4*l**3 - 28*l + 242 - 16*l - 8*l**4 - l**4 + 7*l**4 - 240*l**2.
-2*(l - 11)**2*(l - 1)*(l + 1)
Find t such that -32/5*t**4 + 4/5 - 16/5*t**3 - 34/5*t + 78/5*t**2 = 0.
-2, 1/4, 1
Suppose 81 - 103*r + 436*r + 55*r**3 + 258*r**2 - 9*r**4 - r**3 + 54 - 3*r**5 = 0. What is r?
-3, -1, 5
Suppose 1779 - 1793 = -7*r. Let t(s) be the first derivative of -2/3*s**6 + 4/5*s**5 + 0*s**3 + 0*s**4 + 0*s + 0*s**r - 12. Suppose t(v) = 0. What is v?
0, 1
Suppose 0 = 45*v - 7*v. Let h(b) be the first derivative of v*b + 3 - 3/2*b**3 + 1/2*b**2. Factor h(k).
-k*(9*k - 2)/2
Let h(l) = -9*l**2 + 2*l + 5. Let g(o) = 2*o**2 + o + 1. Let r(f) = -10*g(f) - 2*h(f). What is j in r(j) = 0?
-5, -2
Solve 289 + 1/2*i**3 + 18*i**2 + 357/2*i = 0 for i.
-17, -2
Determine n, given that 162*n**3 - 6*n**2 + 0*n**4 - n**4 + 7*n**2 - 6*n - 156*n**3 = 0.
-1, 0, 1, 6
Let i(a) be the third derivative of a**7/1470 - 7*a**6/60 + 767*a**5/140 + 175*a**4/6 + 1250*a**3/21 + 116*a**2. Factor i(k).
(k - 50)**2*(k + 1)**2/7
Let y(t) be the second derivative of 0*t**4 - 2/45*t**5 - 1/9*t**2 + 0 - 10*t + 1/9*t**3. Determine f, given that y(f) = 0.
-1, 1/2
Factor -2/7*z + 1/7 + 1/7*z**2.
(z - 1)**2/7
Let c be (8 - 564/70)/((-7)/49). Let 2/5 + 0*p - c*p**2 = 0. Calculate p.
-1, 1
Find v, given that 2/7*v**3 - 2/7*v - 10/21*v**2 + 8/21*v**4 + 2/21 = 0.
-1, 1/4, 1
Let w(f) be the third derivative of -f**8/84 + 22*f**7/105 - 43*f**6/30 + 23*f**5/5 - 6*f**4 - 59*f**2. Suppose w(p) = 0. What is p?
0, 1, 3, 4
Suppose 26*u = 27*u - 4. Let o(n) be the second derivative of -u*n + 0 + 4/7*n**2 + 1/7*n**3 - 1/42*n**4. Let o(g) = 0. Calculate g.
-1, 4
Let g(r) be the third derivative of -r**5/60 + 35*r**2. Let b(f) = -3*f**3 + 21*f**2 + 3*f - 12. Let z(m) = b(m) + 9*g(m). Factor z(y).
-3*(y - 4)*(y - 1)*(y + 1)
Let p(m) = m**3 - 19*m**2 + 14*m - 680. Let k be p(20). Suppose 0 - 1/3*f**4 + 1/9*f**5 - 4/9*f**3 + 0*f + k*f**2 = 0. What is f?
-1, 0, 4
Let h(w) be the first derivative of -w**4/16 + w**3/3 - w**2/8 - 3*w/2 + 380. Factor h(c).
-(c - 3)*(c - 2)*(c + 1)/4
Let u(b) = 605*b**2 + 135*b + 5. Let k(m) = m. Let j(y) = 3*y - 7. Let c be j(-6). Let v(r) = c*k(r) + u(r). Solve v(z) = 0 for z.
-1/11
Let b(l) be the first derivative of l**5/15 - 5*l**2 - 15. Let w(q) be the second derivative of b(q). Factor w(f).
4*f**2
Let d = 10 + -7. Factor -22*k**2 + 4*k**2 + 3*k**4 + 15*k**d - 5*k**4 - 3*k**3.
-2*k**2*(k - 3)**2
Factor -2/9*o**3 - 10/9*o**2 + 2 - 2/3*o.
-2*(o - 1)*(o + 3)**2/9
Let z = 216 - 363. Let t = z + 150. Suppose -9/2*n - 1/2*n**3 + t*n**2 + 0 = 0. What is n?
0, 3
Let h = 39 + -32. Let s(y) be the third derivative of -1/210*y**h + 1/240*y**6 + 0 + 0*y + 1/672*y**8 + 0*y**5 + 0*y**4 - 5*y**2 + 0*y**3. Factor s(i).
i**3*(i - 1)**2/2
Let s = 95428/39 - 2447. Let k = s - -181/195. What is v in -4/5*v + 8/5*v**5 + 18/5*v**2 + 0 - 18/5*v**4 - k*v**3 = 0?
