12)/(-1). Factor 1/2*k + u*k**2 + 0.
k*(6*k + 1)/2
Let b(w) = -w**3 - 3*w**2 + 5*w + 6. Let f be b(-4). Suppose f = 2*m + m - 2*t, 3*t = -3*m + 12. Factor -3*i**m + 2*i**2 + i + i - i**2.
-2*i*(i - 1)
Suppose 3*r = 3 - 6. Let p be (7 - r) + -2 - 4. Determine c, given that 2*c - 5*c - 3*c**2 - 8*c**p + 12*c**3 + 2*c**2 = 0.
-1/4, 0, 1
Factor -85*d - 194*d + 62*d**2 + 42 - 29*d**2 + 6*d**2.
3*(d - 7)*(13*d - 2)
Factor 351 + 345 + 3*p**2 - 696 - 18*p.
3*p*(p - 6)
Let m be 30/(-40) - ((-1870)/24)/(-5). Let n = m - -17. Let -2*q**2 + 0*q - n*q**3 + 0 = 0. What is q?
-3, 0
Let a be (-3 + 0)*1 + 5. Let -250/13 - 30/13*f**a + 2/13*f**3 + 150/13*f = 0. Calculate f.
5
Let x(a) be the first derivative of -a**7/1120 + a**6/240 - 5*a**3 + 5. Let g(i) be the third derivative of x(i). Factor g(o).
-3*o**2*(o - 2)/4
Let y be (105/(-5))/7*8/(-6). Suppose 4*q + 5*m = 5, 6*q - 4*m = q - y. Factor q*s - 6*s**4 - 2/3*s**5 - 18*s**2 + 0 - 18*s**3.
-2*s**2*(s + 3)**3/3
Suppose 4*l - 15 = 1. Factor 24*p**2 + 78*p**3 - 43*p**3 + l*p + 16*p**4 + p**3.
4*p*(p + 1)**2*(4*p + 1)
Let t(i) = -11*i**2 + 14*i - 14. Let a(k) = 13*k**2 - 15*k + 14. Let n(y) = -5*a(y) - 6*t(y). Suppose n(j) = 0. What is j?
2, 7
Let x(c) = -2*c**5 + 2*c**4 + 6*c**3 + c**2 + 4*c. Let w(q) = -12*q**3 + q - q**5 + q + q**2 + q**4 + 15*q**3. Let f(p) = 11*w(p) - 6*x(p). Factor f(k).
k*(k - 1)**3*(k + 2)
Let x(q) be the first derivative of q**3/30 - 17*q**2/20 + 8*q/5 + 124. Factor x(u).
(u - 16)*(u - 1)/10
Factor -266/11*j - 24 - 2/11*j**2.
-2*(j + 1)*(j + 132)/11
Let t(x) be the third derivative of 8*x**2 - 1/4*x**6 + 0*x - 1/1008*x**8 + 1/42*x**7 + 0 + 3/2*x**5 + 27/2*x**3 - 45/8*x**4. Let t(f) = 0. Calculate f.
3
Let t(d) = -d - 3. Suppose -29 = 2*r - 23. Let p be t(r). Factor -1/4*f**5 + 0 - 1/4*f**4 + p*f**3 + 0*f + 0*f**2.
-f**4*(f + 1)/4
Suppose -58 = h - 60. Determine w, given that w**2 - 9*w**3 + 7*w**3 + 6*w**4 - 7*w**h + 2*w**5 = 0.
-3, -1, 0, 1
Let j(h) = 14*h**2 - 2*h - 11. Let n(v) = -11*v**2 + 3*v + 10. Let w(i) = 4*j(i) + 5*n(i). Factor w(z).
(z + 1)*(z + 6)
Let k(t) be the second derivative of t**7/840 - t**6/40 + 9*t**5/40 - t**4/3 + 3*t. Let a(c) be the third derivative of k(c). Find w such that a(w) = 0.
3
Let w(q) be the first derivative of q**4/5 - 32*q**3/15 + 2*q**2 + 56*q/5 - 184. Factor w(s).
4*(s - 7)*(s - 2)*(s + 1)/5
Let v(i) be the third derivative of 0*i**7 - 8*i**2 + 5/336*i**8 + 0*i**3 - 1/24*i**6 + 0*i**5 + 0 + 0*i + 0*i**4. Determine u so that v(u) = 0.
-1, 0, 1
Let l(v) be the third derivative of -v**7/5880 + v**6/560 + 5*v**4/12 - v**2. Let t(b) be the second derivative of l(b). Let t(a) = 0. Calculate a.
0, 3
Suppose -4*n + 5*p = -76, -116 = -4*n - 9*p + 4*p. Let z = 28 - n. What is r in 0*r - 25/3*r**z - 4/3*r**2 + 20/3*r**3 + 0 = 0?
