2
Let p(t) be the first derivative of 10 - 1/16*t**4 + 5/12*t**3 - 7/8*t**2 + 3/4*t. Factor p(j).
-(j - 3)*(j - 1)**2/4
Let g(i) be the third derivative of i**8/336 + 11*i**7/210 + 19*i**6/60 + 13*i**5/15 + i**4 - 11*i**2 - 5*i. Factor g(u).
u*(u + 1)*(u + 2)**2*(u + 6)
Let r(h) be the third derivative of 49*h**5/60 - 14*h**4/3 + 32*h**3/3 + h**2 + 50*h. Factor r(j).
(7*j - 8)**2
Factor -14 - 23/3*i - 1/3*i**2.
-(i + 2)*(i + 21)/3
Let y be (-4)/10*-16 + 219/365. Let k(l) be the third derivative of -l**4 + 0*l**3 - 3/20*l**6 + 0 + 3/5*l**5 + 1/70*l**y + 4*l**2 + 0*l. Factor k(d).
3*d*(d - 2)**3
Let b = -11 - -13. Factor -2 + 3*a**2 + 2 - 4*a**b.
-a**2
Let z(n) be the third derivative of -64/3*n**3 - 1/30*n**5 + 56*n**2 - 4/3*n**4 + 0*n + 0. Determine a so that z(a) = 0.
-8
Suppose 0 = -5*z + 3*x + 19, 2*x = 6*x + 12. Let q be ((-2)/10*9)/((-12)/45). Factor -3/2 - 3/4*p**4 - q*p**z + 15/4*p**3 + 21/4*p.
-3*(p - 2)*(p - 1)**3/4
Let s(o) = -8*o**5 + 32*o**4 - 68*o**3 + 65*o**2 + 82*o - 96. Let h(l) = -l**5 + l**4 + 2*l**3 + l**2 + 2*l. Let p(n) = -5*h(n) + s(n). Factor p(v).
-3*(v - 4)*(v - 2)**3*(v + 1)
Suppose -4*d + 0 + 3 = m, 5*m - 15 = d. Let g = -204 - -208. Factor 3*n**4 - n**4 - 4 + d*n**2 + g*n - 4*n**3 - n**4 + 3*n**2.
(n - 2)**2*(n - 1)*(n + 1)
Suppose 72*y + 54*y**2 + 159*y**3 - 551*y**5 - 48*y**4 + 277*y**5 + 277*y**5 - 89*y**2 - 151*y**2 = 0. Calculate y.
0, 1, 2, 12
Let x(i) be the second derivative of 0 + 24*i - 40*i**2 + 20/3*i**3 - 5/12*i**4. Factor x(b).
-5*(b - 4)**2
Let f = 39/43 + 313/129. Let 4/3 + 2*g - f*g**2 = 0. Calculate g.
-2/5, 1
What is u in -9*u**3 - 5*u**4 - 341*u + 4*u**3 + 20*u**2 + 361*u = 0?
-2, -1, 0, 2
Let b(y) be the first derivative of y**7/105 - y**6/15 + y**5/6 - y**4/6 + 6*y**2 + 12. Let s(w) be the second derivative of b(w). Factor s(n).
2*n*(n - 2)*(n - 1)**2
Suppose -s = 3*h + h - 57, -5*h + 4*s = -66. Factor h*t**2 - 4*t - 8*t**3 + 12*t**2 + 2*t**4 - 16*t**2.
2*t*(t - 2)*(t - 1)**2
Let -3*s**2 - 5656 + 279*s - 3*s - 4748 + 4056 = 0. Calculate s.
46
Let g(l) be the first derivative of -5/3*l**3 + 5*l - 5/2*l**2 + 5/4*l**4 + 8. Let g(k) = 0. What is k?
-1, 1
Let j be (-217)/(-882) + 6/(-27). Let p(u) be the second derivative of -j*u**3 - 4*u + 0 + 0*u**2 - 1/84*u**4. Suppose p(m) = 0. Calculate m.
-1, 0
Let j be (-3)/(-3)*12/20. Let n(l) be the third derivative of 0 + 0*l - 1/20*l**4 - 1/300*l**6 - 2*l**2 - 1/30*l**5 + j*l**3. Determine a, given that n(a) = 0.
-3, 1
Suppose -4*s = -4, 3*k = -2*k + s - 1. Let a(u) be the second derivative of k + 1/20*u**4 - u + 1/10*u**2 - 1/100*u**5 - 1/10*u**3. Factor a(d).
-(d - 1)**3/5
Let j be 0 + 24/9 + 2/6. Factor h**j + 0*h**2 + 3*h + 18 - 27 + 5*h**2.
(h - 1)*(h + 3)**2
Suppose 4*p + 3*y = -19, 0*p - 2*p - 3*y = 11. Let n be (-10)/p*6/30. Factor -n*m + 1/4*m**2 + 1/4.
