2.
(f - 12)*(f - 1)
Let n(h) be the first derivative of -h**6/2 + 27*h**5/5 - 45*h**4/2 + 44*h**3 - 36*h**2 + 208. Solve n(y) = 0 for y.
0, 2, 3
Let x(f) be the third derivative of 0*f - 1/42*f**7 + 1/30*f**5 + 0*f**4 + 0 + 0*f**3 + 17*f**2 - 1/40*f**6. What is b in x(b) = 0?
-1, 0, 2/5
Suppose -11*q + 0*q = 0. Let v(s) be the third derivative of -81/32*s**6 + s**2 + 243/280*s**7 - 29/24*s**4 + 0*s + 99/40*s**5 + q + 1/3*s**3. Factor v(k).
(k - 1)*(9*k - 2)**3/4
Let f be 6 + 1/1*-1 + -3. Let j(h) be the first derivative of 2 - h**3 + 3*h + 3/2*h**f - 3/4*h**4. Find y such that j(y) = 0.
-1, 1
Let m(s) be the third derivative of s**7/2520 - s**6/720 + 7*s**4/24 - 12*s**2. Let t(n) be the second derivative of m(n). Suppose t(q) = 0. Calculate q.
0, 1
Suppose -3*l + 6 = -0, 4*o + 3*l = 18. Let r(u) be the first derivative of 5*u**4 - 21/5*u**5 - u**2 + u**o + 2 + 0*u. Suppose r(y) = 0. Calculate y.
-1/3, 0, 2/7, 1
Let g(w) be the second derivative of -6*w**6/5 + 48*w**5 + 347*w**4/3 - 620*w**3/3 + 112*w**2 - 20*w - 9. Solve g(k) = 0.
-2, 1/3, 28
Suppose 0 = -3*h + 8 + 4. Factor x**4 + h*x**3 + 2*x**4 - x**5 + 6*x + 11*x**3 + 17*x**2.
-x*(x - 6)*(x + 1)**3
Let p(j) be the third derivative of 0*j**3 + 19*j**2 + 1/180*j**6 + 1/315*j**7 + 0*j**5 + 0*j**4 + 0*j + 0. Solve p(v) = 0.
-1, 0
Let a(p) = -p**3 + p**2 + 3*p - 2. Let b be a(4). Let m = 51 + b. Suppose -13*x + m*x**2 - 4*x**3 + 33*x - 12*x**2 + 8 + 11*x**2 - 4*x**4 = 0. What is x?
-1, 2
Let c(f) be the second derivative of -3/20*f**2 - 26*f - 1/300*f**6 - 1/100*f**5 + 1/30*f**3 + 0 + 1/30*f**4. Find x, given that c(x) = 0.
-3, -1, 1
Suppose -3*b - 26 = -4*i, -93*b + 91*b - 14 = -i. Determine u, given that -3/7*u**3 - 30/7 - 24/7*u**i - 51/7*u = 0.
-5, -2, -1
Let h be (-34)/30 + 125/(-75) + (-2 - -5). Solve -1/5*i**4 + 1/5*i**2 + h*i**3 + 0 - 1/5*i = 0 for i.
-1, 0, 1
Suppose 3*k = 4*z + 5 + 2, -5*k + 4 = z. Let q be (3 + z)*12/8. Factor -2*h + 4*h**4 + 4*h**2 - 5*h**4 + q*h - 3*h**4 - h**3.
-h*(h - 1)*(h + 1)*(4*h + 1)
Let l(n) = 2*n**2 + 14*n + 16. Suppose -18*m - 6 = -21*m. Let h(p) = -4*p**2 - 27*p - 33. Let x(k) = m*h(k) + 5*l(k). Determine z, given that x(z) = 0.
-7, -1
Let s(f) be the second derivative of -f**8/840 - f**7/140 - f**6/60 - f**5/60 - 7*f**3/6 + 5*f. Let z(c) be the second derivative of s(c). Factor z(g).
-2*g*(g + 1)**3
Suppose s - 17 = -12. Find l such that -12*l + 4*l**4 + 7 + 24*l**3 - 4*l**2 - 12*l**s - 4*l**2 - 3 = 0.
-1, 1/3, 1
Let w be (16/(-20))/((741/(-65))/((-3)/(-2))). Factor 4/19*z + w*z**4 - 4/19*z**3 + 0*z**2 - 2/19.
2*(z - 1)**3*(z + 1)/19
Let v(g) = -11*g**4 - 76*g**3 - 756*g**2 - 3234*g - 5143. Let b(x) = 4*x**4 - x**3 - 1. Let j(c) = -2*b(c) - v(c). Factor j(y).
