w - 1)**2*(w + 1)**3
Let x = -1843 - -1847. Let u(c) be the first derivative of 15 - 1/3*c**2 - 1/6*c**x + 0*c + 4/9*c**3. What is p in u(p) = 0?
0, 1
Solve v**4 + 58*v - 5 - 58*v + 5 + 2*v**3 = 0.
-2, 0
Suppose 0*q + 105 = 5*q. Let l(p) = -p + 16. Let a be l(13). Find y, given that 10*y - 6 - 3*y**4 - q*y + 8*y + 3*y**a + 9*y**2 = 0.
-1, 1, 2
Let t(x) be the second derivative of 27*x**7/56 - 27*x**6/40 - 189*x**5/80 + 7*x**4/16 + 5*x**3/2 + 3*x**2/2 - 383*x. Suppose t(b) = 0. What is b?
-1, -1/3, 2/3, 2
Let s(v) be the first derivative of -v**4/12 - 7*v**3/3 - 49*v**2/2 + 7*v + 15. Let c(r) be the first derivative of s(r). Factor c(g).
-(g + 7)**2
Factor 16*w**3 + 62*w**2 - 176*w**2 + 60*w**2 + 20*w**4 + 8*w**5 + 58*w**2.
4*w**2*(w + 1)**2*(2*w + 1)
Suppose 45*j**2 - 11*j**5 + 55*j**3 - 3*j**5 - 6*j**5 + 21*j**2 - 135*j**4 + 69*j**2 - 35*j = 0. Calculate j.
-7, -1, 0, 1/4, 1
Let x be ((-3)/(-4))/(2133/13904). Factor -4/9*m**3 - 140/9*m + 100/9 + x*m**2.
-4*(m - 5)**2*(m - 1)/9
Let h**2 - h**2 + 1922 - h**2 + 3*h**2 - 95*h - 29*h = 0. Calculate h.
31
Suppose 0 = -5*p - 25, 5*p - 215 = 2*g - 0*g. Let j be ((-5)/8)/(100/g). Solve 0 - 9/8*d**2 - j*d = 0 for d.
-2/3, 0
Let g be (-3)/6 + 1528/16. Suppose -2*x - 91 = -g. Factor -12/5 - 3/5*n**x - 12/5*n.
-3*(n + 2)**2/5
Let f(v) be the third derivative of v**8/112 - 3*v**6/20 + 2*v**5/5 - 3*v**4/8 - 3*v**2 + 12. Factor f(r).
3*r*(r - 1)**3*(r + 3)
Let t(b) be the second derivative of -b**4/42 + 4*b**3/7 + 13*b**2/7 + 7*b - 10. Solve t(c) = 0.
-1, 13
Suppose -29*r - 2*y - 4 = -25*r, -5*y - 10 = -2*r. Determine w, given that r - 2*w - 2/9*w**3 + 4/3*w**2 = 0.
0, 3
Let f = -341 - -649. Let r = 310 - f. Factor 24 + 3/2*k**r - 12*k.
3*(k - 4)**2/2
Let b(h) = h**2 + 12. Let w be b(0). Let p = -641 + 1924/3. Suppose 4*n + p + w*n**2 = 0. Calculate n.
-1/6
Let b(a) be the first derivative of 3*a**4/28 - a**3 - 6*a**2/7 + 12*a + 368. Determine y, given that b(y) = 0.
-2, 2, 7
Let q = 194/603 - 20/201. Factor 2/9*u**2 + q*u - 4/9.
2*(u - 1)*(u + 2)/9
Let m(z) be the third derivative of 12*z**2 + 0*z + 0*z**3 + 1/36*z**4 + 0 + 1/180*z**5 - 1/360*z**6. Factor m(t).
-t*(t - 2)*(t + 1)/3
Let 20*x + 14*x + 4*x**3 - 6 - 3*x**3 - 65*x + 24*x = 0. What is x?
-2, -1, 3
Let q(t) be the first derivative of 55*t**4 - 5*t**3 - 5*t**2 + 77. Let q(f) = 0. Calculate f.
-2/11, 0, 1/4
Let m be (-12)/14*14/(-3). Suppose -g + m*g = 21. Factor 3*j**3 + 3*j - g*j**2 + 0*j + j**2.
3*j*(j - 1)**2
Let k(n) be the second derivative of n**7/14 - 3*n**5/5 + n**4/2 + 3*n**3/2 - 3*n**2 + 279*n. Solve k(z) = 0.
-2, -1, 1
Let b(u) be the second derivative of 3*u**5/80 + 3*u**4/4 + 9*u**3/2 + 12*u**2 - 2*u + 11. Suppose b(y) = 0. Calculate y.
