4/16 + 11*y**3/8 + 39*y**2/4 + 11*y - 1. Suppose l(p) = 0. Calculate p.
-2, 13
Let u be -5 + 196/76 + -2 + 4. Let c = u + 62/57. Suppose -8/3*h + c - 10/3*h**2 = 0. Calculate h.
-1, 1/5
Let h(l) be the second derivative of -l**7/147 + 6*l**6/35 - 29*l**5/35 + 4*l**4/7 + 59*l**3/21 - 6*l**2 + 854*l. Determine n, given that h(n) = 0.
-1, 1, 3, 14
Let s(r) = -r**3 + r - 2. Let c(f) = 8*f**3 - 28*f**2 - 95*f - 26. Let o(m) = -2*c(m) - 6*s(m). Factor o(v).
-2*(v - 8)*(v + 2)*(5*v + 2)
Suppose 0 = -4*d + 30 - 10. Factor 7*f**2 - d*f - 3*f**2 - 11*f + 4*f.
4*f*(f - 3)
Let p(t) be the third derivative of 11*t**8/8064 + t**7/84 + t**6/72 - 29*t**5/30 + 10*t**2 + 2. Let b(m) be the third derivative of p(m). Factor b(z).
5*(z + 2)*(11*z + 2)/2
Let q be (-190)/(-12) - 6/(-36). Find o, given that 14*o**4 - 15*o**3 + 6*o**2 - 2*o**4 - q - 3*o**5 + 16 = 0.
0, 1, 2
Let z be ((-4)/6)/(10/(-45)). Factor -3*d**4 + d**5 - 2*d**4 - 2*d**3 + z*d**5 + 3*d**3.
d**3*(d - 1)*(4*d - 1)
Suppose h + 11*h = 900. Factor -t**2 - 9*t**2 - 5*t**5 - h*t**4 - 8*t**3 + 55*t**4 - 17*t**3.
-5*t**2*(t + 1)**2*(t + 2)
Let s(o) be the first derivative of -o**9/5292 - o**8/2940 + o**7/1470 + o**6/630 - 10*o**3/3 - 1. Let f(w) be the third derivative of s(w). Factor f(q).
-4*q**2*(q - 1)*(q + 1)**2/7
Let p(s) = -s**2 + s - 1. Let y(f) be the first derivative of -20*f**3/3 + 10*f**2 - 16*f + 10. Let r(u) = 16*p(u) - y(u). Factor r(d).
4*d*(d - 1)
Factor -g**4 - 2*g**4 + 5*g**4 - 27*g**2 - 20*g + 8*g**3 + 21*g**2 + 16.
2*(g - 1)**2*(g + 2)*(g + 4)
Let p = 2 + -5. Let v be 80/84 + 1/p*2. Find w such that -2/7*w**2 + 1/7*w**5 + 3/7*w**4 + v*w**3 - 3/7*w - 1/7 = 0.
-1, 1
Let v = 7625 - 114367/15. Find m, given that -v*m - 2/15*m**2 - 8/15 = 0.
-2
Factor c + 0*c**3 + 5*c**3 + 73 - 159 + 76 - 16*c.
5*(c - 2)*(c + 1)**2
Let g(y) be the third derivative of 0 + 0*y**4 + 0*y + 0*y**3 + 1/300*y**5 + 29*y**2 - 1/600*y**6. Factor g(m).
-m**2*(m - 1)/5
Suppose 72 = -h + 10*h + 27. Find u such that -4*u**3 + 4/5 - 1/5*u**4 + 6/5*u**h - 9/5*u**2 + 8/5*u = 0.
-1, -1/2, 2/3, 2
Let g be (-2)/(-21)*(7 - 4). Suppose -3*t + 10*t = -8*t. Suppose g*y - 5/7*y**3 + 1/7*y**4 + t + 3/7*y**5 - 1/7*y**2 = 0. Calculate y.
-1, 0, 2/3, 1
Let p(t) be the third derivative of t**7/2100 + t**6/300 + t**5/150 + t**3/3 + 5*t**2. Let r(w) be the first derivative of p(w). Factor r(x).
2*x*(x + 1)*(x + 2)/5
Let r(i) be the second derivative of i**6/15 + 3*i**5/5 + 4*i**4/3 + 134*i + 2. Determine z so that r(z) = 0.
-4, -2, 0
Let t(w) be the third derivative of w**8/4480 + w**7/280 + w**6/40 + w**5/10 + 13*w**4/24 - 24*w**2. Let s(g) be the second derivative of t(g). Factor s(q).
3*(q + 2)**3/2
Let k(a) = 5*a + 2. Let r be k(6). What is g in 120*g - 45 + g**2 + 4*g**2 + 80*g**4 - 88*g**3 - r*g**3 - 40*g**2 = 0?
