10*p(n) + 4*z(n). Find j such that w(j) = 0.
0, 1
Let l = -1297/36 - -145/4. Let s(t) be the third derivative of -t**2 - l*t**3 + 0 - 1/18*t**4 + 0*t - 1/180*t**5. Let s(y) = 0. What is y?
-2
Let n(o) be the first derivative of 8/3*o + 43/6*o**4 - 16/3*o**2 - 11 - 5/3*o**6 + 22/15*o**5 - 2/3*o**3. Determine p so that n(p) = 0.
-1, 1/3, 2/5, 2
Let d(s) be the first derivative of -s**6/90 - s**5/30 + s**4/12 + 4*s**3/9 + 2*s**2/3 + 7*s - 1. Let p(u) be the first derivative of d(u). Factor p(r).
-(r - 2)*(r + 1)**2*(r + 2)/3
Let 225*w**3 - 16*w - 4*w - 490*w**4 + 245*w**5 + 0*w + 40*w**2 = 0. Calculate w.
-2/7, 0, 2/7, 1
Let o be 7 + -1 - 12 - (-3 - 5). Factor 3/8 - 1/2*y + 1/8*y**o.
(y - 3)*(y - 1)/8
Solve -24334/13*c**3 + 16/13 + 6348/13*c**2 - 552/13*c = 0 for c.
2/23
Let f(k) be the first derivative of -k**6/60 + k**5/30 - k**2 - 3. Let u(b) be the second derivative of f(b). Factor u(x).
-2*x**2*(x - 1)
Let n(t) be the second derivative of -t**5/10 - t**4/6 + 16*t. Factor n(w).
-2*w**2*(w + 1)
Let o(i) be the second derivative of 3*i**5/20 - i**4/2 - i**3/2 + 3*i**2 - 10*i. Factor o(h).
3*(h - 2)*(h - 1)*(h + 1)
Let j(h) be the second derivative of 4*h**7/105 + h**6/60 - 2*h**5/15 - h**4/12 + h**2/2 - 2*h. Let v(a) be the first derivative of j(a). Factor v(o).
2*o*(o - 1)*(o + 1)*(4*o + 1)
Let m(a) = -3*a**3 - a**2. Let l be m(-1). Factor 2*w**3 + 4*w**3 - l*w**4 - 4*w**3.
-2*w**3*(w - 1)
Let r(s) be the first derivative of s**5/30 - s**4/4 + 13*s**3/18 - s**2 + 2*s/3 + 22. Factor r(u).
(u - 2)**2*(u - 1)**2/6
Find n, given that 8*n**5 - 12*n**5 + 8*n**3 - 4*n**3 = 0.
-1, 0, 1
Suppose -3/2*f**2 - 3/2*f + 3 = 0. Calculate f.
-2, 1
Let k = 1573/14 - 112. Let j(i) be the second derivative of -4/7*i**3 - 4/7*i**2 + k*i**4 - i - 2/35*i**5 + 0. Find z, given that j(z) = 0.
-1/4, 2
Suppose 4*g = -2*m + 6, 0*m + 3*g - 4 = -m. Let i = -3 + 5. Factor -2 + 3 + i*h**2 + m - 4*h.
2*(h - 1)**2
Let v(a) = a**2 + 17*a - 32. Let h be v(-19). Determine u so that -14/3*u**4 + 10/3*u**2 - 6*u**3 + 4/3 + h*u = 0.
-1, -2/7, 1
Let m be 0 - 1 - (-27)/24. Let g(v) be the second derivative of -2*v - m*v**4 + 2/3*v**3 - v**2 + 0. Suppose g(u) = 0. What is u?
2/3, 2
Suppose -4*v + 3 - 15 = -3*k, 4 = k + 5*v. Factor 12*c**3 - 6 - 2*c + 3*c**2 + 7*c**k + 6.
c*(c + 1)**2*(7*c - 2)
Factor -10/3*u - 5/3*u**2 + 0.