3*(y + 5)*(y + 7)**3
Let w(n) = n**5 + 2*n**3 - n**2 + n - 1. Let t(y) = -7*y**5 - 3*y**4 - 12*y**3 + 10*y**2 - 6*y + 6. Let z(v) = -t(v) - 6*w(v). Suppose z(h) = 0. Calculate h.
-2, 0, 1
Suppose -18 = -5*g - 3*a + a, a = -4*g + 15. Let n be 2 + 0/((-1)/(-1)). Let 9*b**3 + 5*b**4 - g*b**3 - 6*b**4 - n - 9*b**2 + 7*b = 0. What is b?
1, 2
Let u(q) be the second derivative of q**5/570 + q**4/76 + 2*q**3/57 - 7*q**2 + 10*q. Let i(c) be the first derivative of u(c). Let i(l) = 0. Calculate l.
-2, -1
Suppose 301*a - 327*a = -182. Let f(n) be the third derivative of -1/2*n**4 + 1/20*n**6 + 2*n**3 + 0*n + 0 - 7*n**2 + 1/70*n**a - 3/20*n**5. Factor f(w).
3*(w - 1)**2*(w + 2)**2
Let o(w) = 9*w**2 - 10*w - 11. Let v(p) = -11*p**2 + 10*p + 10. Let c(a) = -6*o(a) - 5*v(a). Factor c(s).
(s + 2)*(s + 8)
Let z(h) = h**2 + 2*h - 12. Let x be z(-5). Factor -36*y + 17*y + 16*y - 6*y**x - 9*y**2.
-3*y*(y + 1)*(2*y + 1)
Let f be (36 - 3379/93) + (-5)/(-3). Solve 0 + 5/3*v**2 - f*v - 5/3*v**4 + 1/3*v**5 + v**3 = 0 for v.
-1, 0, 1, 4
Let y be -3 + ((-2)/9 - 203/(-63)). Let z(r) be the third derivative of 0*r + 0*r**3 + 1/350*r**7 + 6*r**2 + 1/150*r**5 + 7/600*r**6 + 0*r**4 + y. Factor z(p).
p**2*(p + 2)*(3*p + 1)/5
Let r(o) = -11*o**3 + 36*o**2 - 24*o - 64. Let p(l) = 6*l**3 - 18*l**2 + 12*l + 32. Let q(i) = -7*p(i) - 4*r(i). Factor q(k).
2*(k - 8)*(k - 2)*(k + 1)
Let l(i) be the third derivative of 0*i - 8*i**2 + 0*i**5 + 0*i**6 + 0*i**3 + 1/448*i**8 + 3/280*i**7 + 0 + 0*i**4. Factor l(x).
3*x**4*(x + 3)/4
Let k = 1 - -4. Suppose -3*j + 4 = -4*z - 6, 3*j - k*z - 11 = 0. Factor 20 + l**3 - 21 - 3*l - 2*l**3 - 3*l**j.
-(l + 1)**3
Let g = -183/7 + 577/21. Factor -2/3*u**3 + 0 - 2/3*u + g*u**2.
-2*u*(u - 1)**2/3
Let s(n) be the third derivative of 0*n**3 + 0 + 1/672*n**8 - 1/105*n**7 + 1/30*n**5 + 1/80*n**6 + 32*n**2 - 1/12*n**4 + 0*n. Suppose s(b) = 0. What is b?
-1, 0, 1, 2
Let d(w) be the third derivative of -w**6/3600 + w**5/200 - 3*w**4/80 + 8*w**3/3 - w**2. Let v(n) be the first derivative of d(n). Factor v(f).
-(f - 3)**2/10
Let d = -445 + 451. Determine b so that 8/5*b**4 + 32/5*b**2 + 6/5*b - 4/5 + d*b**3 = 0.
-2, -1, 1/4
Let g be 3 + -3*(0 + 1). Let c be (-6 + 4)*(-1 - g). What is z in -z**2 + 9*z + 0*z**c - 8*z = 0?
0, 1
Let u(d) = -15*d**4 + 9*d**3 + 10*d**2 - 4*d + 4. Let m(f) = -2*f**4 + f**3 + 2*f**2 - f + 1. Let q(t) = 4*m(t) - u(t). Find b, given that q(b) = 0.
-2/7, 0, 1
Let f = 9 - 3. Solve -3 - 3*n**2 - 2*n - 5*n + 7*n + f*n = 0 for n.
1
Suppose -5*k = -m - 17, -m = -0*m - 3*k + 7. Suppose 4*v + 4*l = m, -v - 5*l = -2*l + 2. Factor n**2 + 0 + 0*n**3 + 2/3*n - 1/3*n**v.
-n*(n - 2)*(n + 1)**2/3
Let g(n) be the third derivative of -12*n**2 + 1/780*n**6 + 0 + 0*n**3 + 0*n - 1/78*n**4 - 1/390*n**5. Factor g(q).