-1, 3/4, 1
Suppose 5*o = 5*i + 165, 2*o - 3*i + 18 - 82 = 0. Let l = o - 33. Factor -9/2*m**5 + 0*m + 3/2*m**3 + 0 + 3*m**l - 6*m**4.
-3*m**2*(m + 1)**2*(3*m - 2)/2
Suppose 30*t - 219 - 51 = 0. Let o(x) be the third derivative of -1/330*x**5 + 1/33*x**4 + 0*x + 0 - 1/11*x**3 - t*x**2. Let o(f) = 0. What is f?
1, 3
Let p = 7492/3 + -2497. Determine b, given that -p - 1/3*b**3 + 1/3*b + 1/3*b**2 = 0.
-1, 1
Let h = 184 + -184. Determine g so that 3*g + 3/4*g**3 + 3*g**2 + h = 0.
-2, 0
Solve -18 - q**4 + 35*q**2 - 28 + 2*q**4 - 12*q + 12*q**3 + 10 = 0 for q.
-6, -1, 1
Let a(m) be the first derivative of -4/5*m**5 + 4/3*m**3 + 0*m + 2*m**2 - 12 - m**4. Factor a(o).
-4*o*(o - 1)*(o + 1)**2
Let m(b) be the third derivative of b**6/120 + b**5/5 + 7*b**4/8 - 49*b**3/3 - 55*b**2. Solve m(s) = 0 for s.
-7, 2
Suppose 3*z = -3*d + 24, 3*d + 20 = -2*z + 3*z. Solve 6*g**2 - z*g + 0*g**2 - 5*g**2 - 2*g**2 - 10 = 0 for g.
-10, -1
Let i(o) be the first derivative of -2*o**6/3 + 8*o**5 - 32*o**4 + 128*o**3/3 - 22. Let i(p) = 0. Calculate p.
0, 2, 4
Let v(m) be the first derivative of m**6/51 + 16*m**5/85 + 6*m**4/17 - 36*m**3/17 - 189*m**2/17 - 324*m/17 - 251. Determine s, given that v(s) = 0.
-3, -2, 3
Let y = -23 - -18. Let q(b) = 9*b**3 - 3*b**2 + 4*b - 5. Let n(f) = -10*f**3 + 2*f**2 - 4*f + 6. Let u(g) = y*n(g) - 6*q(g). Solve u(z) = 0 for z.
0, 1
Let q(n) = n**2 - n + 7. Let m(g) = -2 + 10 - g - 9. Let t(z) = -15*m(z) - 5*q(z). Factor t(b).
-5*(b - 2)**2
Let i(l) be the second derivative of -2*l**6/5 + l**5 - 2*l**4 + 4*l**2 - 19*l. Let j(t) = t**4 + t**3 - 1. Let z(g) = i(g) + 8*j(g). Factor z(d).
-4*d**2*(d - 6)*(d - 1)
Suppose 5*v = 7*v - 2*u, 0 = -4*v - u + 15. Let b(y) be the first derivative of -y**2 + 1/2*y**4 + 0*y - 2 + 0*y**v. Suppose b(s) = 0. Calculate s.
-1, 0, 1
Let o(d) be the second derivative of -d**4/3 - 20*d**3/3 - 18*d**2 + 25*d. Determine p so that o(p) = 0.
-9, -1
Suppose -6*y + 16*y - 120 = 0. Let u be y/7 + 8/28. Factor 9/5*p + 21/5*p**3 - 36/5*p**u + 6/5.
3*(p - 1)**2*(7*p + 2)/5
Solve 0 - 2/7*g**4 - 26/7*g**2 + 4*g**3 + 0*g = 0 for g.
0, 1, 13
Let d = -38 + 41. Factor -26*j**4 + 13*j**5 - d*j**5 - 12*j**3 - 12 + 12.
2*j**3*(j - 3)*(5*j + 2)
Let w be (-78)/15*250/(-60). Let u = -194/9 + w. Solve u*q**4 + 0 + 4/9*q**3 + 2/9*q + 5/9*q**2 = 0 for q.
-2, -1, 0
Let k(x) be the first derivative of 6*x**2 + 0*x**3 + 14 + 0*x - 9/4*x**4 - 3/5*x**5. Determine w so that k(w) = 0.
-2, 0, 1
Suppose 4*i = 2*r - 2, -r = i - 0*i - 7. Factor -43*s - 63*s**2 + 99*s**i + 108 - 4*s**3 - 65*s.
-4*(s - 3)**3
Let j(d) be the third derivative of d**6/600 - 11*d**5/300 + d**4/4 - 55*d**2 + 2*d. Factor j(m).
m*(m - 6)*(m - 5)/5
Let g(i) = -2*i**3 - 11*i**2 - i - 14. Let n be g(-6). What is a in 5*a**2 + 7*a**2 + 4*a**2 - 12*a**2 - n*a = 0?
