w).
-(w + 1)*(w + 3)/2
Let -64*d + 475*d**3 + 44*d**2 - 12*d**2 - 479*d**3 = 0. Calculate d.
0, 4
Let g(f) = -f**4 - 2*f**3 + f**2 + f - 1. Let u(b) = -5*b**4 + 8*b**3 + 3*b**2 + 3*b - 3. Let o(q) = -6*g(q) + 2*u(q). Factor o(p).
-4*p**3*(p - 7)
Let p(w) be the third derivative of w**5/12 + 110*w**4/3 + 19360*w**3/3 - 7*w**2 - 3. Factor p(d).
5*(d + 88)**2
Let k(r) = r**2 - 6*r - 12. Let j be k(8). Factor -3*y**5 + j*y**5 + 3*y**2 - 5*y**2 - 115*y**4 - y**3 + 117*y**4.
y**2*(y - 1)*(y + 1)*(y + 2)
Let d = 112396/9 + -12488. What is u in -10/9*u**3 - 2*u**2 - d - 14/9*u - 2/9*u**4 = 0?
-2, -1
Suppose 2*i + 0*a + 2*a = 4, -16 = -5*i + a. Let f = -159 - -161. Suppose -4*u**i - f*u**4 - u**4 + u**4 - 6*u**2 + 4*u**4 = 0. What is u?
-1, 0, 3
Let i(c) be the first derivative of 5*c**4/48 - 45*c**2/8 - 4*c - 41. Let u(l) be the first derivative of i(l). Suppose u(n) = 0. What is n?
-3, 3
Suppose 0 = 111*d - 109*d - 8. Let n(w) be the first derivative of 1/6*w**d - 1/15*w**5 + 0*w**2 + 4 - 1/9*w**3 + 0*w. Factor n(z).
-z**2*(z - 1)**2/3
What is t in -2/7*t**3 - 132/7 + 34/7*t + 20/7*t**2 = 0?
-3, 2, 11
Factor -2344 - 383*s + 2084 - 5*s**4 - 95*s**3 - 435*s**2 - 222*s.
-5*(s + 1)**2*(s + 4)*(s + 13)
Determine d, given that 93/5 + 183/5*d + 87/5*d**2 - 3/5*d**3 = 0.
-1, 31
Let l be ((-684)/(-28)*2)/((-2)/(-14)). What is u in -l + 20*u**2 + 342 + 8*u = 0?
-2/5, 0
Factor -15876*z - 666792 - 126*z**2 - 1/3*z**3.
-(z + 126)**3/3
Let o be (-6 - (2 - 6))/(-1). Solve -6*p**o + 10*p + 0*p**2 + 18 + p**2 - 3 = 0 for p.
-1, 3
Let s(v) be the third derivative of -5*v**7/126 + 41*v**6/18 - 161*v**5/45 + 16*v**4/9 + 3*v**2 - 2*v. Factor s(r).
-r*(r - 32)*(5*r - 2)**2/3
Let p be 4 + (-8)/(-12)*(-14)/(1568/600). Factor 0 + 0*f + p*f**3 + 1/7*f**5 - 3/7*f**4 - 1/7*f**2.
f**2*(f - 1)**3/7
Let s be -1*((-4)/6 + (-76)/12). Suppose 14*d = s*d. Factor d*w**4 + 0 + 1/3*w**5 - 1/3*w**3 + 0*w + 0*w**2.
w**3*(w - 1)*(w + 1)/3
Let c(r) = -8*r**5 - 8*r**4 + 24*r**3 - r**2 - 7*r - 9. Let t(g) = -4*g**5 - 4*g**4 + 12*g**3 - 4*g - 4. Let p(l) = 4*c(l) - 9*t(l). Factor p(n).
4*n*(n - 1)**2*(n + 1)*(n + 2)
Suppose -3*o = -5*w + 28 - 64, -2*o - 2*w - 8 = 0. Determine s so that 24/7*s + 57/7*s**4 - 18/7*s**3 + 0 - 12*s**o + 3*s**5 = 0.
-2, 0, 2/7, 1
Suppose 12*z + z = 3*z. Let t(j) be the first derivative of -1/10*j**4 + 0*j**3 + 1/25*j**5 + z*j + 0*j**2 + 5. Factor t(o).
o**3*(o - 2)/5
Factor -1/6*h**2 - 9/2*h - 12.
-(h + 3)*(h + 24)/6
Factor 3*c**2 - 2728 - 6*c + 2692 - c**2.
2*(c - 6)*(c + 3)
Let s(x) = 4*x**5 - 13*x**4 - 12*x**3 - 5*x**2 + 5*x + 5. Let l(r) = 2*r**5 - 6*r**4 - 6*r**3 - 2*r**2 + 2*r + 2. Let u(f) = -5*l(f) + 2*s(f). Factor u(h).
