/5
Let v(w) = -w**5 + w**2 - 1. Let p(u) = 4 + 0*u**4 - 10*u - 8*u**4 - 1 - 5 + 10*u**2 - 4*u**5 + 8*u**3. Let b(g) = p(g) - 6*v(g). Solve b(s) = 0.
-1, 1, 2
Let x(k) = k + 3. Let y be x(-1). What is c in 2*c**3 - 16 - 12*c**y + 20*c - 4*c + 8*c = 0?
2
Suppose 45*y**3 + 4 + 183*y - 118*y + 4*y**2 + 96*y**2 + 6 = 0. Calculate y.
-1, -2/9
Let m(p) be the second derivative of -5*p**4/12 - 25*p**3/6 + 15*p**2 - 21*p + 2. Determine y so that m(y) = 0.
-6, 1
Suppose -6*z - 4 = -8*z. Factor 0*p**2 - p**2 + 3*p - 3*p**2 - z*p.
-p*(4*p - 1)
Let a(i) be the second derivative of i**7/3360 + i**6/480 - i**4/24 - 2*i**3/3 - 22*i. Let z(x) be the second derivative of a(x). Find d, given that z(d) = 0.
-2, 1
Factor -6*w**2 - 6*w**3 - 2*w - 2/9.
-2*(3*w + 1)**3/9
Let h(s) be the first derivative of -3*s**4/10 - 22*s**3/3 - 18*s**2/5 + 66. What is j in h(j) = 0?
-18, -1/3, 0
Let y(k) = -k**2 + 28*k - 128. Let m be y(6). Factor 2/7*s**3 + 2/7*s**5 + 0 + 0*s + 0*s**2 + 4/7*s**m.
2*s**3*(s + 1)**2/7
Let a(x) be the second derivative of -x**6/150 - 7*x**5/100 - x**4/6 + 197*x + 1. Solve a(b) = 0.
-5, -2, 0
Suppose -14*q + 13*q = -2. Let f(o) be the first derivative of 1/3*o + 4 - 1/12*o**4 + 1/6*o**q - 1/9*o**3. Determine z, given that f(z) = 0.
-1, 1
Determine c so that 250/3 + 763/6*c**4 + 4099/6*c**3 + 8285/6*c**2 + 49/6*c**5 + 1900/3*c = 0.
-5, -2/7
Let n(o) be the second derivative of -2*o**3/3 + 12*o**2 + 45*o. Let p be n(6). Factor 1/5*k + p + 2/5*k**2 + 1/5*k**3.
k*(k + 1)**2/5
Let g(d) = -2*d**2 + 2*d. Let w(l) = l**2 - 9*l - 9. Let j be w(10). Let q be g(j). Factor 5*m**2 - 3*m**4 + m**2 + q*m**2 - 3.
-3*(m - 1)**2*(m + 1)**2
Let z(y) be the first derivative of -25*y**4/4 + 110*y**3/3 - 20*y**2 - 165. Factor z(x).
-5*x*(x - 4)*(5*x - 2)
Let d = -84402 + 13504527/160. Let b = d + -3/32. Factor -b*s**2 + 0 - 3/5*s**3 + 9/5*s.
-3*s*(s - 1)*(s + 3)/5
Let l(v) = -v**2 + 76*v - 711. Let k be l(65). Find x, given that 3/4*x**k + 3/4 - 3/2*x**2 + 1/4*x**5 + 1/4*x - 1/2*x**3 = 0.
-3, -1, 1
Let h be (1/4 - -1) + (-21093)/19908. Determine f so that -2/21*f**3 + h*f**2 - 2/21*f + 0 = 0.
0, 1
Factor -3*y**3 - 10 + 3*y + 3 - 21*y**2 - 32 + 60*y**2.
-3*(y - 13)*(y - 1)*(y + 1)
Solve -6*s**2 + 8 + 2*s**3 + 1203*s - 1203*s = 0 for s.
-1, 2
Suppose -2/7*b**2 - 62/7*b - 60/7 = 0. Calculate b.
-30, -1
Let r(o) be the first derivative of 98*o**3/33 - 84*o**2/11 + 72*o/11 + 200. Determine i so that r(i) = 0.
6/7
Let t(y) be the second derivative of -y**6/15 - 3*y**5/5 - 2*y**4/3 + 2*y**3 + 5*y**2 - 92*y. Determine d so that t(d) = 0.
-5, -1, 1
Factor 3*d**3 + 0*d**3 + 985 + 249*d**2 - 1101*d - 285 + 69*d + 344.
3*(d - 2)**2*(d + 87)
Let p(i) be the third derivative of 0*i**3 + 0*i + 0 + 7/60*i**6 - 4/3*i**4 + 5*i**2 + 1/105*i**7 + 4/15*i**5. Determine w so that p(w) = 0.