0, 7
Factor -4*p**2 - 8*p + 0 - 1/2*p**3.
-p*(p + 4)**2/2
Let s be (-1 + (-13)/(-5))/(24/60). Let v(g) be the third derivative of 0 - 1/84*g**6 - 19/28*g**s - 16/105*g**5 - 6/7*g**3 + 0*g - 6*g**2. Factor v(w).
-2*(w + 3)**2*(5*w + 2)/7
Let r(l) be the first derivative of 4/15*l**3 + 1/5*l**4 - 4/5*l**2 + 0*l - 37. Factor r(s).
4*s*(s - 1)*(s + 2)/5
Factor 414*m - 3/4*m**2 - 57132.
-3*(m - 276)**2/4
Let a = 9409/105 - 448/5. Let w(j) be the second derivative of 0 + 0*j**2 - 8*j + 0*j**3 + 0*j**5 + 0*j**4 + a*j**6. Factor w(l).
2*l**4/7
Let h be 4*1*2/4. Factor -12*l - 6*l**2 - l**2 + 9 + 10*l**h.
3*(l - 3)*(l - 1)
Let 7*v - 5*v - 3*v**3 + v**5 - v**2 + 20*v**4 - 19*v**4 = 0. What is v?
-2, -1, 0, 1
Let v be (-221)/102 - 22/(-6). Let i(p) = p**2 - 2. Let z be i(-2). Factor -v*x**z + 3*x - 3/2.
-3*(x - 1)**2/2
Let y(c) be the third derivative of -1/6*c**3 + 0*c + 7/360*c**6 + 0 + 1/72*c**4 + 11/180*c**5 - 20*c**2. Determine m, given that y(m) = 0.
-1, 3/7
Let w be (3*3/24)/(72/48). Factor w*m**2 + 1/4*m**4 + 1/2*m**3 + 0*m + 0.
m**2*(m + 1)**2/4
Let i(d) be the third derivative of 1/210*d**7 + 3*d**2 + 1/540*d**5 - 7/360*d**6 + 1/24*d**4 + 1/27*d**3 + 0*d + 0. Factor i(y).
(y - 2)*(y - 1)*(3*y + 1)**2/9
Let l(p) be the third derivative of 2/9*p**4 + 0 + 0*p + 2/15*p**5 + 2/315*p**7 + 2/45*p**6 + 11*p**2 + 2/9*p**3. Solve l(v) = 0 for v.
-1
Let i = -253 + 393. Solve i*q**4 - 5*q**2 - 7*q**2 + 73*q**3 + 28*q**2 + 23*q**3 = 0.
-2/5, -2/7, 0
Let j(p) = -9*p**3 + 181*p**2 - 172*p + 5. Let z(k) = 28*k**3 - 544*k**2 + 516*k - 16. Let g(s) = -16*j(s) - 5*z(s). Factor g(b).
4*b*(b - 43)*(b - 1)
Let y = 8 + 26. What is m in -9*m**3 + y*m**4 - 6*m**2 - 75*m**4 + 38*m**4 = 0?
-2, -1, 0
Let u(o) be the first derivative of o**5/5 - o**4/4 - 2*o**3 + 2*o**2 + 8*o + 92. Factor u(n).
(n - 2)**2*(n + 1)*(n + 2)
Let m(d) be the third derivative of 0 + 0*d + 1/240*d**5 + 7/48*d**4 + 49/24*d**3 + 9*d**2. Suppose m(a) = 0. Calculate a.
-7
Suppose 0 - 5/4*y**2 + 27/4*y = 0. What is y?
0, 27/5
Let j be 112/((-42)/(-54) - 1). Let o be (140/j)/(5/(-3)). Factor -1/3 + 1/6*m**2 - o*m.
(m - 2)*(m + 1)/6
Factor 0 + 1/2*x**2 - 21/2*x.
x*(x - 21)/2
Let c(v) be the third derivative of -v**8/10080 + v**7/630 - v**6/90 - 7*v**5/15 - 46*v**2. Let i(r) be the third derivative of c(r). Factor i(p).
-2*(p - 2)**2
Suppose 74 = -4*v - 246. Let t be v/28*49/(-42). Find c such that 0 + 0*c + t*c**3 + 0*c**2 - 5/3*c**4 = 0.
0, 2
Let d be 2/4*42/7. Let u be -2*d*6/(-4). Solve -2*w**3 - 6*w**2 + 2*w**3 - 2*w**3 - u*w + 6*w**4 + 11*w = 0.
-1, 0, 1/3, 1
Let v be -6 - ((-2436)/133)/6*2. Factor -8/19*x**2 + 0 + v*x**3 + 8/19*x.
2*x*(x - 2)**2/19
