- 624. Let x(d) be the first derivative of -2*d + z*d**3 - 1 + 7/2*d**2. Factor x(u).
(u + 2)*(4*u - 1)
Suppose 1571*c - 1550*c - 42 = 0. Suppose 0*o - 2*o**c + 2/3*o**3 + 8/3 = 0. What is o?
-1, 2
Let g be 21/84 - ((-10)/(-35) - (-99)/(-84)). Factor 10/7*y**2 + 2/7*y**3 + 16/7*y + g.
2*(y + 1)*(y + 2)**2/7
Let w = 40 + -35. Suppose -19 = w*l + 6, 4*t = -2*l - 2. Factor -8/13 - 8/13*b - 2/13*b**t.
-2*(b + 2)**2/13
Let z(y) be the third derivative of y**7/70 + 3*y**6/10 - 27*y**5/20 + 7*y**4/4 + 5*y**2 - 4*y. Find c such that z(c) = 0.
-14, 0, 1
Suppose -2*c = 5*d - 6, -2*c + 3*c = 2*d - 6. Suppose 3*o - 4*z - 32 = 0, 3*z - z + 2 = -d*o. Factor -4*w**o + 6*w**4 - w**5 + w**4 + w**2 - 3*w**3.
-w**2*(w - 1)**3
Let c(x) be the first derivative of -35*x**6/2 - 64*x**5 - 80*x**4 - 30*x**3 + 25*x**2/2 + 10*x - 27. Find p, given that c(p) = 0.
-1, -1/3, 2/7
Factor -175/4*q**2 + 40*q + 15/4.
-5*(q - 1)*(35*q + 3)/4
Factor -4*o + 24/7 + 4/7*o**2.
4*(o - 6)*(o - 1)/7
Let t(z) be the third derivative of 0*z**3 + 1/90*z**5 + z**2 - 22*z + 0 + 5/12*z**4. Find i, given that t(i) = 0.
-15, 0
What is w in -564*w**3 - 481*w**2 - 6 - 100*w**4 - 84*w + 144*w**3 + 2 = 0?
-2, -1/10
Let b(o) be the third derivative of -o**8/11760 + o**7/5880 + o**6/2520 - o**5/840 + 4*o**3/3 - o**2. Let q(j) be the first derivative of b(j). Factor q(l).
-l*(l - 1)**2*(l + 1)/7
Let r(s) = -s**4 + s**3 + s**2 + s. Let w(h) = -12*h**4 - 56*h**3 + 80*h**2 + 88*h - 68. Let f(x) = -16*r(x) + w(x). What is n in f(n) = 0?
-1, 1, 17
Let o = 7 - -57. Let c = 302 - 300. What is d in 32 - 16 - 3*d**c - 24*d - o = 0?
-4
Let r = 19 - 15. Factor 27 + 23 - h**2 - 20*h - r*h**2 + 7*h**2.
2*(h - 5)**2
Suppose 0 = -36*p + 20*p + 48. Let q(z) be the third derivative of 0*z + 2*z**2 + 1/20*z**5 + 9/2*z**p + 0 - 3/4*z**4. What is y in q(y) = 0?
3
Suppose 5*q + 8 = -5*u + 18, -3*u = 2*q - 2. Factor -3*l**5 + 10*l**4 - l**q - 6*l**4.
-3*l**4*(l - 1)
Suppose -10 = -2*g - 2*j, 5*j - 8*j + 9 = 0. Factor -2/21*s**3 - 16/21 - 4/3*s - 2/3*s**g.
-2*(s + 1)*(s + 2)*(s + 4)/21
Let y(u) be the third derivative of -u**5/120 + u**4/3 + 17*u**3/12 + 7*u**2 - 3. Determine t, given that y(t) = 0.
-1, 17
Let y(p) be the second derivative of 0 + 0*p**2 - p - 5/2*p**3 + 5/12*p**4. Suppose y(w) = 0. Calculate w.
0, 3
Let d be (-1)/((-90)/64) + 9766/(-171) + 57. Determine t, given that d - 2/5*t - 1/5*t**2 = 0.
-3, 1
Suppose -162/5*x + 27/5 + 72*x**2 - 70*x**3 + 25*x**4 = 0. Calculate x.
3/5, 1
Let p(m) be the third derivative of -m**5/24 - 5*m**4/3 - 275*m**3/12 + 2*m**2 + 200*m. What is y in p(y) = 0?
-11, -5
Let h(u) = 5*u - 8*u**2 - 50 + 3*u**2 + 4*u - 35*u. Let f(y) = -y**2 - y - 1. Let r(l) = 2*f(l) - h(l). Let r(w) = 0. What is w?
-4
Let x = -28983/5 - -5797. Factor 2/5 - x*m**2 + 2/5*m**3 - 2/5*m.
