 + 20*k.
-(k - 2)*(k - 1)*(k + 5)**2
Let v(g) be the third derivative of -g**7/840 + 3*g**6/80 - 5*g**2. Determine n so that v(n) = 0.
0, 18
Let j(a) = a**2 + 16*a - 19. Let h be j(-17). Let g be ((-9)/(-6) + h)/(-1). Factor -g*m**2 + 0*m + 5/2*m**3 + 0.
m**2*(5*m - 1)/2
Suppose -g = 4*u + 257 - 61, 3*u + 199 = -g. Let r = 208 + g. Solve r*v**2 - 2/7*v + 0 + 2/7*v**3 = 0.
-1, 0, 1
Let d be (52/(-2) - 2)*(-3)/12. Let u(l) be the third derivative of 0 + 0*l + 0*l**4 + 1/840*l**8 + 0*l**3 + 0*l**5 - 1/300*l**6 + 0*l**d + 5*l**2. Factor u(y).
2*y**3*(y - 1)*(y + 1)/5
Let a be 12 + (1 - 13)*4/(-8). Let h(b) be the second derivative of -a*b**2 + 0 - 1/3*b**4 + 4*b + 4*b**3. Factor h(r).
-4*(r - 3)**2
Let h = -2281 - -6851/3. Factor h*y - 2/3*y**2 - 2.
-2*(y - 3)*(y - 1)/3
Let t be (1/3)/(4/12). Let z be (-4)/(-8)*(3 + t). Factor -4*j**2 - 16 + 2*j**2 - 16*j - z*j**2.
-4*(j + 2)**2
Suppose 18*j = -29*j + 94. Let w(d) be the first derivative of -j + 1/3*d**3 - 1/8*d**4 - d + 1/4*d**2. What is k in w(k) = 0?
-1, 1, 2
Factor -6*s + 0*s**2 - 36 + 5*s + 4*s**2 + s.
4*(s - 3)*(s + 3)
Let c(o) = 5*o**5 + 37*o**4 + 134*o**3 + 90*o**2 - 131*o - 131. Let i(b) = 2*b**4 - b**3 - b - 1. Let q(a) = c(a) + 4*i(a). Factor q(w).
5*(w - 1)*(w + 1)*(w + 3)**3
Suppose -3*b + z = -5, -3*b + 70 = -4*z + 68. Let k(y) = 2*y - 16. Let o be k(8). Factor 1/2*u**b + o + 1/2*u.
u*(u + 1)/2
Let q(m) be the first derivative of 7*m**6/2880 - 3*m**5/320 + m**4/96 - 2*m**3 + 6. Let w(b) be the third derivative of q(b). Factor w(i).
(i - 1)*(7*i - 2)/8
Factor -384 - 3/8*i**2 + 24*i.
-3*(i - 32)**2/8
Factor 1/3*c**2 + 52/3 - 53/3*c.
(c - 52)*(c - 1)/3
Let d(t) be the first derivative of -18/7*t**2 + 2/21*t**3 + 21 + 162/7*t. Factor d(z).
2*(z - 9)**2/7
Let t(p) be the third derivative of -p**7/2100 + p**6/450 + p**5/100 + 5*p**3/3 + 11*p**2. Let r(w) be the first derivative of t(w). Factor r(z).
-2*z*(z - 3)*(z + 1)/5
Factor 0*i + 2/9*i**2 - 2.
2*(i - 3)*(i + 3)/9
Let f(z) be the second derivative of 0 - 1/9*z**4 + 0*z**2 - 1/90*z**5 - 1/3*z**3 + 36*z. Factor f(m).
-2*m*(m + 3)**2/9
Let v = -1751 - -1756. Let s(n) be the third derivative of -3/8*n**4 + 0*n + 0 + 2*n**3 - 1/20*n**v + 9*n**2. Factor s(i).
-3*(i - 1)*(i + 4)
Let g be 0*3/12*-2. Let h = 3 - g. Factor -18*y**h - 10*y + 53*y**2 - 14*y**2 + 12 + 3*y**4 - 26*y.
3*(y - 2)**2*(y - 1)**2
Factor -4/3*t**2 + 4/3*t - 4/3*t**3 + 4/3*t**4 + 0.
4*t*(t - 1)**2*(t + 1)/3
Let f(p) = p**3 + 35*p**2 - 69*p + 188. Let n be f(-37). Determine z, given that 1/4*z**2 + 3/2*z**n + 1/4*z**4 + 4 - 6*z = 0.
-4, 1
Solve -30*u**4 + 112*u**4 + 12*u**2 - 32*u**4 - 3*u**5 - 35*u**4 - 24*u**3 = 0.
0, 1, 2
Let i = 705/44 - 168/11. Factor -3/8 - i*s - 3/8*s**2.