-8, -2
Suppose -2*n + 0 = -u - 1, 2*u = -2*n + 10. Let w(j) = -2*j**2 + 8*j - 2. Let l be w(u). Factor 12*f**2 + 4*f + 13*f**3 + 0*f**l - 2*f**3 + 3*f**4.
f*(f + 1)*(f + 2)*(3*f + 2)
Let i(x) be the first derivative of x**8/3528 - 2*x**7/2205 + x**5/315 - x**4/252 + 15*x**2 - 10. Let o(w) be the second derivative of i(w). Factor o(g).
2*g*(g - 1)**3*(g + 1)/21
Let h = 3 - -21. What is p in -48 + p + h*p - 3*p**2 - p = 0?
4
Factor 1122*y + 2*y**4 - 35*y**3 + 1524*y + 1134*y**2 + 125*y**3.
2*y*(y + 3)*(y + 21)**2
Let j(g) = -g**2 + 3*g - 2. Let a be j(2). Let z(u) be the second derivative of 0*u**3 - 1/10*u**2 + 3*u + 1/60*u**4 + a. Suppose z(q) = 0. Calculate q.
-1, 1
Let i = 66 - 64. Suppose 2*h**3 - 2*h**4 - 8*h**3 - 9*h**i + 5*h**2 = 0. What is h?
-2, -1, 0
Let x(j) be the third derivative of j**7/1680 + j**6/960 - 3*j**5/160 - 3*j**4/64 - 14*j**2. Factor x(v).
v*(v - 3)*(v + 1)*(v + 3)/8
Suppose 0*q + 0*q**3 - 294 + 36*q**2 + 4*q - 36*q - 3*q**3 - 31*q = 0. What is q?
-2, 7
Solve 816*n**2 + 117/2*n**4 - 336*n**3 - 384 - 576*n - 15/4*n**5 = 0.
-2/5, 4
Let l(n) be the second derivative of -3*n**5/7 + 61*n**4/21 - 4*n**3/21 - 16*n**2/7 + 71*n. Solve l(k) = 0 for k.
-1/3, 2/5, 4
Let x(y) be the first derivative of -8*y**2 - 4*y - 4*y**4 + 15 - 8*y**3 - 4/5*y**5. Find m such that x(m) = 0.
-1
Let z(g) be the third derivative of 1/270*g**5 - 1/108*g**4 + 0*g + 14*g**2 + 0 - 2/27*g**3. Factor z(s).
2*(s - 2)*(s + 1)/9
Let l(s) = 16*s**3 - 8*s**2 + 2*s. Let j(a) = 5*a**3 - 3*a**2 + a. Let b be (-14)/(-28) + 78/4. Let m = -17 + b. Let k(r) = m*l(r) - 10*j(r). Factor k(i).
-2*i*(i - 2)*(i - 1)
Let q = -68096/3 + 22700. Factor 44/3*o**3 + 100/3*o + 0 + q*o**4 + 140/3*o**2.
4*o*(o + 1)*(o + 5)**2/3
Let b(n) be the third derivative of n**5/210 - n**4/28 - 6*n**3/7 - 37*n**2. Solve b(f) = 0.
-3, 6
Suppose -14*q + 18*q - 24 = 0. Suppose 0 = q*t - 10*t + 12. Factor i**t - 4*i**2 + 2 + 5*i**2 + 3*i**2 + 7*i - 2*i.
(i + 1)**2*(i + 2)
Let d = -2/101 + -1348/3333. Let m = -1/11 - d. Find h such that 0 + 0*h**2 - m*h**5 + 0*h**4 - 1/3*h + 2/3*h**3 = 0.
-1, 0, 1
Let z(m) be the second derivative of 0*m**2 + 3/40*m**5 - 1/84*m**7 - 12*m - 1/6*m**3 + 0 - 1/60*m**6 + 1/24*m**4. Find j, given that z(j) = 0.
-2, -1, 0, 1
Let u(h) be the first derivative of h**4/18 - 56*h**3/27 - 97*h**2/9 + 248*h/9 + 829. Factor u(j).
2*(j - 31)*(j - 1)*(j + 4)/9
Let z(r) be the third derivative of r**8/168 + 4*r**7/35 + 7*r**6/12 - 2*r**5/5 - 3*r**4 + 2*r**2 + 20*r. Suppose z(f) = 0. What is f?
-6, -1, 0, 1
Let u(o) be the second derivative of -o**4/90 - o**3/3 - 44*o**2/15 - 187*o. Factor u(l).
-2*(l + 4)*(l + 11)/15
Suppose 3 + 22 = 5*c. Suppose c*o = 120 - 110. Factor 0 - 2/7*a**4 + 0*a**o + 0*a**3 + 0*a.
-2*a**4/7
Find a, given that 4 - 21*a**3 + 141*a**2 + 57*a**4 - 4 - 146*a**3 + 6*a**5 - 36*a - a**3 = 0.
