et c(y) = y**4 + 12*y**3 - 3*y**2 - 10*y + 3. Let i(j) = -c(j) + 3*s(j). Suppose i(d) = 0. What is d?
-1/2, 0, 1, 4
Let v be (-146)/42 - 6/(-18). Let j = 226/63 + v. Solve 2/9*m**5 + 0*m**4 + j*m**2 + 0*m + 0 - 2/3*m**3 = 0 for m.
-2, 0, 1
Let h = -64444/5 + 12890. Determine u so that 1/5*u**3 - 4/5 - h*u**2 + 9/5*u = 0.
1, 4
Let k(g) = 12*g**2 - 49 + g**2 + 1865*g**3 - 1864*g**3 + 30*g. Let b(s) = -5*s. Let z(m) = -5*b(m) + 5*k(m). Determine y so that z(y) = 0.
-7, 1
Let y(l) = 9*l**5 + 23*l**4 - 11*l**3 - 51*l**2 - 26*l + 4. Let g(i) = -i**5 - 2*i**4 - i**3 - i**2 - i - 1. Let n(m) = 4*g(m) + y(m). Factor n(r).
5*r*(r - 2)*(r + 1)**2*(r + 3)
Solve 30*d**2 - 56/11*d**3 + 900/11*d + 2/11*d**4 + 0 = 0 for d.
-2, 0, 15
Factor -1/2*c**2 + c**3 + 0 + 0*c.
c**2*(2*c - 1)/2
Let r = -53 + 55. Solve 16*t**r + 75 - 13*t**2 + 5*t - 35*t = 0.
5
Let o = 32 + -30. What is n in -12*n**2 + 5*n**o - n + 6*n**2 = 0?
-1, 0
Let u(h) = 3*h**4 - 25*h**3 - 11*h**2 + 33*h. Let f(y) = 6*y**4 - 48*y**3 - 24*y**2 + 66*y. Let t(d) = -4*f(d) + 9*u(d). Let t(q) = 0. What is q?
-1, 0, 1, 11
Let t(b) be the third derivative of -1/40*b**6 + 0*b**3 - 1/2*b**4 + 1/5*b**5 + 0 - 12*b**2 + 0*b. Factor t(w).
-3*w*(w - 2)**2
Let u = 30 + -23. Suppose -u*w - 8 = -11*w. Factor t**3 + 4/3*t - 8/3*t**w + 0.
t*(t - 2)*(3*t - 2)/3
Let u(g) be the third derivative of g**6/630 + g**5/70 + g**4/21 + 4*g**3/63 - 149*g**2 - 2*g. Find t, given that u(t) = 0.
-2, -1/2
Let g be (36/(-8))/((-6)/8). Factor -4*a**4 + 0*a**2 - g*a**3 - 2*a**2 + 2*a**3 + 2*a**4.
-2*a**2*(a + 1)**2
Let s be -2 - -10 - (-2162)/(-235) - -2. Find y, given that s + 6/5*y + 2/5*y**2 = 0.
-2, -1
Let l be (111/30)/(10/(-4)) + 1. Let i = l + 158/225. Factor 0*b + 0 + i*b**5 - 2/3*b**4 - 2/9*b**2 + 2/3*b**3.
2*b**2*(b - 1)**3/9
Let f be 3/12*(4/(-12) - -3). Let n(d) be the first derivative of f*d + 2/3*d**3 + 4 + d**2 + 1/6*d**4. Factor n(a).
2*(a + 1)**3/3
Let h = 138 - 67. Let v = -495/7 + h. What is u in -v + 1/7*u + 1/7*u**2 = 0?
-2, 1
Factor -26*c**4 + 8*c**5 - 4*c**5 - 48*c**3 + 64*c + 16*c**4 + 14*c**4 + 16*c**2.
4*c*(c - 2)**2*(c + 1)*(c + 4)
Determine a so that -18*a**2 - 8*a - 35*a**2 - 3*a + 4*a**3 - 9*a + 37*a**2 = 0.
-1, 0, 5
Let r(u) be the second derivative of u**5/10 + 11*u**4/6 + 20*u**3/3 - 32*u**2 - 115*u. Factor r(f).
2*(f - 1)*(f + 4)*(f + 8)
Factor 0*s**3 + 6*s**2 + 3*s**4 + 96*s - 33*s**3 - 2*s**3 + 63 + 2*s**3 + 9*s**3.
3*(s - 7)*(s - 3)*(s + 1)**2
Let y(s) = 5*s**2 - 21*s - 38. Let b be y(-17). Determine q, given that 3*q**3 - 8133 - 99 + b*q + 36*q**2 - 162*q**2 = 0.
14
Let i(f) = f**2 + f - 2. Let t be i(2). Suppose -19 + 7 = -t*b. What is w in -w**2 - 2*w**b - w**5 + w**4 - w - 3*w + 5*w**3 + 2*w = 0?