-2*h**3*(h - 3)*(h + 1)
Let w = 17 - 28. Let z(d) = -4*d**4 + 12*d**3. Let f(q) = q**5 + 11*q**4 - 35*q**3 + q. Let v(k) = w*z(k) - 4*f(k). What is l in v(l) = 0?
-1, 0, 1
Let k(i) = 8*i**4 + 9*i**3 + 27*i**2 + 45*i - 2. Let c(v) = -3*v**4 - 4*v**3 - 14*v**2 - 22*v. Let m(y) = -14*c(y) - 6*k(y). What is r in m(r) = 0?
-1, -2/3, 3
Let n be (-4)/6 - 1065/36. Let h = -30 - n. Factor -h*l**3 - 3/4*l - 3/4*l**2 - 1/4.
-(l + 1)**3/4
Let h = -19 - -21. Factor -4 + h*p**2 + 20 + 4*p - 16*p + 2.
2*(p - 3)**2
Let g(k) be the second derivative of 3*k**6/4 - 33*k**5/40 + k**4/4 - 95*k. Suppose g(v) = 0. Calculate v.
0, 1/3, 2/5
Let a(o) be the second derivative of o**7/168 - o**6/40 + o**5/80 + o**4/16 - o**3/12 + 31*o - 2. Factor a(m).
m*(m - 2)*(m - 1)**2*(m + 1)/4
Let s be 12/(-18) + 7/6. Factor s*z**3 - 3/2 + 7/2*z - 5/2*z**2.
(z - 3)*(z - 1)**2/2
Suppose 5*v = -58 + 88. Let s(r) be the third derivative of -v*r**2 - 1/360*r**5 + 1/144*r**4 + 0*r + 0*r**3 + 0. What is g in s(g) = 0?
0, 1
Let u be ((-132)/(-176))/(15/4). Let j(c) be the first derivative of 2 + 9/10*c**2 + u*c**3 + 0*c. Factor j(v).
3*v*(v + 3)/5
Let p(k) = -9*k**3 - 33*k**2 + 69*k - 27. Let o(l) = 26*l**3 + 98*l**2 - 206*l + 82. Let i(x) = 6*o(x) + 17*p(x). Determine h, given that i(h) = 0.
-11, 1
Suppose 5*i - 1 = 4*j, i + 3 = -0. Let r = j + 6. Factor -9*m**4 - 3*m**r + 2*m**2 + 3*m**4 - 2*m**5 - 6*m**3 - m**2.
-2*m**2*(m + 1)**3
Let d(b) be the first derivative of -4/5*b**5 + 4*b**4 + 0*b - 20/3*b**3 + 4*b**2 + 3. Factor d(t).
-4*t*(t - 2)*(t - 1)**2
Suppose 0 = -4*f - 8, -x - 3*f = 4*x - 9. Factor -7*d**x - 4 + 9*d**3 - 3 + 3 + 4*d**2 - 2*d.
2*(d - 1)*(d + 1)*(d + 2)
Factor 210 - 10*c + 3*c - 12*c**2 + 7*c**2 + 12*c.
-5*(c - 7)*(c + 6)
Let a be -1*8/12*-9. Let c(k) = k**3 - k**2 - k. Let l(t) = 3*t**3 - 12*t**2 - 6*t. Let p(n) = a*c(n) - l(n). Suppose p(g) = 0. What is g?
-2, 0
Let g(s) = -4*s**2 - 82*s - 4. Let t(j) = 20*j**2 + 411*j + 22. Let l(i) = 11*g(i) + 2*t(i). Factor l(m).
-4*m*(m + 20)
Let h(l) be the first derivative of -1 + 0*l**3 - 2*l + 1/120*l**6 + 0*l**2 - 1/48*l**4 + 0*l**5. Let v(u) be the first derivative of h(u). Factor v(c).
c**2*(c - 1)*(c + 1)/4
Let s(d) be the second derivative of d**4/30 + 4*d**3/15 - 12*d**2/5 - 68*d. What is l in s(l) = 0?
-6, 2
Let j = -229 + 231. Let i(w) be the third derivative of 1/945*w**7 + 0 + 0*w**3 + 0*w**4 + 0*w**6 + 0*w + 4*w**j - 1/270*w**5. What is f in i(f) = 0?
-1, 0, 1
Let c(l) be the first derivative of -l**3/3 + 3*l**2/2 + 4*l - 336. Factor c(o).
-(o - 4)*(o + 1)
Let a(i) be the first derivative of 0*i - 5*i**3 - 5 + 5/2*i**2. Suppose a(v) = 0. Calculate v.
0, 1/3
Let m(u) be the third derivative of u**9/52920 + u**8/7840 - u**6/630 - 3*u**4/8 - 5*u**2 - 2. Let o(g) be the second derivative of m(g). What is k in o(k) = 0?
