 - 2)/3
Let y(r) be the first derivative of -2*r**3/21 + 166*r**2/7 - 13778*r/7 + 109. Determine z, given that y(z) = 0.
83
Let s be -1 + (-12 - (-7292)/560). Let p(u) be the second derivative of -11*u + 0 + 5/28*u**4 + s*u**5 + 9/14*u**2 + 1/2*u**3. Find z such that p(z) = 0.
-3, -1
Find w, given that 0*w + 0 + 0*w**2 + 1/2*w**5 - 1/2*w**4 - w**3 = 0.
-1, 0, 2
Suppose m - 6 = -h, 0 = -3*h - m + 2*m + 14. Suppose 0 = 4*n + 3*n - 14. Let 0*a**3 - 2*a - a**3 + h*a**n - 2*a**3 + a**4 - a**3 = 0. What is a?
0, 1, 2
Let l(b) be the third derivative of b**8/1680 + b**7/2520 - b**6/135 + b**5/90 - 35*b**3/6 + 16*b**2. Let y(w) be the first derivative of l(w). Factor y(a).
a*(a - 1)*(a + 2)*(3*a - 2)/3
Let z(h) = -6*h**4 + 44*h**3 + 50*h**2 - 56*h - 32. Let r(n) = 2*n**4 - 14*n**3 - 17*n**2 + 19*n + 10. Let o(x) = 16*r(x) + 5*z(x). Factor o(b).
2*b*(b - 4)*(b - 1)*(b + 3)
Let x(p) = -p**4 - p**3 - p**2 - p. Let u(y) = -5*y**2 - 13*y**4 - 12*y**3 + 24*y**3 - 15*y - 23*y**3. Let i(s) = 2*u(s) - 22*x(s). Solve i(o) = 0 for o.
-2, 0, 1
Factor 37*o + o**2 + 103 + 22*o + 72*o - 17*o - 10*o.
(o + 1)*(o + 103)
Let y(a) = -a**3 + 40*a**2 - 204*a. Let c be y(6). Let 2/3*q**3 - 8/3*q + c*q**2 + 0 = 0. Calculate q.
-2, 0, 2
Let q be (130/52 + -1)*((-18)/(-14) - 1). Factor -q*c**3 - 6/7*c**2 + 0*c + 0.
-3*c**2*(c + 2)/7
Factor 45/4*c**3 + 30*c**2 + 0 + 20*c.
5*c*(3*c + 4)**2/4
Let b = 18172 + -127192/7. Find p such that 0 - 2/7*p**2 + b*p = 0.
0, 6
Let i(u) be the third derivative of u**6/40 - 3*u**5/20 - 3*u**4/4 + 4*u**3 - u**2 + 124*u. Solve i(y) = 0 for y.
-2, 1, 4
Let a be -8*(42/(-483) + 10/(-414)). Let f = 4 - 1. Factor 8/9*z**4 - 20/9*z**2 + a*z - 2/9*z**5 - 2/9*z**f + 16/9.
-2*(z - 2)**3*(z + 1)**2/9
Suppose 4*y - 6 = j, -10*y = -6*y - 5*j - 30. Find u, given that 0*u + y - 2/3*u**4 + 4/3*u**2 + 2/3*u**3 = 0.
-1, 0, 2
Let l = -80 + 84. Suppose -z - 12 = -2*c + z, 0 = 3*c - 5*z - 26. Factor -2*u + 17*u**2 - l*u**5 + 24*u**3 + 6*u + 16*u**4 + 8*u**5 - u**c.
4*u*(u + 1)**4
Let s(a) be the third derivative of -a**9/56 + a**8/20 + a**7/15 - 2*a**6/45 + a**3 - 31*a**2. Let t(g) be the first derivative of s(g). Solve t(n) = 0 for n.
-2/3, 0, 2/9, 2
Factor 7/4*s - 3/4*s**3 + 3/4*s**2 - 3/2 - 1/4*s**4.
-(s - 1)**2*(s + 2)*(s + 3)/4
Let p(f) be the second derivative of -f**6/80 + 39*f**5/80 - 169*f**4/32 + 21*f. Factor p(t).
-3*t**2*(t - 13)**2/8
Suppose 0 = -5*z + 47 - 7. Factor h**5 - 58*h + z*h**4 - 8*h**2 + 62*h - 5*h**5.
-4*h*(h - 1)**3*(h + 1)
Let -96/7 + 44/7*r - 4/7*r**2 = 0. What is r?
3, 8
Suppose 7*m = x + 11*m - 2, 3*x + 4 = -2*m. Let g be -6*((-3)/x + -2). Suppose -2/5*q - 2/5*q**g + 4/5*q**2 + 0 = 0. Calculate q.