0, 2/5
Let a(t) = -2*t - 14. Let x be a(-11). Let m(w) = w**3 - 9*w**2 + 10*w + 9. Let l be m(x). Factor -3*d**3 + 12 + 13 - l + 3*d**2.
-3*d**2*(d - 1)
Determine m, given that -15 + 528*m - 181*m**2 - 79*m**2 - 1 = 0.
2/65, 2
Let t = 2682/29 + -18600/203. Solve 2/7*b**2 - 10/7*b**4 + 0*b + 0 - t*b**5 - 2/7*b**3 = 0.
-1, 0, 1/3
Let m(u) be the first derivative of -9/16*u**6 + 45/32*u**4 + 5/12*u**3 + 0*u**5 - u - 37 - 5/4*u**2. Solve m(s) = 0 for s.
-2/3, 1
Let n(y) = -7*y**4 - 14*y**3 - 28*y**2 + 18*y + 23. Let i(k) = 8*k**4 + 13*k**3 + 29*k**2 - 18*k - 22. Let s(z) = -4*i(z) - 5*n(z). Solve s(v) = 0.
-3, -1, 1
Let m(c) be the first derivative of c**5/5 - c**4 + c**3 + 2*c**2 - 4*c - 39. Factor m(y).
(y - 2)**2*(y - 1)*(y + 1)
Let c(n) be the first derivative of 7*n**3/3 - 53*n**2/2 - 60*n + 14. Let r(b) = 5*b**2 - 35*b - 40. Let q(j) = -5*c(j) + 8*r(j). Factor q(h).
5*(h - 4)*(h + 1)
Let i be 58/6 + 684/(-76). Factor 0 - i*a**2 - 4/3*a.
-2*a*(a + 2)/3
Let h(j) be the first derivative of -36 + 1/12*j**2 - 1/12*j**6 + 11/30*j**5 - 7/12*j**4 + 1/3*j**3 - 1/6*j. Factor h(b).
-(b - 1)**4*(3*b + 1)/6
Let u(z) be the second derivative of 19*z**5/5 - z**4/12 - 5*z**3/6 + z + 135. Determine o, given that u(o) = 0.
-1/4, 0, 5/19
Find v such that 4 - 12*v - 18 + 11*v**2 - 27*v**2 + 18*v**2 = 0.
-1, 7
Let k be (56/7 - 6)*30/20. Factor 0 - 2/7*s**k + 2/7*s**2 + 0*s.
-2*s**2*(s - 1)/7
Let b = -236 - -86. Let p = b + 601/4. Factor u**4 - u**2 + 0 - 1/4*u**3 + p*u.
u*(u - 1)*(u + 1)*(4*u - 1)/4
Suppose 0 = -5*d - 9*d. Let x(g) be the third derivative of 0*g**3 + 8*g**2 + 0 - 1/8*g**4 + d*g**5 + 1/40*g**6 + 0*g. Find l such that x(l) = 0.
-1, 0, 1
Factor 11 - 23*u + 1/4*u**4 - 4*u**3 + 63/4*u**2.
(u - 11)*(u - 2)**2*(u - 1)/4
Let b(t) be the first derivative of -t**3/2 - 63*t**2/4 - 2. Factor b(k).
-3*k*(k + 21)/2
Let h = -3630 - -3634. Factor -6*y**2 + 0 - 18/5*y**3 - 14/5*y - 2/5*y**h.
-2*y*(y + 1)**2*(y + 7)/5
Suppose -f - 5*i + 2*i = 147, 0 = -3*f + 4*i - 402. Let l = 140 + f. Suppose 3/2*n**l - 3/2 - 3/2*n + 3/2*n**3 = 0. Calculate n.
-1, 1
Let w(z) be the first derivative of -z**4/3 + 4*z**3/9 + 4*z**2/3 - 13. Find f, given that w(f) = 0.
-1, 0, 2
Let j(m) = -14*m + 125. Let k(y) = -y - 1. Let q(o) = -j(o) + 5*k(o). Let u be q(15). Factor 2/3*p**u - 4/3*p**4 + 0*p + 0*p**2 + 2/3*p**3 + 0.
2*p**3*(p - 1)**2/3
Let o = 12917 + -77477/6. Let 0*c + 0 + o*c**5 + 5*c**4 - 6*c**3 + 4/3*c**2 = 0. What is c?
-2, 0, 2/5
Let l be 38/6 + 2/(-6). Let d(p) = -p + 10. Let y be d(0). Determine i so that l + 6*i**2 - 2*i**3 - 4*i + 4 - y = 0.
0, 1, 2
Factor 2/3*k**2 - 36*k + 486.
2*(k - 27)**2/3
Suppose -19 = -22*f + 3*f. Let v(t) be the first derivative of 5/24*t**4 + 1/3*t + 1/2*t**3 + 1/30*t**5 + 7/12*t**2 + f. Factor v(p).
