5, 1
Let a(h) be the first derivative of h**7/189 - h**5/90 - 14*h + 10. Let r(l) be the first derivative of a(l). Find m, given that r(m) = 0.
-1, 0, 1
Let j(h) = -2*h**2 + 2. Let p(y) = 10*y**2 - 18*y + 20. Let z(w) = 4*j(w) + p(w). Factor z(k).
2*(k - 7)*(k - 2)
Let o be 7 - (8/1 - 4). Factor -7*n**2 + 7*n**o + 8*n + 16 - 3*n**3 + 0*n**2 - 3*n**3.
(n - 4)**2*(n + 1)
Suppose -3872*i - 88*i**2 - 1/2*i**3 + 0 = 0. Calculate i.
-88, 0
Let v(c) be the second derivative of 9*c**5/70 + 43*c**4/42 - 64*c**3/21 + 12*c**2/7 + c + 18. Let v(k) = 0. Calculate k.
-6, 2/9, 1
Let s(k) = -5*k**4 + 56*k**3 - 339*k**2 + 828*k - 538. Let f(g) = 21*g**4 - 225*g**3 + 1356*g**2 - 3312*g + 2151. Let w(d) = 2*f(d) + 9*s(d). Factor w(c).
-3*(c - 6)**2*(c - 5)*(c - 1)
Let c(v) = 6*v**4 - 5*v**3 + 3*v**2 + 1. Let q be (12/10)/(24/80). Let o(x) = 5*x**4 - 4*x**3 + 2*x**2 + 1. Let u(p) = q*c(p) - 5*o(p). Factor u(r).
-(r - 1)**2*(r + 1)**2
Let a(q) be the second derivative of 2*q**7/35 + q**6/3 + 5*q**5/6 - 17*q**4/12 + 40*q. Let j(r) be the third derivative of a(r). Factor j(u).
4*(6*u + 5)**2
Let a(j) be the second derivative of 25*j**7/14 - 31*j**6/2 - 102*j**5/5 - 7*j**4 - 833*j. Factor a(g).
3*g**2*(g - 7)*(5*g + 2)**2
Let h(k) = -16*k - 93. Let m be h(-6). Let r(l) be the first derivative of 0*l**2 - 3 - l**m + 3/5*l**5 + 0*l + 3/4*l**4 - 1/2*l**6. Let r(s) = 0. Calculate s.
-1, 0, 1
Let y(i) be the first derivative of 5*i**3/12 + 155*i**2/2 + 4805*i + 325. Find t, given that y(t) = 0.
-62
Solve -9*k - 32*k + 4*k**3 + 24*k**2 - 35*k + 16 + 112*k = 0 for k.
-4, -1
Let q(z) = -18*z - 156. Let s be q(-9). Let y(f) be the second derivative of -1/150*f**s + 4*f - 2/15*f**4 + 2/15*f**3 + 0*f**2 + 0 + 1/20*f**5. Factor y(u).
-u*(u - 2)**2*(u - 1)/5
Let d = 20 - 14. Let b = -4 + d. Factor -4*o**2 + 0*o**2 + 0*o + 5*o**b + o.
o*(o + 1)
Let s(b) = -1. Let u(c) = -15*c**2 + 36*c - 10. Let x = -44 + 45. Let n(z) = x*u(z) + 2*s(z). Determine i, given that n(i) = 0.
2/5, 2
Let m = 123 - 121. Factor -2*h**2 + h**m - 21*h + 42*h - 14*h.
-h*(h - 7)
Suppose 61*q - 22*q - 24*q = 0. Factor 0 + 4/5*k**3 + q*k + 1/5*k**5 + 0*k**2 - k**4.
k**3*(k - 4)*(k - 1)/5
Let j(b) be the third derivative of 0 + 0*b**4 + 4/15*b**3 - 1/150*b**5 + 0*b + 8*b**2. Factor j(z).
-2*(z - 2)*(z + 2)/5
Let c(s) be the first derivative of -2*s**3/15 - 22*s**2/5 - 192*s/5 + 563. Factor c(i).
-2*(i + 6)*(i + 16)/5
Let f be (30/(-180))/((-5)/60). Factor -39/5*p**3 + 0 - 36/5*p**f - 18/5*p**4 - 12/5*p - 3/5*p**5.
-3*p*(p + 1)**2*(p + 2)**2/5
Suppose 93 + 105 = 11*c. Let p be (-11)/(-6) + -2 + 3/c. Factor p + 0*j + 4/13*j**2 + 6/13*j**3 + 2/13*j**4.
2*j**2*(j + 1)*(j + 2)/13
Let d = 17521/4 + -4380. Factor -1/4*s**2 - d*s**3 + 0 + 0*s.