-5*u*(u + 2)/3
Suppose 2*o = -c + 8, 2*o = -2*o - 5*c + 28. Suppose 0 = -2*m - 2*t - 0*t + 18, -o*m - 17 = -5*t. Factor k + m*k**2 - 5*k**2 - 3*k**2 + 4*k**3.
k*(2*k - 1)**2
Let v(m) = m - 1. Let z be v(3). Let q = z - -2. Factor 0 - 6/5*a**q - 2/5*a**5 - 2/5*a**2 + 0*a - 6/5*a**3.
-2*a**2*(a + 1)**3/5
Let y(i) be the second derivative of i**6/1260 + i**5/420 - i**4/42 - i**3/6 - i. Let p(v) be the second derivative of y(v). Factor p(n).
2*(n - 1)*(n + 2)/7
Solve -p**2 + 3*p**3 + 5*p**2 + 2*p**2 = 0 for p.
-2, 0
Let 1/3*a**3 - 8/3 + 2/3*a**2 - 4/3*a = 0. Calculate a.
-2, 2
Let v be 5/((-10)/(-8)) + -1. Suppose 0 = 5*x - v - 32. Factor -2 + 27 + 11*w**2 - 1 + x*w**2 + 3*w**3 + 36*w.
3*(w + 2)**3
Let d(k) be the second derivative of -3*k**4 - 26*k**3/3 - k**2 - 5*k. Let q(a) = -24*a**2 - 35*a - 1. Let c(w) = -5*d(w) + 7*q(w). Let c(b) = 0. Calculate b.
-1, -1/4
Factor 67 + 36*c + 3*c**2 + 41 - 8*c**2 + 8*c**2.
3*(c + 6)**2
Let n(d) be the second derivative of 1/5*d**2 - 1/10*d**3 - 3*d - 1/30*d**4 + 0. Factor n(m).
-(m + 2)*(2*m - 1)/5
Factor 0 + 5/8*r**2 - 1/2*r**3 + 1/8*r**4 - 1/4*r.
r*(r - 2)*(r - 1)**2/8
Find j such that 0 + 0*j**4 - 4/5*j + 8/5*j**3 - 4/5*j**5 + 0*j**2 = 0.
-1, 0, 1
Let p(v) be the third derivative of -v**10/10080 + 3*v**8/2240 - v**7/420 - v**4/12 + v**2. Let r(x) be the second derivative of p(x). Solve r(b) = 0.
-2, 0, 1
Suppose 2*k = 8, -k = 3*s - 2*k - 311. Let c be (-3)/(s/(-12) - -2). Suppose -2/9*o**2 - 2/9 + c*o = 0. Calculate o.
1
Let l(p) = -4*p**3 + 6*p**2 + 3*p + 5. Let k(u) = 3*u**3 - 5*u**2 - 2*u - 4. Let d(i) = 5*k(i) + 4*l(i). Determine s so that d(s) = 0.
-2, 0, 1
Let k be 4/(3*(-2)/(-6)). Factor -k*p**2 - 2*p - p**4 + 3*p**3 + p**2 + 3*p.
-p*(p - 1)**3
Solve 3*p**3 - 3*p - 3 - 2*p**3 + 2*p + 2*p**2 + 1 = 0 for p.
-2, -1, 1
Let z(y) be the first derivative of -2*y - 2 - 5/2*y**3 - 4*y**2. Find r, given that z(r) = 0.
-2/3, -2/5
Suppose 0 = -4*u - r - 2*r + 4, -u + 5*r + 24 = 0. Suppose -u*t + t - w = -3, 2*w = -4*t + 6. Factor -2*m**2 + t*m**2 + m**2.
-m**2
Let i(h) = -3*h**3 - 1. Let u(d) = d**3 + d - 1. Let k be u(0). Let w be i(k). Factor t + t**5 - w*t**3 - 9 + 9.
t*(t - 1)**2*(t + 1)**2
Let o =