0, 1
Let h(v) = v**2 - 27*v - 118. Let g be h(-4). Let b(i) be the first derivative of g + 1/5*i**3 + 3/5*i**2 + 3/5*i. Solve b(u) = 0.
-1
Factor 0*k**3 + 2/11*k + 3/11*k**2 - 1/11*k**4 + 0.
-k*(k - 2)*(k + 1)**2/11
Let s(c) be the second derivative of c**6/30 - c**4/4 + c**3/3 - 194*c. Let s(p) = 0. What is p?
-2, 0, 1
Let q(h) be the first derivative of h**5/90 + h**4/18 + 2*h**3/27 - 24*h - 4. Let z(d) be the first derivative of q(d). Solve z(m) = 0 for m.
-2, -1, 0
Let j(v) = 14*v**3 + 74*v**2 - 134*v + 74. Let r(z) = -31*z**3 - 150*z**2 + 267*z - 149. Let g(k) = 9*j(k) + 4*r(k). Find a such that g(a) = 0.
-35, 1
Suppose 3*z - 39 + 21 = 0. Let d(t) be the third derivative of 0*t - 2*t**2 + 0*t**5 + 1/40*t**4 - 1/200*t**z + 0*t**3 + 0. Factor d(l).
-3*l*(l - 1)*(l + 1)/5
Let d(m) be the second derivative of m**5/4 + m**4 + 2*m**3/3 + 112*m. Factor d(q).
q*(q + 2)*(5*q + 2)
Let v(l) be the second derivative of l**7/63 - l**6/9 + 4*l**5/15 - 2*l**4/9 + 30*l + 1. Factor v(i).
2*i**2*(i - 2)**2*(i - 1)/3
Let g be (-1)/(1 - 8/4). Suppose -3*u = -8 - g. Suppose -3*a**u + 2*a**2 + 3*a**3 - a**3 - a**2 = 0. Calculate a.
0, 1
Let a be 0*(-3)/6 + 3. Suppose 108 = u + 3*u. Factor -36*p**2 + 3*p**a + u*p**2 + 12*p - 3 - 3*p.
3*(p - 1)**3
Let m(r) be the second derivative of r**5/80 + 61*r**4/24 - r**3/24 - 61*r**2/4 - 12*r + 9. Factor m(n).
(n - 1)*(n + 1)*(n + 122)/4
Factor -q**3 + 40*q**2 - 119*q**2 + 162*q - 33*q**3 - 2*q**4 - 47*q**2.
-2*q*(q - 1)*(q + 9)**2
Let f be (11/44 - (-6)/(-8))*-16. Let h = -10 + 15. What is a in -3*a + f*a + 2*a**2 - h*a = 0?
0
Suppose 0*k + 32 = 3*a + k, a = -2*k + 4. Let t = 14 - a. Factor -1 + 3*o**2 + 1 + o + t*o.
3*o*(o + 1)
Let w = 982 + -82487/84. Let j(c) be the third derivative of 0 + 0*c**3 + 0*c - w*c**4 - 1/210*c**5 + 9*c**2. Solve j(u) = 0.
-1, 0
Let b(h) be the third derivative of -1/60*h**5 + 1/9*h**3 - 10*h**2 + 0*h - 1/72*h**4 + 1/360*h**6 + 0 + 1/630*h**7. Determine j so that b(j) = 0.
-2, -1, 1
Let o(v) be the third derivative of 0*v - 1/80*v**6 + 1/20*v**5 + 0 - 1/2*v**3 + 12*v**2 + 1/16*v**4. Determine f so that o(f) = 0.
-1, 1, 2
Suppose -7*k + 3*k = -20, -f + 2*k = 8. Let y(x) be the second derivative of -7/60*x**4 + 1/5*x**f + x + 0 - 1/6*x**3. Determine g, given that y(g) = 0.
-1, 2/7
Let b(v) = 2*v - 11 + 0*v - v + 0*v - 7*v**3 + 5*v**2. Let o(y) = 34*y**3 - 26*y**2 - 6*y + 54. Let l(k) = -14*b(k) - 3*o(k). Factor l(n).
-4*(n - 2)*(n - 1)*(n + 1)
Let j be 1 + (2/4 - (-17)/34). Suppose 1 = m - j*g - 8, -5*g - 27 = -4*m. Find a such that 0*a + 4/7*a**2 + 0 - 6/7*a**m = 0.
0, 2/3
Let q(n) be the third derivative of n**8/112 + 2*n**7/35 - 11*n**6/40 + 3*n**5/10 + 75*n**2. Factor q(i).
3*i**2*(i - 1)**2*(i + 6)
Let m(h) be the third derivative of -1/16*h**4 + 1/8*h**5 + 28*h**2 + 0 - 1/20*h**6 + 0*h**3 + 0*h. Factor m(s).