-s**2*(s + 1)/4
Let u(f) be the first derivative of -4*f**3/15 + 6*f**2 + 64*f/5 + 95. Determine b, given that u(b) = 0.
-1, 16
Let g(l) be the third derivative of 0*l + 0*l**3 - 1/360*l**5 - 15*l**2 + 1/72*l**4 + 0. Find u such that g(u) = 0.
0, 2
Let i = 7 - 7. Suppose 8*k - 49 = -1. Solve i*d - 6*d - 4*d**2 - k*d = 0 for d.
-3, 0
Let t(d) be the second derivative of -d**7/280 + d**6/240 + d**5/40 - d**4/16 + d**3 + 4*d. Let b(o) be the second derivative of t(o). Factor b(h).
-3*(h - 1)*(h + 1)*(2*h - 1)/2
Let c = 116 - 122. Let f(m) = -6*m - 34. Let q be f(c). Determine u so that -1/3*u**q + 0*u + 0 + 1/3*u**3 = 0.
0, 1
Determine q so that 0 - 16/13*q - 2/13*q**3 - 12/13*q**2 = 0.
-4, -2, 0
Factor -14*p - 16*p**2 - 985*p**3 + 488*p**3 + 495*p**3.
-2*p*(p + 1)*(p + 7)
Let o be 1/((-1)/6*-2). Suppose 0 = -a + o. Determine m, given that 2 + 6*m + a*m**2 + 7 - 2 - 4 = 0.
-1
Let z = -27 + 19. Let q be (z/20)/(4/(-20)). Factor 3*i**3 - 2*i**4 + 10*i**q + i**3 - 3*i**4 + i**3.
-5*i**2*(i - 2)*(i + 1)
Let s(n) be the second derivative of 1/150*n**6 - 1/10*n**3 + 3/100*n**5 + 0 - 3*n + 0*n**2 - 1/60*n**4. Factor s(d).
d*(d - 1)*(d + 1)*(d + 3)/5
Let c(t) be the first derivative of -t - 1/12*t**4 + 0*t**2 + 7 - 1/24*t**3. Let y(l) be the first derivative of c(l). Factor y(j).
-j*(4*j + 1)/4
Let n(b) be the third derivative of 0*b + 11/6*b**6 + 1/6*b**7 + 115/12*b**4 + 0 + 25/4*b**5 + 20/3*b**3 + 11*b**2. Suppose n(m) = 0. Calculate m.
-4, -1, -2/7
Let f(y) be the first derivative of 2*y**5/5 - 5*y**4/2 + 4*y**3/3 + 20*y**2 - 48*y + 684. Factor f(h).
2*(h - 3)*(h - 2)**2*(h + 2)
Let r = 7607 - 7604. Let -2/7*y**4 + 0 - 6/7*y**r + 2/7*y**5 + 2/7*y**2 + 4/7*y = 0. What is y?
-1, 0, 1, 2
Let k(z) be the third derivative of 1/10*z**5 + 1/40*z**6 - z**3 + 0*z + z**2 - 1/8*z**4 + 0. Find j, given that k(j) = 0.
-2, -1, 1
Let p(a) be the first derivative of 0*a**2 + 1/10*a**5 - 2 - 1/3*a**3 + 2*a + 0*a**4. Let x(w) be the first derivative of p(w). Factor x(u).
2*u*(u - 1)*(u + 1)
Let t(j) = j**2 - 29*j + 33. Let w(s) = s - 2. Let i(b) = -t(b) - 5*w(b). Factor i(r).
-(r - 23)*(r - 1)
Let s = -110 - -115. Let d(i) = -6*i**3 - 18*i**2 - 7*i - 5. Let u(g) = -2 - 9*g**3 - 9 - 10*g - 27*g**2 + 3. Let k(z) = s*u(z) - 8*d(z). Factor k(r).
3*r*(r + 1)*(r + 2)
Let t(i) be the third derivative of 7/120*i**6 + 0*i - 1/12*i**4 + 0 + 0*i**3 + 1/12*i**5 - 4*i**2. Factor t(d).
d*(d + 1)*(7*d - 2)
Find h, given that -16 + 3*h + h**2 + h**2 + 2*h + 5*h - 14*h = 0.
-2, 4
Let g(c) be the first derivative of c**7/840 + c**6/120 - c**4/6 - 16*c**3/3 - 5. Let t(j) be the third derivative of g(j). Let t(u) = 0. Calculate u.
-2, 1
Let s(k) be the third derivative of 0*k**3 + 0*k**4 - 1/280*k**7 + 0 + 1/1344*k**8 - 1/120*k**6 + 0*k + 0*k**5 + 15*k**2. Factor s(n).
n**3*(n - 4)*(n + 1)/4
Let o(b) be the second derivative of -b**7/294 + b**6/30 + 3*b**5/70 - 25*b**4/42 + 59*b**3/42 - 3*b**2/2 - 415*b. Factor o(h).