-1, 0, 1/4, 1, 2
Suppose 5*n = n. Suppose c + n*c - 2 = 0. Factor -c*o**3 - 1 + 2*o**2 - 2*o**4 + 2*o + 1.
-2*o*(o - 1)*(o + 1)**2
Let a(r) be the first derivative of -4*r**5/5 - 3*r**4 + 64*r**3/3 - 24*r**2 - 1. Solve a(x) = 0 for x.
-6, 0, 1, 2
Suppose -4*q + 26 = -3*l + 6, 3*q + 2*l = -2. Suppose 8/15 - 2/15*f**q + 2/5*f = 0. What is f?
-1, 4
Suppose j + 2*l = -j + 18, -5*j = 4*l - 41. Suppose 3*q = -j*z + 9 - 29, -12 = 3*q + 3*z. Factor -6/5*n**3 + q + 0*n**2 + 3/5*n**4 + 0*n.
3*n**3*(n - 2)/5
Factor -4/7*j**3 - 8/7 + 4/7*j + 8/7*j**2.
-4*(j - 2)*(j - 1)*(j + 1)/7
Let a(w) be the third derivative of w**8/6720 + w**7/1680 - w**5/10 + 18*w**2. Let t(s) be the third derivative of a(s). Factor t(z).
3*z*(z + 1)
Let m be (-246)/(-120) - (-3)/(-12). Factor -9/5*i**2 + 3/5*i**3 + m*i - 3/5.
3*(i - 1)**3/5
Let w(m) be the third derivative of m**5/150 + 7*m**4/120 + m**3/10 + 11*m**2 - 2. Factor w(r).
(r + 3)*(2*r + 1)/5
Let c(o) be the first derivative of 2*o**3/3 + 11*o**2 - 22*o - 75. Let b be c(-12). Factor 0*j + 0 - 2/7*j**b + 2/7*j**3.
2*j**2*(j - 1)/7
Let l be (12/(-14))/(4 - 208/42). Let r(p) be the first derivative of -3 + 0*p - l*p**2 + 4/5*p**3 - 3/20*p**4. Factor r(c).
-3*c*(c - 3)*(c - 1)/5
Suppose -14*c = 13*c. Let q(o) be the third derivative of 1/18*o**4 + 1/6*o**3 + c*o + 0 + 3*o**2 + 1/180*o**5. Factor q(f).
(f + 1)*(f + 3)/3
Let i = -45 + 227/5. Let f = 411/7 + -1677/35. Factor f + 18/5*a**2 - i*a**3 - 54/5*a.
-2*(a - 3)**3/5
Factor -60 + 424*o**3 - 399*o**3 + 41*o**2 - 6*o**2 - 140*o.
5*(o - 2)*(o + 3)*(5*o + 2)
Let s(q) be the third derivative of -q**6/780 - q**5/30 + 7*q**4/78 - 11*q**2. Factor s(o).
-2*o*(o - 1)*(o + 14)/13
Let t(r) be the second derivative of -r**7/3360 + r**6/288 - 7*r**5/480 + r**4/32 - 4*r**3/3 - 3*r. Let a(h) be the second derivative of t(h). Factor a(n).
-(n - 3)*(n - 1)**2/4
Let w(s) be the first derivative of 12*s**3 + 30*s**2 + 25*s + 98. Find o, given that w(o) = 0.
-5/6
Let o be (-3)/(-2) + 2*1/(-2). Let x(b) be the second derivative of 2*b - o*b**4 + 0 + 1/10*b**5 - b**2 + b**3. Determine f, given that x(f) = 0.
1
Let z(d) be the second derivative of 5*d**7/42 + 7*d**6/6 + 3*d**5 - 5*d**4/3 - 40*d**3/3 + 2*d - 16. Factor z(a).
5*a*(a - 1)*(a + 2)**2*(a + 4)
Let c(x) be the first derivative of 16/39*x**3 - 7/26*x**4 - 1/13*x**2 + 0*x - 10. Factor c(d).
-2*d*(d - 1)*(7*d - 1)/13
Let o(v) be the third derivative of -v**8/112 - 3*v**7/70 - v**6/20 + 137*v**2. Find d such that o(d) = 0.
-2, -1, 0
Factor -12 - 11*w + 16*w**3 + 47*w - 3*w**4 + 31*w**3 - 29*w**3 - 39*w**2.
-3*(w - 2)**2*(w - 1)**2
Let z(r) be the first derivative of 2*r**5/5 - r**4/2 - 8*r**3 - 271. Factor z(b).