-3*s*(s - 1)*(4*s - 1)/2
Let n(v) be the first derivative of v**6/120 + v**5/40 - v**4/48 - v**3/12 - 3*v + 9. Let g(l) be the first derivative of n(l). Solve g(z) = 0 for z.
-2, -1, 0, 1
Let x(b) = -b**2 - 11*b - 2. Let r(g) = -2*g**2 - 21*g - 6. Let s(t) = 4*r(t) - 7*x(t). Let s(o) = 0. What is o?
-5, -2
Let c(v) = -92*v + 4143. Let y be c(45). Factor -16/3 - 8/3*p**4 - 2/3*p**5 + 8/3*p - 2/3*p**y + 20/3*p**2.
-2*(p - 1)**2*(p + 2)**3/3
Let o = -2209 + 6635/3. Let -2 + o*l - 2/3*l**2 = 0. What is l?
1, 3
Let d = 1222 + -31771/26. Let l(g) be the first derivative of -7 + 0*g + 0*g**3 + 0*g**2 + d*g**4. Determine y so that l(y) = 0.
0
Suppose 0 = -5*y - 5*y - 12*y. Let i(v) be the third derivative of 1/300*v**6 - 1/75*v**5 + 0*v**4 + 6*v**2 + y*v + 0*v**3 + 0. Factor i(g).
2*g**2*(g - 2)/5
Let a(r) be the third derivative of r**7/210 - 2*r**6/15 + 22*r**5/15 - 8*r**4 + 24*r**3 + 43*r**2 - 2. Determine m so that a(m) = 0.
2, 6
Let z(s) be the third derivative of -s**6/30 - 34*s**5/15 - 289*s**4/6 + 2*s**2 + 29*s. Determine g, given that z(g) = 0.
-17, 0
Let j(b) be the second derivative of 3*b**5/10 - 215*b**4/12 + 88*b**3/3 - 35*b**2/2 + 638*b. Factor j(d).
(d - 35)*(2*d - 1)*(3*d - 1)
Suppose 0 = 2*u + 7*u - 27. Let -3 + 0*k**2 - 4*k - u*k**2 + 1 + k**2 = 0. What is k?
-1
Let h = 78 + -78. Let u(x) be the third derivative of 0*x**4 - 3*x**2 - 1/480*x**6 + 0*x**3 + 0*x + 1/240*x**5 + h. Find z such that u(z) = 0.
0, 1
Suppose -165 + 46*u + 17*u - 5*u**2 - 42*u + 49*u = 0. What is u?
3, 11
Let b be 82/861 - 4/91. Let x(s) be the first derivative of b*s**3 + 2/65*s**5 + 0*s**2 + 8 + 0*s - 1/13*s**4. Solve x(k) = 0 for k.
0, 1
Let m(y) be the third derivative of -135*y**8/112 - 21*y**7/4 - 33*y**6/4 - 113*y**5/24 + 5*y**4/6 + 5*y**3/3 + 104*y**2 + 1. Solve m(v) = 0.
-1, -2/3, -2/9, 1/6
Let s(f) be the third derivative of -3*f**2 - 1/264*f**4 + 1/1320*f**6 + 1/220*f**5 + 0*f + 0 - 1/22*f**3. Solve s(o) = 0.
-3, -1, 1
Suppose 18 + 222 = -8*t. Let f be (-51)/34 - 49/t. Factor 2/15*n**2 + 0*n - 2/15*n**5 + 0 - 2/15*n**4 + f*n**3.
-2*n**2*(n - 1)*(n + 1)**2/15
Let o(y) be the third derivative of y**9/10584 - y**8/5880 - 11*y**3/3 + 17*y**2. Let r(q) be the first derivative of o(q). Let r(l) = 0. What is l?
0, 1
Let k(l) = -4*l**4 - 22*l**3 - 26*l**2 - 4*l - 4. Let p(u) = u**3 + u - 1. Let x be p(0). Let h(b) = b - 1. Let z(o) = x*k(o) + 4*h(o). Factor z(m).
2*m*(m + 1)*(m + 4)*(2*m + 1)
Solve -1248*c**2 + 1243*c**2 - c**3 - 4*c**3 = 0.
-1, 0
Let m(i) = i**5 + 16*i**4 - 21*i**3 - 5*i**2 - 5. Let k(d) = 8*d**4 - 10*d**3 - 2*d**2 - 2. Let v(h) = -5*k(h) + 2*m(h). Factor v(t).
2*t**3*(t - 2)**2
Let f(j) = j**3 - 7*j**2 + 7*j - 4. Let k be f(6). Let u(c) = c**2 + 2*c**k - 2*c**2. Let q(p) =