-4, 0, 1
Let z = -124/69 - -1176/23. Factor -z*j + 78*j**2 + 8 - 35/3*j**3.
-(j - 6)*(5*j - 2)*(7*j - 2)/3
Let s be (4/3)/((-13)/(117/(-4))). Let t be 135/90 - (s/2 + 0). Factor 0 - 1/3*r**2 + t*r.
-r**2/3
Let x = 201 + -134. Let v = x - 62. Find h such that 0*h + 2/5*h**v - 2/5*h**3 - 2/5*h**2 + 0 + 2/5*h**4 = 0.
-1, 0, 1
Let m(o) be the first derivative of o + 1/18*o**3 + 5/12*o**2 - 44. Factor m(x).
(x + 2)*(x + 3)/6
Let z(o) = 2*o**2 - 2*o + 4. Let s(n) = 4*n**2 + 12 - 2*n - 13 - n**2 + 5. Let a(m) = -4*s(m) + 5*z(m). Factor a(g).
-2*(g - 1)*(g + 2)
Find l such that -9/8*l**3 + 9/2 - 1/8*l**4 - 23/8*l**2 - 3/8*l = 0.
-4, -3, 1
Factor -12*n**3 - 5476/3 - 4588/3*n + 284*n**2.
-4*(n + 1)*(3*n - 37)**2/3
Let c(v) be the third derivative of -v**6/160 - v**5/5 + 19*v**4/8 - 10*v**3 + 205*v**2. Factor c(s).
-3*(s - 2)**2*(s + 20)/4
Suppose -24 = 4*a - 32. Determine h, given that 6*h**4 - 15*h**3 + 10*h**a - 8*h**2 - 11*h**2 = 0.
-1/2, 0, 3
Let t(x) be the first derivative of 13 + 4*x**3 - 23 - 12 - 4 - 18*x**2 + 27*x. Determine p so that t(p) = 0.
3/2
Let t(u) be the third derivative of 0 + 1/4*u**4 + 11*u**2 + 1/80*u**6 + 0*u**3 - 1/10*u**5 + 0*u. Suppose t(l) = 0. Calculate l.
0, 2
Let t(o) = 14*o + 58. Suppose 26*y - 29*y - 16 = v, 0 = 5*v - y + 16. Let h be t(v). Let 0*g**h + 5/4*g**5 + 5/4*g + 0*g**4 + 0 - 5/2*g**3 = 0. Calculate g.
-1, 0, 1
Suppose 259*b = 375*b - 348. Factor 0 + 0*x + 4/17*x**4 + 0*x**b + 0*x**2 + 2/17*x**5.
2*x**4*(x + 2)/17
Let w be 9/(-27)*((-15)/(-2))/(-5). Let d(q) be the first derivative of -w*q + 1/8*q**4 - 1 - 1/2*q**3 + 3/4*q**2. Let d(x) = 0. What is x?
1
Let v be ((-1)/3)/(1/(-6)). Suppose -121 = -8*b - 105. Let -5*p + b*p - 11*p**4 - 23*p**3 + 5*p**3 - 3*p**5 - 12*p**v - p**4 = 0. What is p?
-1, 0
Let v(y) be the third derivative of -y**7/525 - 2*y**6/15 - 4*y**5 - 200*y**4/3 - 2000*y**3/3 + 2*y**2 + 9*y. Factor v(b).
-2*(b + 10)**4/5
Let c(x) be the first derivative of 2*x**5/15 - 11*x**4/6 + 38*x**3/9 - 3*x**2 - 195. Factor c(m).
2*m*(m - 9)*(m - 1)**2/3
Let o(j) be the third derivative of j**7/1890 + 7*j**6/540 + 53*j**5/540 + 19*j**4/54 + 2*j**3/3 + 23*j**2 - 4. Find x such that o(x) = 0.
-9, -2, -1
Suppose 99 = 5*u + 89. Let y(p) be the third derivative of 1/56*p**4 + 0*p + 3/14*p**3 - 3/140*p**5 - 1/280*p**6 + 0 + 10*p**u. Factor y(l).
-3*(l - 1)*(l + 1)*(l + 3)/7
Let m be 16/10*(-45)/(-18). Suppose k = 3*k - m. Factor 6 - 6*i**3 - k - 3*i**4 + 6*i - 1.
-3*(i - 1)*(i + 1)**3
Let f(r) = -r**3 - 7*r**2 + 9*r + 8. Let n be f(-8). Let q(w) = -2*w. Let h be q(-1). Suppose -4*t + n*t**3 + 4 + h*t**3 + 0*t - 2*t = 0. What is t?
