2*j + 3. Let k be n(-4). Factor 2*a**2 - 3*a**2 - 4*a**3 - 4*a**2 - 2*a**4 + 3*a**k.
-2*a**2*(a + 1)**2
Let z(v) = -v**2 - v. Let j(t) = t**2 - 44*t + 147. Let s(c) = -j(c) + 2*z(c). Factor s(n).
-3*(n - 7)**2
Solve -3*u**4 - 3*u**3 - 4*u**4 + 20*u + 20*u**5 - 37*u**3 + 10*u**2 - 5 + 2*u**4 = 0 for u.
-1, 1/4, 1
Let v be (1/15)/(10 + 6). Let d(y) be the third derivative of 2*y**2 + 0 - 1/48*y**4 - 1/24*y**3 - v*y**5 + 0*y. Factor d(m).
-(m + 1)**2/4
Let a(z) be the second derivative of z**4/14 + 5*z**3/21 + 2*z**2/7 - 8*z. Solve a(p) = 0 for p.
-1, -2/3
Suppose -5*d = -35 - 5. Let s = d + -5. Factor 0 - 4/9*w - 2/9*w**2 + 2/3*w**s.
2*w*(w - 1)*(3*w + 2)/9
Suppose c = -1 + 3. Solve 2/7*x + 2/7*x**3 + 0 + 4/7*x**c = 0 for x.
-1, 0
Let p be 3 + (-66)/(-4) + -2. Let q = 18 - p. Factor 0*y + 1/2*y**3 + q*y**2 + 0.
y**2*(y + 1)/2
Let x(r) be the third derivative of -r**8/168 + r**7/105 + r**6/20 - r**5/30 - r**4/6 + 3*r**2. Suppose x(h) = 0. What is h?
-1, 0, 1, 2
Suppose 5*b - 7*l + 146 = -3*l, b + 5*l = -35. Let y = b - -34. What is m in 0*m**y + 2/3*m**3 + 0*m**2 + 0 + 0*m - 2/3*m**5 = 0?
-1, 0, 1
Let t be (-13 + 14)*(6/21 + 0). Solve 2/7*q**3 + 0*q + 0 - t*q**2 = 0 for q.
0, 1
Let i(n) = 2*n - 9. Let d be i(6). Let y(v) be the third derivative of 1/30*v**5 + 4/3*v**d - v**2 + 1/3*v**4 + 0*v + 0. Factor y(k).
2*(k + 2)**2
Let f = 979 + -6843/7. Find k, given that f*k**2 + 6/7 - 2*k - 2/7*k**3 = 0.
1, 3
Let u be 1/(-3) + 14/6. Let c(n) = -n**3 + 5*n**2 - 3*n + 2. Let m be c(3). Let -7 + m*k**2 + 18*k - 35*k**u + 3 + 10*k**3 = 0. What is k?
2/5, 1
Suppose -51*y = -89*y + 76. Suppose -1/8*g + 0 + g**2 + y*g**5 - 15/8*g**3 - g**4 = 0. Calculate g.
-1, 0, 1/4, 1
Let k be 10/(-4) + 5/2. Factor 1/3 + k*p - 1/3*p**2.
-(p - 1)*(p + 1)/3
Let t(v) be the third derivative of v**5/360 + v**4/144 - v**3/18 + 18*v**2. Factor t(p).
(p - 1)*(p + 2)/6
Let x be 0/(-1)*-1 + 4. Let n be 4 - (-2 + -2 + x). Factor 2*g - 3*g**2 - 2*g**2 + n*g**2 - 1.
-(g - 1)**2
Suppose 2*l - 33 = 5. Let b = -35/2 + l. Determine s, given that -3/2*s + 1/2*s**5 + s**2 - b*s**4 + s**3 + 1/2 = 0.
-1, 1
Let w(j) be the second derivative of -j**6/70 + 9*j**5/140 - 3*j**4/28 + j**3/14 + 5*j. What is d in w(d) = 0?
0, 1
Let z(f) = 28*f**4 - 7*f**3 - 72*f**2 + 80*f - 23. Let x(c) = 365*c**4 - 90*c**3 - 935*c**2 + 1040*c - 300. Let p(a) = -3*x(a) + 40*z(a). Factor p(v).
5*(v - 1)**2*(v + 2)*(5*v - 2)
Let w(b) be the second derivative of b**7/3360 - b**6/720 + b**5/480 - b**3/2 - 3*b. Let k(f) be the second derivative of w(f). Factor k(h).
h*(h - 1)**2/4
Let y(q) be the first derivative of -3*q**5/5 + 3*q**4/2 - q**3 - 15. Suppose y(v) = 0. Calculate v.
0, 1
Let k(r) be the third derivative of -r**8/8400 - r**7/4200 + r**6/900 - r**3/6 + 4*r**2. Let n(f) be the first derivative of k(f). Factor n(l).