(m - 1)**2/4
Factor 1/5*o**4 + 0*o + 0 + 0*o**2 + 0*o**3.
o**4/5
Let t = -1123 - -14623/13. Let p = t - 57/52. Solve 3/4*b**3 + 3/4*b**2 - 3/4*b - p*b**4 + 0 = 0.
-1, 0, 1
Suppose 0 = -5*r - 10, 4*i - 9 = -3*r + 5. Let y(h) be the first derivative of -2*h**4 - 4/3*h**3 - 1/3*h**6 - 4*h + 5*h**2 + 8/5*h**5 - i. Factor y(z).
-2*(z - 2)*(z - 1)**3*(z + 1)
Let k = 6994 + -6992. Find x such that 10*x**k + 15*x**3 + 5/3*x + 20/3*x**4 + 0 = 0.
-1, -1/4, 0
Factor -4*t**2 - 9*t**2 - 9*t**2 - 33*t + 30 + 25*t**2.
3*(t - 10)*(t - 1)
Let s(m) be the first derivative of 21 + 4/3*m**3 - 6*m**2 + 8*m. Factor s(d).
4*(d - 2)*(d - 1)
Suppose -4*b + 18 = 3*u - 2*u, 4*u - 24 = -4*b. Suppose 10*y - 24 - 6 = 0. Suppose -u*l - l**2 + 2 - l**2 + 4 + 2*l**y - 4 = 0. Calculate l.
-1, 1
Let w = 14 - 6. Suppose -3*s + w = -s. Determine u so that 0 - 1/3*u**s + 0*u**3 + u**2 + 2/3*u = 0.
-1, 0, 2
Determine y so that -153 + 13*y + 5*y**2 + 233 - 63*y = 0.
2, 8
Let l = 4/231 + 199/1848. Let b(o) be the first derivative of 1/24*o**6 + 0*o**3 + 0*o - 6 + 0*o**5 - l*o**4 + 1/8*o**2. Determine t so that b(t) = 0.
-1, 0, 1
Let f(z) be the second derivative of -3*z**5/20 + z**4 - 5*z**3/2 + 3*z**2 + 54*z. Factor f(h).
-3*(h - 2)*(h - 1)**2
Let v(i) be the third derivative of 0*i - 1/70*i**7 + 0 + 1/8*i**6 - i**3 - 9/20*i**5 + 7/8*i**4 + 4*i**2. Solve v(q) = 0.
1, 2
Let v = 7588 + -30349/4. Find t such that 43/4*t**2 + v - 11/2*t - 3*t**3 = 0.
1/4, 1/3, 3
Let g be ((-11)/3 + 4)*(12 - 12). Let y(j) be the first derivative of 6/25*j**5 - 2 + 4/5*j**4 + g*j + 14/15*j**3 + 2/5*j**2. Solve y(x) = 0 for x.
-1, -2/3, 0
Let o(t) be the third derivative of -1/168*t**7 - 1/12*t**3 + 21*t**2 + 0 - 17/480*t**6 + 0*t - 11/96*t**4 - 7/80*t**5. Factor o(v).
-(v + 1)**3*(5*v + 2)/4
Suppose -4*t = -4*b + 32, 5*b - 6*b + 20 = -5*t. Let n(q) be the third derivative of 1/150*q**b - 1/60*q**4 + 0 - q**2 + 0*q - 2/15*q**3. Factor n(g).
2*(g - 2)*(g + 1)/5
Let g(u) = -5*u + 22. Let t be g(6). Let y be (45/(-2))/(-9)*t/(-10). Solve -1/3 + 2/3*m + m**y = 0 for m.
-1, 1/3
Let l(o) = 7*o**4 + 8*o**3 + 15*o**2 - o. Let s(v) = -8*v**3 - 6*v**4 - 14*v**2 - 76 + 76. Let a(y) = 4*l(y) + 5*s(y). Suppose a(h) = 0. What is h?
-2, -1, 0
Let b be 2 + 16/(-5) + (-142)/(-71). Factor 0*x + b*x**2 - 8/5*x**3 + 0 + 4/5*x**4.
4*x**2*(x - 1)**2/5
Let l = -2748/7 + 8300/21. Factor 2*k**2 + 0 - l*k**3 + 2/3*k.
-2*k*(k - 1)*(4*k + 1)/3
Let x be (3 - 20/8) + 64/(-128). Factor x + 3/8*r**3 - 9/8*r**2 + 3/4*r.
3*r*(r - 2)*(r - 1)/8
Let m be 18/(-4)*680/(-60). Suppose 10*l = -7*l + m. Factor 0*x + 0 + 1/3*x**2 + 1/3*x**l.
x**2*(x + 1)/3
Let w(d) be the second derivative of d**5/40 - 7*d**4/6 + 3*d + 27. Factor w(k).
k**2*(k - 28)/2
Let c(g) be the first derivative of -g**4/6 + 40*g**3/3 - 279*g**2 - 3844*g/3 - 178. Factor c(u).