-12, 0, 1/2, 1
Let h = -29 - -72. Let p = 43 - h. Suppose 3/2*v**3 - 3/2*v**4 + p*v - 3/2*v**5 + 3/2*v**2 + 0 = 0. What is v?
-1, 0, 1
Let b(w) = 2*w - 19. Let m = 14 - 3. Let p be b(m). Let 6 - 11*k**p + 8*k**4 + 4*k**5 - 16*k**2 - 3 + 5 + 3*k**3 + 4*k = 0. Calculate k.
-2, -1, 1
Let k(d) be the first derivative of d**8/336 + d**7/42 + 5*d**6/72 + d**5/12 - 5*d**3/3 + 18. Let c(q) be the third derivative of k(q). Factor c(o).
5*o*(o + 1)**2*(o + 2)
Let i be (20/84)/((-395)/(-948)). Factor -i*s**2 - 4/7*s + 0 - 1/7*s**3.
-s*(s + 2)**2/7
Suppose -40*h**2 - 12*h**3 - 2/3*h**4 + 400/3*h + 0 = 0. What is h?
-10, 0, 2
Let j(q) be the second derivative of q**8/112 - q**6/20 + q**4/8 - 11*q**2/2 + 2*q. Let m(c) be the first derivative of j(c). Factor m(b).
3*b*(b - 1)**2*(b + 1)**2
Suppose 3*x - 5*x = -4*t + 62, -4*x - 3*t = 124. Let l = x + 33. Factor -6*c**l + 3*c + 0*c**2 - c.
-2*c*(3*c - 1)
What is v in 6 + 2687*v**2 + v - 1341*v**2 - 1347*v**2 = 0?
-2, 3
Let l be (-123)/(-2) + ((-171)/18)/(-19). Let n = -59 + l. Factor 2/5*g**4 + 0*g + 0*g**n - 2/5*g**2 + 0.
2*g**2*(g - 1)*(g + 1)/5
Suppose 3*v + 5*t - 30 = -2*v, -5*t + 22 = 4*v. Factor v*y**3 - 9258 + 5*y**2 - 5*y**3 + 9257 + y.
(y + 1)**2*(3*y - 1)
Suppose 122 = 7*y + 906. Let v be y/42*9/(-4). Solve -3/5*p**2 - v*p - 15 = 0 for p.
-5
Let d(u) = -220*u**2 - 10 + 300*u - 20*u**3 + 50 + 125*u**3. Let a(w) = -8*w**3 + 17*w**2 - 23*w - 3. Let s(k) = 40*a(k) + 3*d(k). Factor s(r).
-5*r*(r - 2)**2
Let j(b) = b**3 + 5*b**2 + 8*b + 5. Let v be j(-3). Let a be (0/(-2))/(9 + -7 + v). Solve 2/3*q**2 + 8/3*q + a = 0.
-4, 0
Let c(k) be the second derivative of -k**4/102 + 5*k**3/51 - 4*k**2/17 - 106*k. Factor c(i).
-2*(i - 4)*(i - 1)/17
Solve d**2 + 1/4*d - 1 - 1/4*d**3 = 0.
-1, 1, 4
Let w(h) be the second derivative of -h**2/2 - 15*h. Let q(b) = -2*b**2 + 2*b - 2. Let g(f) = 2*q(f) - 12*w(f). Factor g(l).
-4*(l - 2)*(l + 1)
Let r(q) be the first derivative of 0*q**2 + 0*q**4 - 10/9*q**3 + 2/15*q**5 + 41 + 8/3*q. Solve r(v) = 0 for v.
-2, -1, 1, 2
Factor -5/4*c + 0 - 1/4*c**2.
-c*(c + 5)/4
Let s(o) = -o**3 + 17*o**2 - 88*o + 128. Let m be s(8). Solve -10/7*i**2 - 2/7*i + m = 0.
-1/5, 0
Let k(g) be the third derivative of 0 + 1/36*g**4 + 1/90*g**5 + 0*g + 3*g**2 + 0*g**3. Factor k(c).
2*c*(c + 1)/3
Let l(m) be the second derivative of m**7/14 + 3*m**6/5 + 9*m**5/10 - 4*m**4 - 15*m**3/2 + 27*m**2 + 315*m. Let l(c) = 0. What is c?
-3, -2, 1
Suppose 3*b + 141*f = 146*f + 2, 3*b = f + 10. What is h in -2*h**3 - 8/13*h**2 - 10/13*h**b + 0 + 8/13*h = 0?
-2, -1, 0, 2/5
Factor 0*o**3 - 6*o**2 + o**3 + 136*o + o**3 + 9*o**2 + 128 + 37*o**2.
2*(o + 2)**2*(o + 16)
Let w = 629/4 + -157. Let u(q) be the sec