-1, 0, 1, 2
Let o(w) be the first derivative of -3/25*w**5 - 1/10*w**6 + 0*w**2 + 3/20*w**4 + 0*w - 11 + 1/5*w**3. Factor o(a).
-3*a**2*(a - 1)*(a + 1)**2/5
Let r = -17 - -341/20. Let c(k) be the second derivative of r*k**4 + 0*k**2 + 0 + 8*k - 3/10*k**3. Factor c(v).
3*v*(v - 3)/5
Let -g**5 - 1/2*g - 21/2*g**3 + 3/4 - 23/4*g**4 - 7*g**2 = 0. Calculate g.
-3, -1, 1/4
Suppose 2*j + 5*d - 14 = 0, -4*j - 143*d + 146*d = -2. Factor 0 + 1/3*t + 1/6*t**j.
t*(t + 2)/6
Let i(v) be the first derivative of -2/3*v - 1/3*v**2 + 2/9*v**3 + 1/6*v**4 + 1. Factor i(d).
2*(d - 1)*(d + 1)**2/3
Let k = 2003/3 - 667. Let v(s) be the second derivative of k*s**3 + 0*s**6 + 0*s**4 - 2/5*s**5 + 2/21*s**7 + 0 - s + 0*s**2. Suppose v(z) = 0. Calculate z.
-1, 0, 1
Let d(x) be the second derivative of x**5/2 + 11*x**4/3 + 8*x**3/3 - 99*x + 1. Determine v, given that d(v) = 0.
-4, -2/5, 0
Let o(j) be the second derivative of -3/10*j**5 - 1/42*j**7 + 0 - 1/3*j**4 - 3*j - 1/6*j**3 - 2/15*j**6 + 0*j**2. Factor o(w).
-w*(w + 1)**4
Let b(a) be the first derivative of a**4/2 - 34*a**3/3 + 16*a**2 - 30. Factor b(d).
2*d*(d - 16)*(d - 1)
Let s = -2341 + 16419/7. Let p be 7/98*4 - (-4 - (4 + -6)). Factor -p*y + 2/7*y**2 + s.
2*(y - 4)**2/7
Let h(f) be the first derivative of -4*f**5/5 + 9*f**4 + 28*f**3 + 22*f**2 + 3. Suppose h(s) = 0. Calculate s.
-1, 0, 11
Solve -801*r**4 - 144*r**4 + 2880*r + 7602*r**2 - 20*r**5 - 531451*r**3 + 520656*r**3 + 1278*r**2 = 0.
-24, -1/4, 0, 1
Let h(q) be the first derivative of q**6/660 + q**5/165 - q**4/132 - 2*q**3/33 - 3*q**2/2 - 12. Let b(l) be the second derivative of h(l). Solve b(g) = 0.
-2, -1, 1
Let u(y) be the third derivative of 2/3*y**3 + 0 + y**2 + 1/180*y**6 + 0*y + 1/12*y**4 + 1/30*y**5. Let q(v) be the first derivative of u(v). Solve q(s) = 0.
-1
Let i(b) = -9*b**2 + 23*b + 1. Let r(z) be the second derivative of -1/2*z**2 + 6*z - 1/6*z**3 - 1/12*z**4 + 0. Let s(c) = i(c) + 5*r(c). Factor s(n).
-2*(n - 1)*(7*n - 2)
Factor 86*l + 13*l + 28*l**2 - 98*l**2 - 23*l**2 + 3 - 9.
-3*(l - 1)*(31*l - 2)
Let i be ((-2)/(-6))/(10/60). Suppose 0 = 2*d - a - 7, 3*a - i = 7. Let 3*q - 4*q**2 - 3*q**5 + 6*q**4 + 0*q**d - 2*q**2 = 0. What is q?
-1, 0, 1
Suppose 4*w + 17 = 29. Suppose 3 = 3*f, w*b + 5 = 5*b - f. Factor 0*r**2 + 2/3*r**b + 0 + 0*r.
2*r**3/3
Suppose -178*h = -186*h + 40. Let t(z) be the first derivative of -21/5*z**h + 3 + 3*z**2 + 7*z**3 + 0*z - 3/2*z**4. Let t(m) = 0. Calculate m.
-1, -2/7, 0, 1
Let c = -3090 - -21680/7. Factor 2/7*x**2 + c + 20/7*x.
2*(x + 5)**2/7
Let z be (24/(-45))/((-6)/(-9))*5. Let x be (z/8)/(21/(-36)). Determine o, given that x*o**2 + 16/7*o - 6/7*o**5 + 26/7*o**4 - 34/7*o**3 - 8/7 = 0.
-2/3, 1, 2
Suppose -2*i - 10 = 3*i. Let n be 2 + ((-2)/i - 1). Factor 9 - 18 + n*k**3 + 15*k - 7*k**2 - k**3.