-3*(s + 1)**2/8
Let h = -22 - -24. Suppose -h*n - 17 = -21. Factor 0 + 1/7*t**n + 0*t - 1/7*t**3.
-t**2*(t - 1)/7
Suppose -11*z - 3*s = -12*z - 9, 0 = 4*z - 3*s. Find r, given that -2/7*r**2 - 6/7 + 10/7*r - 2/7*r**z = 0.
-3, 1
Let g = -139 + 140. Let h be 8/8*((-4)/(-3))/g. Factor 8/3*o**2 - 2/3*o**3 - 10/3*o + h.
-2*(o - 2)*(o - 1)**2/3
Let z(b) be the third derivative of -b**5/12 + 5*b**4/8 - 33*b**2. What is y in z(y) = 0?
0, 3
Suppose 5*r - 5*u - 10 = 0, 3*r - 4*u = 4*r - 2. Let y(o) be the second derivative of 0 - 1/12*o**4 + 2*o - 1/3*o**3 - 1/2*o**r. Factor y(l).
-(l + 1)**2
Let m be -2 - ((-2 - 10) + 0). Let b be (-7)/(-2) + (-5)/m. Let -54*c**2 - 6*c**2 - 10*c**b + 79*c**3 + 12*c - 21*c**4 = 0. What is c?
0, 2/7, 1, 2
Let s = -13124 - -39848/3. Let q = -158 + s. Let -q*m**2 + 8/3 - 2/3*m**3 + 8/3*m = 0. What is m?
-2, -1, 2
Let b(y) = 8*y**2 + 24*y + 20. Let n = 20 + -25. Let j = n + 6. Let q(o) = o**2 + o + 1. Let c(h) = j*b(h) - 4*q(h). Let c(k) = 0. Calculate k.
-4, -1
Let g(r) be the third derivative of -r**7/240 + 13*r**6/240 + r**5/10 - 3*r**4/4 + 2*r**2. Let x(t) be the second derivative of g(t). Factor x(b).
-3*(b - 4)*(7*b + 2)/2
Let a be 16 + 5/(15/(-9)). Suppose 5*g = -4*t + g - 12, 0 = t + 3*g + a. Factor t*v**3 - 7*v - 4*v**2 + 0*v**3 + 7*v.
2*v**2*(v - 2)
Let f(x) be the third derivative of x**7/42 + x**6/6 - 29*x**5/6 - 155*x**4/6 - 105*x**3/2 + 61*x**2. Determine q so that f(q) = 0.
-9, -1, 7
Let n(k) be the second derivative of -k**8/1344 - k**7/126 - 5*k**6/144 - k**5/12 + 2*k**4/3 - 4*k. Let l(f) be the third derivative of n(f). Factor l(x).
-5*(x + 1)**2*(x + 2)
Suppose -33 = -3*o - 0*o. Let t(a) = a - 7. Let w be t(o). Determine s so that w*s**2 + 3*s**3 - 3*s**2 + 0*s**2 + 3*s + 5*s**2 = 0.
-1, 0
Let m(z) be the first derivative of z**3/4 - 87*z**2/8 + 21*z - 4. Determine v, given that m(v) = 0.
1, 28
Suppose 2*a = 8*a - 10*a. Suppose 0*n - 2/9*n**3 + 0 + 2/9*n**5 + a*n**4 + 0*n**2 = 0. Calculate n.
-1, 0, 1
Let d(h) be the first derivative of -h**6/1080 + 7*h**5/540 - 5*h**4/72 + h**3/6 - 8*h**2 + 5. Let g(b) be the second derivative of d(b). Factor g(r).
-(r - 3)**2*(r - 1)/9
Let s(h) = 32*h**3 + 54*h**2 + 6*h - 16. Let u(r) = r**3 + 2*r**2 - 1. Let o(w) = s(w) - 6*u(w). Factor o(b).
2*(b + 1)**2*(13*b - 5)
Let w(h) = 3*h**4 + 19*h**3 - 56*h**2 + 15*h + 39. Let n(a) = -a**4 - 20*a**3 + 53*a**2 - 14*a - 38. Let v(s) = -3*n(s) - 2*w(s). What is x in v(x) = 0?
-2/3, 2, 3
Let l(g) be the second derivative of g**6/30 - 2*g**5/15 - g**4/2 + 21*g**2/2 - 20*g. Let z(i) be the first derivative of l(i). Factor z(j).
4*j*(j - 3)*(j + 1)
Factor -52/11*l**2 - 16 - 2/11*l**3 - 184/11*l.
-2*(l + 2)**2*(l + 22)/11
Let c be (-2 + 10/6)*-12. Suppose 0 + 9 = 3*p. Suppose 1/5*k**c + 0 + 0*k**p - 3/5*k**2 + 2/5*k = 0. What is k?