(p + 1)**3*(p + 2)/6
Let l(d) = d. Let y be l(0). Suppose y = -3*h + 2*h. Factor -4*b**2 + h*b**2 - 2 + b + 6*b - b**2.
-(b - 1)*(5*b - 2)
Let l(y) be the first derivative of y**7/2940 + y**6/630 + y**5/420 - 8*y**3 - 13. Let f(u) be the third derivative of l(u). Solve f(z) = 0.
-1, 0
Let l(v) be the second derivative of 0*v**3 + 0 + 0*v**2 + 5*v - 1/12*v**4. Find y such that l(y) = 0.
0
Let k(f) = 2*f + 2*f**2 + 1 + 15*f - 14*f. Let w(p) = 3*p**2 + 5*p + 3. Let l(a) = 5*k(a) - 3*w(a). Solve l(g) = 0 for g.
-2, 2
Let q(n) be the first derivative of n**3/18 + 5*n**2/12 + 2*n/3 + 1. Factor q(s).
(s + 1)*(s + 4)/6
Suppose 4*a - 22 = 2. Let u(p) = -11*p**4 + 5*p**3 + 5*p**2 - 11*p. Let m(v) = -21*v**4 + 10*v**3 + 10*v**2 - 21*v. Let w(y) = a*m(y) - 11*u(y). Solve w(l) = 0.
-1, 0, 1
Let a(w) be the third derivative of 0*w - 13*w**2 + 1/60*w**5 + 0*w**4 - 1/80*w**6 + 0 + 1/420*w**7 + 0*w**3. What is g in a(g) = 0?
0, 1, 2
Let i(t) = 18*t + 24 + 4*t**4 - 5*t**4 - 24*t**2 - 2*t**4 - 9*t**3. Let u(d) = 3*d**4 + 10*d**3 + 23*d**2 - 17*d - 24. Let n(m) = 5*i(m) + 6*u(m). Factor n(b).
3*(b - 1)*(b + 2)**3
Let n(l) = l**4 - l**2. Let a(j) = -3*j**4 + 45*j**3 + 3*j**2 - 45*j. Let i(t) = a(t) + 6*n(t). Factor i(q).
3*q*(q - 1)*(q + 1)*(q + 15)
Solve -2/3*m**3 + 6 - 10*m + 14/3*m**2 = 0 for m.
1, 3
Let m(g) = -4*g**4 - 36*g**3 + 153*g**2 - 182*g + 84. Let o(w) = -w**4 + w**3 + w + 2. Let t(r) = -m(r) + 5*o(r). Factor t(l).
-(l - 37)*(l - 2)*(l - 1)**2
Suppose -16/11*h + 14/11 + 2/11*h**2 = 0. What is h?
1, 7
Let m(g) be the second derivative of -5/24*g**3 - 4*g - 13/48*g**4 + 0 + 1/8*g**2 - 7/80*g**5. Factor m(i).
-(i + 1)**2*(7*i - 1)/4
Let t(d) = -13*d + 5 - 7 + 17*d - 10. Let i be t(4). Factor 0*b**2 + 3/4*b**3 - 3/4*b**i + 0*b + 0.
-3*b**3*(b - 1)/4
Let j(g) = -4*g - 35. Let q be j(-6). Let m = -75/7 - q. Suppose m*c**2 - 4/7*c**5 + 0 + 6/7*c**3 - 2/7*c - 2/7*c**4 = 0. Calculate c.
-1, 0, 1/2, 1
Let d be 4 + (2 - (-18)/(-3)). Let s be -1 + 4/2 + 1. Let 3*u**3 + 37*u + s - 34*u - 4*u**3 + d = 0. What is u?
-1, 2
Let m(i) = -7*i**3 - 76*i**2 - 241*i - 72. Let b(c) = -c**3 - 2*c**2 - c. Let v(k) = -2*b(k) + 2*m(k). Factor v(f).
-4*(f + 6)**2*(3*f + 1)
Let a(x) = x**2 - 4*x - 16. Let u be a(7). Suppose -14*j**5 - 56*j + 20*j**2 - 5*j**4 + 70*j**3 - u - 11 + j**4 + 0*j**4 = 0. Calculate j.
-2, -1, -2/7, 1, 2
Solve -1/8*p**2 + 3/8 - 5/8*p**3 + 5/8*p - 1/4*p**4 = 0.
-3/2, -1, 1
Let o = 10377 + -10375. Factor -4/19*k**o + 2/19*k**4 + 18/19 - 24/19*k + 8/19*k**3.
2*(k - 1)**2*(k + 3)**2/19
Let o(j) be the first derivative of 0*j**4 + 1/1440*j**6 + 0*j**2 + 0*j - 1/480*j**5 + 1 - 4/3*j**3. Let u(r) be the third derivative of o(r). Factor u(t).
t*(t - 1)