2*(m - 1)**2*(m + 1)/5
Factor 27*f**3 + 210*f**2 + 6*f**3 + 17*f**3 + 40 - 192*f.
2*(f + 5)*(5*f - 2)**2
Factor 4/7*d**2 - 2*d**4 - 26/7*d**3 + 0*d + 0.
-2*d**2*(d + 2)*(7*d - 1)/7
Let j(x) be the first derivative of 0*x**2 + 5/24*x**6 - 5/16*x**4 + 0*x**3 + 0*x + 0*x**5 - 14. Factor j(v).
5*v**3*(v - 1)*(v + 1)/4
Suppose 0 - 972/5*x - 66/5*x**4 - 3/5*x**5 - 471/5*x**3 - 1188/5*x**2 = 0. Calculate x.
-9, -2, 0
Suppose j + 4*b - b = 19, -2*j - 2 = -2*b. Let i(u) be the second derivative of 0*u**2 + 1/4*u**j + 7*u + 1/3*u**3 + 0 + 1/20*u**5. Factor i(v).
v*(v + 1)*(v + 2)
Factor -t**3 + 3*t**3 + 3*t + 0*t**3 - 11*t.
2*t*(t - 2)*(t + 2)
Suppose 5*t - 2*i = 22, 0 = -4*i - 1 - 3. Let f be (-31)/93 - t/42*-5. Factor 0 - 2/7*r**2 + 0*r + 1/7*r**4 + f*r**3.
r**2*(r - 1)*(r + 2)/7
Factor 0 + 61/3*r + 1/3*r**2.
r*(r + 61)/3
Let r(n) be the first derivative of -1 + 0*n + 0*n**2 + 1/4*n**4 - n**3. What is k in r(k) = 0?
0, 3
Let q = 917 - 11919/13. Suppose -5*m + 6 = -2*f, f + 2*m = 5*f - 4. Find u such that -2/13*u**f + 0 + 2/13*u**4 + q*u**5 + 0*u - 2/13*u**3 = 0.
-1, 0, 1
Let t(a) be the third derivative of -a**6/300 - a**5/30 - a**4/10 + 20*a**2 + 3*a. Factor t(p).
-2*p*(p + 2)*(p + 3)/5
Determine r, given that -16*r**3 - 4*r + 4 + 18*r**3 + 2*r**3 - 4*r**2 = 0.
-1, 1
Factor 2/13*m**2 - 228/13 - 226/13*m.
2*(m - 114)*(m + 1)/13
Let a(m) = 2*m**2 + 20*m + 14. Let h(f) = -f - 1. Let q(z) = -2*a(z) - 28*h(z). What is g in q(g) = 0?
-3, 0
Let l(k) be the first derivative of -k**6/40 - k**5/10 + 3*k**4/8 + 27*k**2/2 - 9. Let c(o) be the second derivative of l(o). Factor c(s).
-3*s*(s - 1)*(s + 3)
Let -36/7*d**2 - 87/7*d + 186/7*d**3 - 18/7 - 18/7*d**4 - 27/7*d**5 = 0. What is d?
-3, -1/3, 1, 2
Solve 45*p**4 - 1327 + 3*p**5 - 144*p - 1508 + 3027 + 141*p**3 - 237*p**2 = 0 for p.
-8, -1, 1
Factor -3/5*d**2 + 0*d + 3/5.
-3*(d - 1)*(d + 1)/5
Solve -217 - 4*p**4 + 56*p - 24*p**3 + 32*p + 157 = 0.
-5, -3, 1
Let o(u) be the first derivative of 2 + 0*u**2 + 5*u - 5/3*u**3. Determine w so that o(w) = 0.
-1, 1
Suppose 7 = 2*z + v, 1 = 4*v + 5. Factor 43*y**2 - 21*y**3 + 11*y - 4*y**z + y - 19*y**2 - 11*y**4.
-3*y*(y - 1)*(y + 2)*(5*y + 2)
Let z(t) be the second derivative of -t**5/5 - 194*t**4 - 75272*t**3 - 14602768*t**2 - 3*t - 53. Factor z(p).
-4*(p + 194)**3
Factor -1/3*g**4 - 103968*g**2 + 304*g**3 + 15803136*g - 900778752.
-(g - 228)**4/3
Suppose 0 = -4*s + 14 + 10. Find y such that -4*y**2 + 8*y**2 - s + 16*y + 22 = 0.
-2
Factor -32/7*g + 2/7*g**3 - 6/7*g**2 - 24/7.
2*(g - 6)*(g + 1)*(g + 2)/7
Find t, given that -21/2*t - 45/4 + 3/4*t**2 = 0.
-1, 15
Let s(q) = -q**3 - 2*q**2 - 3*q - 2. Let u be s(-1). Suppose u = l + 3*l - 8. Factor 2*w**2 - 3*w**2 - 12*w + 9 + 4*w**l + 0*w**2.