-l**2*(l - 1)*(l + 2)/5
Let h = 0 + 2. What is k in 2*k**2 + 7*k + h*k**2 - 11*k = 0?
0, 1
Let p be 162/3*4/32. Factor 3/4*z**2 - 9/2*z + p.
3*(z - 3)**2/4
Let f = -277919/180 + 1544. Let u(m) be the third derivative of 0*m + 2*m**2 + 0 - 1/18*m**3 + 0*m**4 + f*m**5. Find t, given that u(t) = 0.
-1, 1
Let b(n) be the second derivative of -n**4/54 - 2*n**3/27 + n**2/3 + 6*n. Factor b(f).
-2*(f - 1)*(f + 3)/9
Solve -40*m - 6*m**2 - 12 - 68 + m**2 = 0 for m.
-4
Find s, given that -17/7*s**2 + 9/7*s + 3/7*s**3 + 5/7 = 0.
-1/3, 1, 5
Suppose 2*b + 0*y - 29 = -5*y, 17 = b + 3*y. Factor -1/6*w**b + 2/3*w - 2/3.
-(w - 2)**2/6
Let q(x) = -x**3 - 3*x**2 + x + 4. Let b be q(-3). Suppose -3*u + b = -5. Factor -u*m**2 + 2*m**4 - 2 + m**5 + 2 - m.
m*(m - 1)*(m + 1)**3
Let k be 11/(-66) - (-14)/36. Factor 0*j + 8/9 - k*j**2.
-2*(j - 2)*(j + 2)/9
Suppose -3/4*c**5 + 9/4*c**3 + 0*c + 3/2*c**2 + 0 + 0*c**4 = 0. Calculate c.
-1, 0, 2
Let w be 3*-1*(6/2 - 4). Factor 14*j**w - 2*j - 2 + 55/2*j**2.
(j + 2)*(4*j + 1)*(7*j - 2)/2
Let d(j) be the third derivative of -2*j**7/105 - 7*j**6/30 - 6*j**5/5 - 10*j**4/3 - 16*j**3/3 + 6*j**2. Factor d(l).
-4*(l + 1)*(l + 2)**3
Let o(l) be the first derivative of -2*l**5/5 + 3*l**4 - 10*l**3/3 + 26. Determine n, given that o(n) = 0.
0, 1, 5
Let p = -34123/37296 - -169/144. Let t = p - -1/37. Factor -2/7*d**5 - t*d + 0*d**2 + 0*d**4 + 4/7*d**3 + 0.
-2*d*(d - 1)**2*(d + 1)**2/7
Let t(z) be the third derivative of z**5/60 - z**4/3 + 5*z**3/2 + 4*z**2. Let g be t(6). Let 0*v - 2/7*v**4 + 0 - 6/7*v**g - 4/7*v**2 = 0. What is v?
-2, -1, 0
Let y(d) be the second derivative of d**6/300 - d**4/20 + 2*d**3/15 - 9*d**2/2 - 5*d. Let f(r) be the first derivative of y(r). Factor f(v).
2*(v - 1)**2*(v + 2)/5
Suppose -t = -v, 3*v - 10 + 4 = -3*t. Suppose 0 = 4*q - 9 + v. Suppose 1/4*i**q + 0*i + 0 = 0. Calculate i.
0
Factor -180*p - 12*p**3 + 3*p**5 + 8 - 2 + 189*p - 6*p**2.
3*(p - 2)*(p - 1)*(p + 1)**3
Factor 0 + 2/9*r**2 - 2/9*r**4 + 0*r + 0*r**3.
-2*r**2*(r - 1)*(r + 1)/9
Factor 0*l**3 - 13*l - 5*l**2 + 3 + l**3 + 3*l**2 - 13.
(l - 5)*(l + 1)*(l + 2)
Suppose 6 + 9 = 3*m. Let k = -421/5 - -85. Let k + 28/5*b**3 + 32/5*b**2 + 18/5*b + 12/5*b**4 + 2/5*b**m = 0. Calculate b.
-2, -1
Let q = 116 + -112. Factor 1/3*s**3 + 0 + 1/3*s**q + 0*s - 1/3*s**5 - 1/3*s**2.
-s**2*(s - 1)**2*(s + 1)/3
Factor 0 + 2/7*o**3 - 4/7*o - 2/7*o**2.
2*o*(o - 2)*(o + 1)/7
Let t = -75 - -75. Factor 0 + 0*z**2 + t*z + 6/7*z**4 - 4/7*z**3 - 2/7*z**5.
-2*z**3*(z - 2)*(z - 1)/7
Let j(h) = 12*h**2 + 10*h - 1. Let u(a) = -a**2. Let w(v) = -4*j(v) - 4*u(v). Factor w(m).
-4*(m + 1)*(11*m - 1)
Let l(o) be the first derivative of -3 - 4/3*o**3 - 2/45*o**5 - 4/9*o**4 + 6*o + 0*o**2. Factor l(z).