-2, 1
Let o(l) be the second derivative of -l**7/3360 + l**6/288 - l**5/120 + l**3/2 + 13*l. Let j(p) be the second derivative of o(p). Find w such that j(w) = 0.
0, 1, 4
Let z(r) be the third derivative of -1/20*r**6 + 0*r**7 + 10*r**2 - 1/15*r**5 + 0 + 1/168*r**8 + 0*r**3 + 0*r + 0*r**4. What is j in z(j) = 0?
-1, 0, 2
Factor -135 + 41*g - 3 + 55*g**2 + 38 - 101*g.
5*(g - 2)*(11*g + 10)
Let t be (-536)/18 + 2/(-9). Let j = t + 159/5. Factor 0 - j*f**3 - 6/5*f + 3*f**2.
-3*f*(f - 1)*(3*f - 2)/5
Let g be 6/(-40)*112/(-28). Factor g*i**4 - 9/5*i**3 + 6/5*i**2 + 0 + 0*i.
3*i**2*(i - 2)*(i - 1)/5
Let k(b) be the third derivative of -2*b**3 + 1/105*b**7 + 0 + 1/20*b**6 - 1/2*b**5 + 0*b + 23*b**2 + 17/12*b**4. Factor k(z).
2*(z - 1)**3*(z + 6)
Let u = 32 + -29. Factor -3*x**5 + 2*x**4 - 18*x**u + x**5 - 12*x**4 - 2*x**4.
-2*x**3*(x + 3)**2
Factor -2*y**2 + 204/5*y - 16.
-2*(y - 20)*(5*y - 2)/5
Let o(w) = -4*w**5 - w**4 + 5*w**3 + 2*w**2 - 4*w - 1. Let v(q) = 9*q**5 + 2*q**4 - 11*q**3 - 4*q**2 + 9*q + 2. Let t(u) = -7*o(u) - 3*v(u). Factor t(n).
(n - 1)**2*(n + 1)**3
Let p(y) be the second derivative of -y**7/168 - y**6/36 - y**5/24 + 2*y**3 - 14*y. Let q(r) be the second derivative of p(r). Determine a, given that q(a) = 0.
-1, 0
Let o(k) = -12*k**3 - 20*k**2 - 8*k + 40. Let m(q) = -q**2 - q - 1. Let a = 39 + -13. Let v = a + -2. Let u(c) = v*m(c) + o(c). Find z such that u(z) = 0.
-2, 1/3
Let t(y) be the second derivative of y**5/20 + 9*y**4 + 648*y**3 + 23328*y**2 - 355*y. Suppose t(h) = 0. What is h?
-36
Let c(x) be the first derivative of 1/3*x**3 - 12 - x**2 + 0*x - 1/6*x**6 - 1/5*x**5 + 3/4*x**4. Factor c(r).
-r*(r - 1)**2*(r + 1)*(r + 2)
Let l(y) be the second derivative of y**7/3780 - y**5/45 + 7*y**4/12 + y. Let p(t) be the third derivative of l(t). Factor p(d).
2*(d - 2)*(d + 2)/3
Factor 15 + 21/2*j - 21*j**2 - 9/2*j**3.
-3*(j - 1)*(j + 5)*(3*j + 2)/2
Let o be ((10/(-8))/(-5))/((-220)/(-160)). Suppose 2/11*f**4 + 2/11*f**3 - 2/11*f**5 + 0*f - o*f**2 + 0 = 0. What is f?
-1, 0, 1
Let q(i) be the second derivative of i**7/210 + i**6/150 - i**5/25 - i**4/15 - 2*i. Factor q(z).
z**2*(z - 2)*(z + 1)*(z + 2)/5
Find h such that -1 - 4*h**2 - 722*h + 1 + 726*h = 0.
0, 1
Let k be (-372)/3960 - 2/(-20). Let c(d) be the second derivative of 0 + 10/33*d**3 + 2/11*d**4 + 3/55*d**5 + 3/11*d**2 + k*d**6 - 10*d. Factor c(j).
2*(j + 1)**3*(j + 3)/11
Let r be (-56)/(-26) - (13 + (-1837)/143). Let h(m) be the first derivative of -3/2*m**r + 0*m - 8 - m**3. Factor h(d).
-3*d*(d + 1)
Let k = 17 - 17. Factor 1 + k*x + 0*x**2 + 2*x + 0 + x**2.
(x + 1)**2
Suppose 3*z - 10 = 2. Suppose 2*k + 0*k - 4 = 5*s, 0 = -3*k + z*s + 6. Suppose 28*u - 5*u**2 + 7*u**k - 4*u**3 + 16 + 6*u**2 = 0. Calculate u.
-1, 4
Let j(m) be the first derivative of -m**5/20 - 45*m**4/16 + 23*m**3/