-2*(u - 31)**2*(u + 2)/3
Let o(q) be the first derivative of -4/9*q**3 + 2/15*q**5 + 0*q - 1/6*q**4 + 17 + 0*q**2. Determine l, given that o(l) = 0.
-1, 0, 2
Let k be -1*(351/(-26) - -13). Determine z so that -k*z - 1/2*z**2 + 1 = 0.
-2, 1
Let h(f) be the third derivative of 0 + 1/900*f**6 - 12*f**2 - 1/180*f**4 + 0*f**3 + 0*f + 0*f**5. Factor h(l).
2*l*(l - 1)*(l + 1)/15
Suppose l = -2*t + 6, 0 = -3*l + 2*t - 138 + 132. Suppose 2/7*c**2 + 0*c**3 - 2/7*c**4 + 0*c + l = 0. What is c?
-1, 0, 1
Suppose -w - 4*w + 10 = 0. Let d = -3404 - -3407. Factor -2/5*o - 6/5*o**d + 0 - 8/5*o**w.
-2*o*(o + 1)*(3*o + 1)/5
Let w(d) = -d**5 - 2*d**4 - 2*d**2 - 3*d + 2. Let f(y) = -2*y**5 - 5*y**4 - y**3 - 5*y**2 - 7*y + 5. Let g(z) = -2*f(z) + 5*w(z). Factor g(q).
-q*(q - 1)**2*(q + 1)**2
Suppose 11*o + 163 - 431 = -56*o. Factor 4/3*t**3 - 4*t**2 + 4/3*t**o + 8/3 - 4/3*t.
4*(t - 1)**2*(t + 1)*(t + 2)/3
Let j(r) be the second derivative of -r**6/75 + 4*r**5/25 + r**4/3 - 8*r**3/15 - 9*r**2/5 + 313*r. What is d in j(d) = 0?
-1, 1, 9
Let m be 6/4 + (-12)/(-8). Find h, given that 34*h**m - 2*h**5 + 6*h**2 - h**5 + 6*h**4 - 12 - 10*h**3 - 21*h = 0.
-1, 1, 4
Suppose -4*x = 3*q - 22, 2*q - 5*x = -3*q + 95. Factor -q + 5*m**2 + 4 + 5.
5*(m - 1)*(m + 1)
Let y(q) be the first derivative of 21/5*q**5 + 0*q - 15/4*q**4 + 0*q**2 - 2*q**3 - 22. Suppose y(i) = 0. What is i?
-2/7, 0, 1
Let u(p) be the first derivative of 3*p**4/4 + 23*p**3 - 75*p**2 + 135. Let u(x) = 0. What is x?
-25, 0, 2
Let k be (2 + 0)/(4 - (-30)/(-9)). Solve -4*d**3 + k - 4 + 1 = 0.
0
Let b(c) be the second derivative of 1/5*c**3 + 0 + 3/40*c**4 + 1/100*c**5 - 6*c - 3/2*c**2. Let i(t) be the first derivative of b(t). Solve i(m) = 0 for m.
-2, -1
Let i(v) = -4*v + 43. Let q be i(10). Factor 2*n**4 + 13*n**q + 0*n**4 - 3*n**5 + n**4 - 3*n**2 - 10*n**3.
-3*n**2*(n - 1)**2*(n + 1)
Suppose 5*c = -113 + 123. Let q(f) be the first derivative of 2 + 4*f**4 + 5*f**c + 6*f - 52/3*f**3. What is k in q(k) = 0?
-1/4, 1/2, 3
Suppose b = -5*x + 3*b + 374, 2*x - 4*b = 140. Let l = 383/5 - x. Find o such that 0*o**2 + 3/5*o - l*o**3 + 0 = 0.
-1, 0, 1
Suppose 24*m + 115*m**2 - 63*m - 31*m - 3*m**3 - 12*m**3 = 0. Calculate m.
0, 2/3, 7
Let p(o) be the first derivative of o**5/35 - 2*o**4/7 - 19*o**3/21 - 5*o**2/7 - 501. Factor p(r).
r*(r - 10)*(r + 1)**2/7
Let a(f) = -7*f**2 - 202*f - 2000. Let k(n) = -2*n**2 - 2*n. Let h(g) = a(g) - k(g). Factor h(t).
-5*(t + 20)**2
Let 0*m**2 - 4*m**2 - 1444 + 1064*m - 1216*m = 0. Calculate m.
-19
Determine h so that 1118*h - 5*h**2 - 2034*h - 500 + 1016*h = 0.
10
Let v be (-502)/(-7) - 42/(-147). Le