2*b**2*(b - 4)*(b + 3)
Let m(j) = j**2 + 10*j + 4. Let u be m(-9). Let v be -2 - -2 - ((-80)/(-3))/u. Let v*x**2 + 0 + 18*x**5 + 0*x + 24*x**3 + 36*x**4 = 0. What is x?
-2/3, 0
Let b(z) = z - 30. Let p be b(4). Let k be ((-16)/p)/((7 - 3) + -2). Determine j, given that 2/13*j**2 - 2/13*j - k = 0.
-1, 2
Let a(l) be the first derivative of 2*l**6/3 - 88*l**5/5 + 172*l**4 - 2336*l**3/3 + 1792*l**2 - 2048*l + 328. What is d in a(d) = 0?
2, 8
Let p = -1/591 + 1189/4137. Let -p*l**4 + 0*l**3 + 4/7*l**2 + 0*l - 2/7 = 0. What is l?
-1, 1
Let f(g) = 55*g**4 + 205*g**3 - 385*g**2 + 120*g + 455. Let a(s) = 9*s**4 + 33*s**3 - 64*s**2 + 20*s + 76. Let k(h) = -25*a(h) + 4*f(h). Factor k(q).
-5*(q - 2)**2*(q + 1)*(q + 4)
Let t be (76/(-228))/((-2)/12). Let g(f) be the first derivative of 2*f + 5/2*f**2 + f**3 - 1/4*f**4 - t - 1/5*f**5. Factor g(a).
-(a - 2)*(a + 1)**3
Let n(o) be the second derivative of 7*o + 0*o**2 - 1/16*o**4 + 3/80*o**5 + 1/24*o**3 + 0 - 1/120*o**6. Factor n(g).
-g*(g - 1)**3/4
Suppose -4*c - 2*x = -2*c, 0 = 4*c - 2*x. Let s(r) be the second derivative of 1/10*r**5 + 2/5*r**2 - 4/15*r**4 + 1/15*r**3 + 6*r + c. Factor s(j).
2*(j - 1)**2*(5*j + 2)/5
Let s(d) be the first derivative of -5*d - 12 - 10/3*d**2 - 5/9*d**3. Find b such that s(b) = 0.
-3, -1
Factor -95/4*m + 5/2 + 45/4*m**2.
5*(m - 2)*(9*m - 1)/4
Suppose -n + 4*c - 9 = 0, n + 7*c - 11 = 6*c. Let w be (n + -5)*-2 - 52/(-10). Factor 4/5*b + w - 2/5*b**2.
-2*(b - 3)*(b + 1)/5
Determine g so that 0 + 5/4*g**4 - 5/2*g**2 - 25/4*g**3 + 30*g = 0.
-2, 0, 3, 4
Let f(c) be the third derivative of -c**5/12 - 25*c**4/24 + 35*c**3/3 + 5*c**2 + 9. Factor f(y).
-5*(y - 2)*(y + 7)
Let o = 2728/5 + -544. Suppose -3*r + 0*z - 5 = z, 10 = -2*z. Factor -o + 6/5*m**3 + r*m + 14/5*m**2.
2*(m + 1)*(m + 2)*(3*m - 2)/5
Let l = 23/42 - 3/14. Let h(o) be the first derivative of 1/2*o**2 + 7 - l*o**3 + 0*o. Factor h(i).
-i*(i - 1)
Let c(d) = -6*d**2 + 16*d - 3. Let m(r) = 3*r**2 - 8*r + 1. Suppose 18*a - 22*a = -24. Suppose 2*u - 1 = 19. Let v(w) = a*c(w) + u*m(w). Factor v(q).
-2*(q - 2)*(3*q - 2)
Let i(b) be the first derivative of b**5/5 - 2*b**3/3 + b + 10. Factor i(j).
(j - 1)**2*(j + 1)**2
Let h be (-18)/(1*(0 - -1)). Let u be (4 - 3)/((-3)/h). Factor -37*c - 33*c + u + 11*c**2 + c**2 + 55*c - 3*c**3.
-3*(c - 2)*(c - 1)**2
Suppose 6*s = 2*s + 16. Find f such that 5*f**3 - s*f - f + 3*f - f**3 - 2*f**5 = 0.
-1, 0, 1
Let c(w) = 224*w - 1996. Let z be c(9). Determine h so that -335*h**2 - 150*h - z - 165/2*h**3 + 375/2*h**5 + 400*h**4 = 0.
-2, -2/5, -1/3, 1
Suppose 3*l + 71 - 77 = -5*k, 5*l = -4*k + 10. Factor -1/2*v**3 + 3/2*v**2 + l*v + 0.
-v*(v - 4)*(v + 1)/2
Let h be (-27)/72*-4*12/(-99)*-4. Fact