3*(w - 3)*(w - 1)
Let s be 14/(-2) + -5*51/(-30). Factor -s*x**4 - 27/4*x + 33/4*x**3 - 9*x**2 + 0.
-3*x*(x - 3)**2*(2*x + 1)/4
Let y(w) = w**4 - 18*w**3 + 81*w**2 - 20*w - 104. Let t(u) = -6*u**4 + 90*u**3 - 405*u**2 + 102*u + 519. Let x(n) = 4*t(n) + 21*y(n). Factor x(r).
-3*(r - 2)**2*(r + 1)*(r + 9)
Let r(f) be the first derivative of f**7/168 - f**6/120 - 16*f + 22. Let h(i) be the first derivative of r(i). Let h(q) = 0. What is q?
0, 1
Suppose 255/2*j - 24*j**2 + 3/2*j**3 - 225 = 0. Calculate j.
5, 6
Let x(t) be the second derivative of t**6/24 - t**5/16 - 5*t**4/48 + 5*t**3/24 - t + 48. Find k, given that x(k) = 0.
-1, 0, 1
Factor -6*f + 3*f**2 + 1043 - f**2 - 75 - 82*f.
2*(f - 22)**2
Let t(m) = m**3 + 5*m**2 + m - 1. Let c be t(-5). Let u be (c - (2 + -2))*9/(-18). Determine g so that -g + 4/3*g**4 + g**u + 1/3 - 5/3*g**2 = 0.
-1, 1/4, 1
Let z(f) be the first derivative of -f**4/2 - 4*f**3/3 + f**2 + 4*f + 237. Factor z(d).
-2*(d - 1)*(d + 1)*(d + 2)
Let q(r) be the third derivative of -r**5/50 - 7*r**4/10 + 19*r**3 - 497*r**2. Factor q(i).
-6*(i - 5)*(i + 19)/5
Suppose -5*r + 3*m + 20 = -0*r, -4*r + m = -16. Factor -2*k**3 + 130*k + 2*k**r - 8*k**3 - 130*k + 8*k**2.
2*k**2*(k - 4)*(k - 1)
Solve -75/2*q - 110/3 - 5/6*q**2 = 0 for q.
-44, -1
Factor -2*z**3 + 0*z**2 + 81 - 3*z**2 - 14*z**2 - 6*z - 57*z + z**3.
-(z - 1)*(z + 9)**2
Suppose 0 = 12*w - 7*w. Solve 0*t**4 + 2*t**2 + 6*t**4 + w*t**4 + t - 8*t**4 - t**5 = 0.
-1, 0, 1
Solve 17/3 + 1/3*u**2 - 6*u = 0 for u.
1, 17
Let y(b) be the third derivative of b**8/171360 + b**7/5355 + 7*b**6/6120 - 7*b**5/30 - 20*b**2. Let p(f) be the third derivative of y(f). Solve p(z) = 0 for z.
-7, -1
Let a(z) be the first derivative of -z**5/150 - z**4/90 + 2*z**3/45 + 9*z + 1. Let j(r) be the first derivative of a(r). Let j(f) = 0. What is f?
-2, 0, 1
Let 27225/2*w + 499125 + 3/8*w**3 + 495/4*w**2 = 0. Calculate w.
-110
Let i(u) = u**4 + u**3 + u**2 - u. Let l(z) = 9*z**4 + 87*z**3 - 57*z**2 - 87*z + 72. Let c(g) = 12*i(g) - l(g). Factor c(v).
3*(v - 24)*(v - 1)**2*(v + 1)
Let f = -69 + 71. Let 3/4*c**f + 3/4*c + 0 = 0. What is c?
-1, 0
Suppose -d = f - 3, -2*d - 3 + 18 = -f. Suppose -4*v**4 - 26*v**5 + 29*v**5 + d*v**2 - 3*v - 2*v**4 = 0. What is v?
-1, 0, 1
Solve -23/6*x + 5/3*x**2 + 7/3 - 1/6*x**3 = 0 for x.
1, 2, 7
Let c be 5/((-5)/(-2)) - -5. Let y be c/2 - 1/2. What is u in -4*u**y - u**3 - 6*u**4 - 9*u**2 + 3*u - 3*u**2 + 20*u**3 = 0?
0, 1/2, 1
Let u = -92 - -96. Suppose 5*c - 11 = -h - 4, 2*c - u = -h. Find n such that -8/7*n**h + 0 + 4/7*n + 4/7*n**3 = 0.
0, 1
Let u be 2/(-17)*(2 + (5 - 8)). Solve 0 - 2/17*v**2 + u*v = 0 for v.
0, 1
Let w(x) be the first derivative of 1/42*x**4 + 1 + 0*x + 1/210*x**5 - 5/2*x**2 +