-2*(z - 1)*(z + 3)**3/9
Let u = -291/4 - -73. Let k(d) be the second derivative of 0*d**2 + 3/20*d**5 - 1/2*d**3 + 3*d + 0 + 1/10*d**6 - u*d**4. Factor k(x).
3*x*(x - 1)*(x + 1)**2
Suppose s = 1 + 1. Factor s*r + 3*r**3 + 2*r - 3*r**2 - r**4 + 8 - 8*r**3 - 3*r**2.
-(r - 1)*(r + 2)**3
Let n = 9 - 21. Let o be 5/9*n/(-10). Factor 4*z**2 + 8*z + 16/3 + o*z**3.
2*(z + 2)**3/3
Let l(d) = -7*d**2 - 4*d - 5. Let w(n) = -8*n + n - 7 - n**2 + n - 9*n**2. Let f(g) = -7*l(g) + 5*w(g). Factor f(c).
-c*(c + 2)
Let w = -7 - -13. Let f = w + -4. Suppose c + 2*c**3 + c**3 + f*c**2 - 2*c**3 = 0. Calculate c.
-1, 0
Let d(l) be the second derivative of -l**9/4320 - l**8/6720 + l**7/720 + l**6/720 - 7*l**4/12 - 5*l. Let b(c) be the third derivative of d(c). Solve b(t) = 0.
-1, -2/7, 0, 1
Let u(y) be the first derivative of -2/15*y**3 - 3/5*y**2 + 2 - 2*y + 1/30*y**4. Let n(p) be the first derivative of u(p). Factor n(m).
2*(m - 3)*(m + 1)/5
Let t(c) be the second derivative of 0*c**3 + 0 + 1/20*c**6 + 0*c**2 - 1/84*c**7 + 1/24*c**4 + 3*c - 3/40*c**5. Factor t(a).
-a**2*(a - 1)**3/2
Let b = -1265/4 + 13987/44. Let -b*y**3 + 0*y + 0 + 8/11*y**4 + 4/11*y**2 = 0. Calculate y.
0, 1/4, 2
Let c(v) be the third derivative of v**6/280 - v**5/70 + v**4/56 + 8*v**2. Factor c(a).
3*a*(a - 1)**2/7
Let o be (415/(-100) - -4)*-2. Let l(p) be the first derivative of 2/3*p**3 - 1/5*p**2 - 2 + 4/15*p**6 - 2/5*p**5 + 0*p - o*p**4. Solve l(z) = 0.
-1, 0, 1/4, 1
Factor -1/6*b**2 + 1/6*b + 0.
-b*(b - 1)/6
Let y(n) = -n**4 + n**3 + 5*n**2 - 3. Let z(f) = -f**4 - f**3 - f**2 + 1. Let d(w) = w + 3. Let l be d(-2). Let i(k) = l*y(k) + z(k). Solve i(v) = 0.
-1, 1
Let h = 295/582 + -2/291. Let r(a) be the second derivative of 1/4*a**4 + h*a**3 + 3*a + 0 - 3*a**2. Suppose r(w) = 0. What is w?
-2, 1
Suppose 25 = -5*g - 5*s, g = -3*g + 2*s - 38. Let q be 40/75*(-100)/g. Find l such that 4/3 + q*l + 25/3*l**2 = 0.
-2/5
Factor 4*a**4 + 24*a**2 - 7*a**2 + 40*a**3 + 18*a**2 + 11*a**4 + 10*a.
5*a*(a + 1)**2*(3*a + 2)
Let x(h) be the first derivative of -h**6/33 + h**4/11 - h**2/11 - 7. Suppose x(z) = 0. What is z?
-1, 0, 1
Suppose -5*d + 12*d + 77 = 0. Let j = d + 13. Factor 0*t**2 - 2/3*t**3 + 4/3 + j*t.
-2*(t - 2)*(t + 1)**2/3
Let a be (36/15 + -2)*-15. Let b be ((-4)/(-6))/((-2)/a). Solve -1/4*d**3 + 0*d**b + 1/2 + 3/4*d = 0 for d.
-1, 2
Let d be 32/176 - (-31)/11. Let n(h) be the first derivative of 0*h**5 + 0*h + 0*h**2 + 0*h**3 - 1/12*h**6 + 1/8*h**4 - d. Factor n(w).
-w**3*(w - 1)*(w + 1)/2
Suppose -19*a - a = -100. Factor 1/2*y**2 + 3/2*y**4 + 1/2*y**a + 0*y + 0 + 3/2*y**3.
y**2*(y + 1)**3/2
Factor 0*v - 2/5*v**5 + 0 - 2/5*v**3 + 0*v**2 + 4/5*v**4.
-2*v**3*(v - 1)**2/5
Let r(z) = -9*z**4 + 