2*q*(q - 2)*(q + 1)/13
Let o be 2542/369 + (-8)/9. Solve 16*w**4 - o*w**5 + 16/3*w**2 - 2/3*w - 44/3*w**3 + 0 = 0 for w.
0, 1/3, 1
Let o(z) = -24*z**5 - 38*z**4 + 26*z**3 + 32*z**2 - 14*z - 6. Let l(q) = q**5 + q**4 + q + 1. Let k(i) = 6*l(i) + o(i). Find t such that k(t) = 0.
-2, -1, 0, 2/9, 1
Let z(m) be the first derivative of -65/2*m**2 + 3 + 55/3*m**3 + 10*m. Factor z(n).
5*(n - 1)*(11*n - 2)
Factor 56 - 17*s**2 - 7*s**2 + 3208*s - 3208*s + 4*s**3 + 72.
4*(s - 4)**2*(s + 2)
Let b = 47 + -44. Determine o so that -10*o**3 + 20*o**2 - 2*o**3 + 25*o - 10 - 3*o**b = 0.
-1, 1/3, 2
Let c(k) be the second derivative of k**7/7 + 13*k**6/15 - 13*k**5/10 - 13*k**4/6 + 10*k**3/3 - 36*k + 6. Suppose c(u) = 0. Calculate u.
-5, -1, 0, 2/3, 1
Let k(b) be the second derivative of b**6/30 - 11*b**5/20 + 19*b**4/6 - 26*b**3/3 + 12*b**2 + 25*b + 4. Factor k(i).
(i - 6)*(i - 2)**2*(i - 1)
Let f(g) be the second derivative of g**7/3360 + g**6/960 - g**5/80 + 3*g**4/4 + 8*g. Let d(n) be the third derivative of f(n). Suppose d(s) = 0. What is s?
-2, 1
Let p(y) = 9*y**3 + 6*y**2 + y. Let w(h) = -4*h**2 + 3*h**2 - 4*h**3 + 3*h**3. Let f(m) = -5*p(m) - 40*w(m). Solve f(b) = 0 for b.
0, 1
Let 699 + 2*u**2 - 8*u**2 + 201 + 7*u**2 + 60*u = 0. What is u?
-30
Let z(c) be the first derivative of 1/2*c**2 + 3/8*c**3 - 1/80*c**5 + 0*c + 1/16*c**4 + 4. Let x(m) be the second derivative of z(m). Solve x(y) = 0 for y.
-1, 3
Let u be (-20)/8*(-12)/(-10). Let a = u + 7. Determine d so that 4*d**3 - 3*d**4 + 2*d**2 + 5*d**a + 0*d**2 = 0.
-1, 0
Let o = -196 + 2160/11. Factor 2/11*c**4 + 0*c**2 - o*c + 4/11*c**3 - 2/11.
2*(c - 1)*(c + 1)**3/11
Let r(f) = -f**2 - f - 1. Let j(u) = 6*u**2 + 285*u + 9. Let a(i) = j(i) + 9*r(i). Suppose a(g) = 0. What is g?
0, 92
Let x(h) be the first derivative of -h**5/20 + 3*h**4/8 - h**3/12 - 3*h**2 - 4*h - 87. Let x(u) = 0. What is u?
-1, 4
Let d = -3535 - -42533/12. Let f = 5/4 + d. Factor -f + 16/3*x - 2/3*x**2.
-2*(x - 4)**2/3
Let o(b) be the third derivative of -b**8/168 - 2*b**7/45 - 13*b**6/540 + 8*b**5/45 + b**4/9 - 16*b**3/27 + 675*b**2. What is v in o(v) = 0?
-4, -1, 2/3
Let m(o) = 16*o - 2. Let j be m(1). Suppose j + 18*r**2 + 0*r**2 + 25 - 7 - 48*r = 0. What is r?
4/3
Let i(p) be the second derivative of -p**2 + 1/20*p**5 + 5/6*p**3 - p + 0 - 1/3*p**4. Solve i(f) = 0.
1, 2
Let t(k) be the second derivative of -k**5/60 - k**4/6 - 5*k**3/18 - k + 9. Let t(m) = 0. What is m?
-5, -1, 0
Let y(k) be the first derivative of 2*k**5/55 - 7*k**4/22 + 4*k**3/11 + 27. Factor y(g).
2*g**2*(g - 6)*(g - 1)/11
Let t(q) be the third derivative of 1/780*q**6 + 1/390*q**5 - 1/39*q**3 + 0*q - 1/156*q**4 + 10*q**2 + 0. Find h, given that t(h) = 0.
-1, 1
Let w(o) = o**3 + o**2 - 3. Let f be w(0). Let h be (f - 