-(h - 7)*(h - 1)**3*(h + 3)/7
Let -196/13*w**3 - 14/13*w**5 + 94/13*w**4 + 48/13*w + 0 + 8*w**2 = 0. What is w?
-2/7, 0, 2, 3
Let z(m) be the third derivative of m**2 + 0 + 1/210*m**5 + 2*m - 10/21*m**3 + 1/28*m**4. Factor z(g).
2*(g - 2)*(g + 5)/7
Factor 57/2*d**3 - 841/2*d + 0 - 1/2*d**4 - 783/2*d**2.
-d*(d - 29)**2*(d + 1)/2
Let g(v) be the second derivative of v**5/20 - 2*v**4/3 + 10*v**3/3 - 8*v**2 - 33*v + 2. Factor g(c).
(c - 4)*(c - 2)**2
Let a(i) be the second derivative of i**4/8 - 11*i**3/2 + 363*i**2/4 + 136*i. Solve a(p) = 0.
11
Suppose -7*j + 5*j = -24. Suppose 0 = a + j - 14. Factor 1/3*s**a + 0*s - 1/3.
(s - 1)*(s + 1)/3
Factor -12547 - 5*u**2 - 15*u + 12547.
-5*u*(u + 3)
Suppose -3*i = -2*h + 3 + 6, 5*i + 15 = 3*h. Let q be 6 - ((2 - -2) + (-2)/2). Factor 0 + 2/5*w**2 - 6/5*w**4 - 4/5*w**5 + 0*w**q + h*w.
-2*w**2*(w + 1)**2*(2*w - 1)/5
Let l(g) be the second derivative of g**6/15 + 3*g**5/20 - 23*g**4/12 - 2*g**3 + 376*g. Factor l(c).
c*(c - 3)*(c + 4)*(2*c + 1)
Let i(c) = -85*c**3 + 4*c**2 + 340*c - 46. Let h(r) = 765*r**3 - 35*r**2 - 3060*r + 415. Let w(q) = -6*h(q) - 55*i(q). Factor w(z).
5*(z - 2)*(z + 2)*(17*z - 2)
Let u(y) be the second derivative of 5/2*y**4 - 29*y + 0 + 5/2*y**2 + 10/3*y**3 + 1/6*y**6 + y**5. Factor u(k).
5*(k + 1)**4
Let w be (-2)/10 + ((-6)/15)/(-2). Suppose -7*d + w*d = -21. Factor -2/7*o**d - 2/7*o**4 + 2/7*o**5 + 2/7*o**2 + 0 + 0*o.
2*o**2*(o - 1)**2*(o + 1)/7
Let w(z) be the first derivative of -2*z**3/9 - 17*z**2/3 - 32*z/3 - 682. Factor w(u).
-2*(u + 1)*(u + 16)/3
Let l(b) be the first derivative of b**6/8 + 3*b**5/20 - 3*b**4/8 - b**3/2 + 3*b**2/8 + 3*b/4 - 81. Let l(y) = 0. Calculate y.
-1, 1
Let u(s) be the second derivative of -s**5/100 + s**4/12 - 4*s**3/15 + 2*s**2/5 + 3*s - 8. Solve u(m) = 0 for m.
1, 2
Let q be 1510/(-4550)*-25 + -1 + (-12)/(-14). Find p, given that 18/13*p**4 + q*p**3 - 14/13*p - 20/13*p**5 - 12/13 + 66/13*p**2 = 0.
-1, -1/2, 2/5, 3
Factor -8/3*u**2 + 5/3*u**3 + 4/3*u + 0 - 1/3*u**4.
-u*(u - 2)**2*(u - 1)/3
Let z(g) be the third derivative of 1/1680*g**8 + 0 + 0*g + 0*g**4 + 0*g**3 + 1/525*g**7 - 1/150*g**5 - 1/600*g**6 - 4*g**2. Factor z(l).
l**2*(l - 1)*(l + 1)*(l + 2)/5
Let z = 3461 - 3459. What is n in 1/3 + 5/6*n + 3/2*n**3 - 8/3*n**z = 0?
-2/9, 1
Let n(x) be the first derivative of -x**4/24 - x**3/3 - 3*x**2/4 + 113. Factor n(l).
-l*(l + 3)**2/6
Let y be (12/(216/45))/((-10)/(-8)). Factor 0 + 1/4*z + 3/4*z**4 + 1/4*z**y - 5/4*z**3.
z*(z - 1)**2*(3*z + 1)/4
Find h, given that 120*h**3 - 360*h**3 + 3*h**2 + 124*h**3 + 115*h**3 = 0