-2, 0, 1
Factor -8/9 + 2/9*i**2 + 0*i.
2*(i - 2)*(i + 2)/9
Let o(g) be the first derivative of -g**4/8 + 8*g**3/3 + 17*g**2/4 + 100. Factor o(b).
-b*(b - 17)*(b + 1)/2
Factor -55*r + 15 + 50*r**2 - 10*r**2 - 60*r**2.
-5*(r + 3)*(4*r - 1)
Let o(d) be the third derivative of d**8/7560 - d**6/810 + d**4/108 + d**3/6 - 2*d**2. Let k(t) be the first derivative of o(t). Determine l so that k(l) = 0.
-1, 1
Let u = 147 - 3527/24. Let t(i) be the third derivative of 1/48*i**4 + u*i**3 + 1/240*i**5 - 2*i**2 + 0*i + 0. Factor t(b).
(b + 1)**2/4
Let q(t) be the first derivative of t**6/3 + 2*t**5 + t**4 - 28*t**3/3 - 3*t**2 + 18*t + 552. Find x such that q(x) = 0.
-3, -1, 1
Let b(f) = f**2 - 58*f + 265. Let n be b(5). Let t(m) be the first derivative of 0*m**3 - 3/4*m**4 + 0*m**2 + n*m - 9/10*m**5 - 1/4*m**6 + 2. Factor t(y).
-3*y**3*(y + 1)*(y + 2)/2
Factor -44/7 - 2/7*a**3 + 26/7*a + 20/7*a**2.
-2*(a - 11)*(a - 1)*(a + 2)/7
Let h(f) be the second derivative of f**5/4 + 55*f**4/12 - 35*f**3/3 - 60*f**2 + 93*f. Suppose h(a) = 0. Calculate a.
-12, -1, 2
Let f be (-4)/10 - 66/(-165). Let b(r) be the third derivative of 0*r + 1/20*r**5 + f - 12*r**2 - 1/4*r**4 + 1/40*r**6 + 0*r**3. Factor b(c).
3*c*(c - 1)*(c + 2)
Find b such that -2/11*b**2 - 6728/11 - 232/11*b = 0.
-58
Let a(q) be the first derivative of -q**4/8 - q**3/6 + 5*q**2/4 - 3*q/2 + 6. Factor a(k).
-(k - 1)**2*(k + 3)/2
Let f(c) be the first derivative of -c**5/150 + c**2 + 18. Let t(d) be the second derivative of f(d). Find v, given that t(v) = 0.
0
Let w(o) = -7*o**2 - 12*o - 9. Let a(m) = -78*m**2 - 135*m - 102. Let k(h) = -4*a(h) + 45*w(h). Solve k(r) = 0 for r.
-1, 1
Let r(p) be the second derivative of 3*p**5/80 + 7*p**4/16 + 7*p**3/4 + 3*p**2 - 35*p. Solve r(b) = 0 for b.
-4, -2, -1
Let l(w) = 2*w - 2. Let y(i) = i**2 - 100*i - 12. Let z(c) = -6*l(c) + y(c). Factor z(t).
t*(t - 112)
Let t(q) be the second derivative of -1/8*q**2 + 8*q - 1/96*q**4 + 0 + 1/16*q**3. Suppose t(f) = 0. Calculate f.
1, 2
Let w(d) = d**3 - 109*d**2 + 114*d - 648. Let f be w(108). Factor 0 + 4/11*o**3 + f*o + 0*o**2 - 2/11*o**4.
-2*o**3*(o - 2)/11
Let k be ((-1)/4)/((-227)/1816). Factor 2*m**k + 2/5*m**4 + 8/5*m**3 + 0 + 4/5*m.
2*m*(m + 1)**2*(m + 2)/5
Let g = 8111 + -8111. Factor -2/5*i**2 + g*i + 8/5.
-2*(i - 2)*(i + 2)/5
Let b(q) = 7*q**3 + 2*q - 1. Let r be b(1). Let h = -8 + r. Factor 3*m**3 - 3*m**4 + 0*m**2 + 2*m**4 + h*m**3 - 2*m**2.
-m**2*(m - 2)*(m - 1)
Let c = -391 + 395. Let d(o) be the second derivative of 3*o + 4/3*o**c + 1/2*o**5 + 0 + 1/3*o**3 - 2*o**2. What is i in d(i) = 0?
-1, 2/5
Let h(a) = a**2 - 1. Let v be h(-1). Let r = -155675/4 - -38919. Factor -r*n**4 + 0 + 0*n**2 - 1/8*n**5 - 1/8*n**3 + v*n.
-n**3*(n + 1)**2/8
Let i(j) = j + 12. Let f be i(-8