-2, 0, 1
Let m(b) = -b**3 - 2*b**2 + 2*b + 6. Let j be m(-2). Let z be j/(12/2)*1. What is a in -z*a**2 - 2/3 - a = 0?
-2, -1
Let i(g) be the second derivative of -g**2 + 5/6*g**3 + 1/20*g**5 - 1/3*g**4 - 5*g + 0. Find b such that i(b) = 0.
1, 2
Suppose -6*k - 45 = 3. Let v = 4 - k. Factor g + v*g - g - 3*g**2 - 12.
-3*(g - 2)**2
Let l(k) be the second derivative of -k**4/4 + 26*k**3/3 - 47*k**2/2 + 33*k. Let b(u) = 35*u**2 - 625*u + 565. Let r(w) = 2*b(w) + 25*l(w). Factor r(a).
-5*(a - 9)*(a - 1)
Let m = 6375 + -95623/15. Let -m*d**2 - 2/15*d**3 + 0 + 0*d = 0. Calculate d.
-1, 0
Let v(c) be the second derivative of 2*c**6/15 + 9*c**5/5 - 7*c**4 + 22*c**3/3 - 18*c. Factor v(s).
4*s*(s - 1)**2*(s + 11)
Determine u so that 60*u**4 + 4941 - 29*u**4 - 41*u**3 - 8336 - 32*u**4 - 5245 - 3888*u - 612*u**2 = 0.
-12, -5
Let x(a) be the second derivative of a**4/9 + 8*a**3/3 - 20*a - 2. Suppose x(o) = 0. What is o?
-12, 0
Suppose -a + 10 = -3*a. Let z be -8*(20/8)/a. Factor -2*p**z + 5*p**2 - p**4 - 4*p**3 + 7*p**3 - 2*p**2 - 3*p**5.
-3*p**2*(p - 1)*(p + 1)**2
Let z(c) be the first derivative of -c**4/12 + 5*c**3/3 - 25*c**2/2 + c - 2. Let w(h) be the first derivative of z(h). Suppose w(q) = 0. Calculate q.
5
Let m(k) = k**2 - 7*k - 10. Let i be m(9). Factor 4*l**2 - i + 0 - 8.
4*(l - 2)*(l + 2)
Let h(f) = -f - 8. Let p be h(-10). Factor -15*l**4 + 5*l**3 + 0*l**p + 7*l**2 - 3*l**5 + 8*l**5 + 8*l**2 - 10*l.
5*l*(l - 2)*(l - 1)**2*(l + 1)
Let c = -299 + 302. Let o(p) be the third derivative of -4/3*p**c - 1/30*p**5 - 6*p**2 + 0 + 0*p - 1/3*p**4. Find b, given that o(b) = 0.
-2
Let f(v) be the second derivative of v**5/15 - 8*v**4/9 + 8*v**3/3 - v - 126. Suppose f(s) = 0. Calculate s.
0, 2, 6
Let x be (-6)/4 - (54/(-12) - 5). Let f = -59 - -99. Factor 2*j**5 + 2*j - 40 + 12*j**3 - x*j**4 - 8*j**2 + f.
2*j*(j - 1)**4
Suppose 3*s + s + n = 213, -2*s + 93 = 5*n. Let i = -266/5 + s. Find p, given that -4/5*p**2 + 4/5 + 4/5*p**3 - i*p = 0.
-1, 1
Let z(q) be the second derivative of -q**5/45 + 17*q**4/27 - 142*q**3/27 + 110*q**2/9 - 164*q. Let z(b) = 0. What is b?
1, 5, 11
Let p(a) be the first derivative of -a**8/84 + 4*a**7/105 - 2*a**5/15 + a**4/6 + 15*a**2/2 - 6. Let y(r) be the second derivative of p(r). Factor y(i).
-4*i*(i - 1)**3*(i + 1)
Solve 3/8*a**3 + 0*a + 93/8*a**2 + 0 = 0.
-31, 0
Let t(v) = 12*v**4 + 22*v**3 + 44*v**2 - 125*v - 154. Let y(s) = 5*s**4 + 11*s**3 + 22*s**2 - 62*s - 76. Let j(h) = -2*t(h) + 5*y(h). Let j(n) = 0. What is n?
-6, -1, 2
Let h(a) be the first derivative of a**6/8 + 3*a**5/5 + 3*a**4/16 - 3*a**3/2 - 102. Let h(c) = 0. Calculate c.
-3, -2, 0, 1
Let d(v) be the second derivative of v**6/75 + 3*v**5/50 - v**4/10 - 11*v**3/15 - 6*v**2/5 - 7*