(k - 3)**2*(k - 1)
Let q = -4718/9 - -525. Let u(n) be the first derivative of -2/9*n - q*n**2 + 16/27*n**3 + 3. Suppose u(y) = 0. What is y?
-1/8, 1
Let b be (-11)/(165/9)*8/(-3). Let t(l) be the first derivative of 49/10*l**4 - 2 - 154/15*l**3 + 32/5*l**2 - b*l. Suppose t(k) = 0. What is k?
2/7, 1
Suppose 3*d = -t + 8, 90 - 88 = -2*t + 3*d. Let v = 341 - 1681/5. Factor 0 + 0*p - v*p**3 - 2/5*p**5 - 16/5*p**t - 12/5*p**4.
-2*p**2*(p + 2)**3/5
Suppose -63*q + 65*q = 0. Suppose 0 = f - 4*h + 12, q = 3*f - 0*f + 3*h - 24. Factor 0*m**2 + 0 - 1/7*m**f + 0*m**3 + 1/7*m**5 + 0*m.
m**4*(m - 1)/7
Factor 16*s**2 - 1417*s**4 - 1421*s**4 + 2834*s**4 - 8*s**3 + 32*s.
-4*s*(s - 2)*(s + 2)**2
Let m(f) = -f**2 + 14*f. Let p be m(14). Let i(q) = -q**2 - 20*q + 49. Let h be i(-22). Factor 2/9*w**4 - 2/9*w**2 + 2/9*w**h + p*w + 0 - 2/9*w**3.
2*w**2*(w - 1)*(w + 1)**2/9
Let f be -4 + 76/3 + -21. Factor -4/3 + f*h**2 - 2/3*h + 1/6*h**3.
(h - 2)*(h + 2)**2/6
Let u(y) be the first derivative of -y**4/24 + y**3/2 + 27*y**2/4 + 45*y/2 + 521. Find h, given that u(h) = 0.
-3, 15
Suppose -w + 117 = i, 2*w + 4*i + 540 = 7*w. Let n = -223/2 + w. Factor 1/4*a**2 + n - 3/4*a.
(a - 2)*(a - 1)/4
Suppose 171*a + 45 + 4*a**3 - 31*a + 50 + 56*a**2 - 7 = 0. What is a?
-11, -2, -1
Suppose -f - 3 = -5. Suppose 3*v - 21 = -5*k, -k = -5*v + 2*k + 1. Determine o so that -f + 2 - o**2 + 0*o**v = 0.
0
Let d(b) = -2*b**2 - 8*b + 1. Let n(t) = -11*t**2 - 46*t + 6. Let h(k) = -34*d(k) + 6*n(k). Factor h(q).
2*(q - 1)**2
Let p(d) be the first derivative of d**3/12 - 5*d**2/8 + 3*d/2 + 15. Factor p(t).
(t - 3)*(t - 2)/4
Let t(y) = 3*y**2 + 9*y - 6. Let b be (24/(-10))/((-7)/35). Suppose 8*c - b = 10*c. Let g(h) = 1. Let l(p) = c*g(p) - t(p). Determine s so that l(s) = 0.
-3, 0
Factor -75*v - 135 + 36 + 3*v**3 - 516*v**2 + 543*v**2.
3*(v - 3)*(v + 1)*(v + 11)
Let w(m) be the first derivative of -m**5/270 + 2*m**4/9 - 16*m**3/3 - 19*m**2 + 31. Let a(g) be the second derivative of w(g). Factor a(d).
-2*(d - 12)**2/9
Factor 159/2*k**2 + 8427/2*k + 148877/2 + 1/2*k**3.
(k + 53)**3/2
What is j in 35/2*j**3 + 145/4*j + 7/2*j**4 + 38*j**2 + 25/2 + 1/4*j**5 = 0?
-5, -2, -1
Let q be -10 + 6 + 618/162. Let s = q - -23/27. Factor 1/3*j**4 - s*j**2 + 0*j + 0*j**3 + 1/3.
(j - 1)**2*(j + 1)**2/3
Let u(y) = -y**5 + y**4 - 2*y**3 + y**2. Let m(g) = -g**5 + 8*g**4 - 50*g**3 + 94*g**2 - 75*g + 22. Let x(a) = m(a) - 2*u(a). Factor x(z).
(z - 2)*(z - 1)**3*(z + 11)
Let z = 5676/3545 + -4/3545. Determine y, given that -z - 2/5*y**2 + 2*y = 0.
1, 4
Solve -25*x**4 + 40*x**3 - 1118 - 40*x + 69*x**2 - 24*x**2 + 1098 = 0.
-1, -2/5, 1, 2
Suppose s = 3*b - 8, 10*b - 12*b = -2*s. Let h(w) be the first derivative of -4 + 1/6*w**b - 1/9*w**3 + 0*w + 1/