k - 2 = -4. Let a(c) = -c**2 + 15*c - 11. Let m(p) = -p + 1. Let s(w) = k*a(w) - 22*m(w). Suppose s(i) = 0. What is i?
0, 4
Let d(v) be the second derivative of -v**6/450 - v**5/30 + 11*v**3/6 + 5*v. Let n(s) be the second derivative of d(s). Factor n(z).
-4*z*(z + 5)/5
Factor 1/2*j**3 + 5/2 - 1/2*j - 5/2*j**2.
(j - 5)*(j - 1)*(j + 1)/2
Let s(l) be the second derivative of 0*l**2 - 17*l + 1/27*l**4 + 16/27*l**3 + 0. Factor s(a).
4*a*(a + 8)/9
Let s be ((-153)/(-17) + -9)/((-2)/(-1)). Let j = 214/1419 + 4/129. Factor -2/11*x**2 - 4/11*x**3 + s + 0*x - j*x**4.
-2*x**2*(x + 1)**2/11
Let r(u) be the second derivative of -u**7/630 - u**6/120 - u**5/90 + 11*u**2/2 + 15*u. Let a(y) be the first derivative of r(y). Suppose a(t) = 0. Calculate t.
-2, -1, 0
Let u = 89 + -88. Let m be (1 - -3)*(-1)/((-7)/u). Let m*g**5 + 2/7*g + 17/7*g**4 + 13/7*g**2 + 0 + 24/7*g**3 = 0. Calculate g.
-2, -1, -1/4, 0
Let b(k) = 5*k**2 + 8*k - 1. Let h(t) = -2*t**2 - t - 1. Let v(a) = b(a) + 3*h(a). What is y in v(y) = 0?
1, 4
Let z(d) be the third derivative of -d**7/350 - 19*d**6/100 - 429*d**5/100 - 323*d**4/10 - 578*d**3/5 + 5*d**2 - 37*d. Suppose z(x) = 0. What is x?
-17, -2
Let -100/13*o**2 + 0 - 64/13*o - 2/13*o**4 - 38/13*o**3 = 0. What is o?
-16, -2, -1, 0
Suppose -2*r = -0*r. Suppose 197*p = -239*p. Let r*w + p*w**2 - 1/4*w**3 + 0 = 0. What is w?
0
Let d(l) be the first derivative of -32/9*l**2 + 64/9*l + 20/27*l**3 + 30 - 1/18*l**4. Factor d(u).
-2*(u - 4)**2*(u - 2)/9
Let v be (-22)/176 + (-105)/(-72). Factor -1/3*h**2 - 4/3 + v*h.
-(h - 2)**2/3
Suppose 37*m - 24*m = 17*m. Let t(q) be the second derivative of 0*q**2 - 7*q + m - 1/27*q**3 + 1/54*q**4. Find b, given that t(b) = 0.
0, 1
Let r(w) be the first derivative of -8*w**6/7 + 148*w**5/35 - 5*w**4/14 - 2*w**3/7 - 212. Let r(j) = 0. What is j?
-1/6, 0, 1/4, 3
Let u(t) be the first derivative of t**4/8 + t**3 + 11*t**2/4 + 3*t - 79. Factor u(n).
(n + 1)*(n + 2)*(n + 3)/2
Factor 4/3*g**2 - 64/3*g + 80.
4*(g - 10)*(g - 6)/3
Let u(s) be the second derivative of -s**5/12 + 5*s**4/12 + 5*s**3/2 - 13*s**2/2 - s. Let j(r) be the first derivative of u(r). Let j(f) = 0. Calculate f.
-1, 3
Determine u, given that -158*u - 6*u**4 - 15*u**4 + 107*u**2 + 2*u**5 + 36*u**3 - 36 + 170*u = 0.
-1, 1/2, 6
Let n(v) be the first derivative of v**3/4 + 573*v**2/4 + 109443*v/4 + 174. Factor n(r).
3*(r + 191)**2/4
Let -121*q + 3*q**2 - 98*q + 263*q - 89*q = 0. What is q?
0, 15
Let h(s) be the first derivative of s**6/30 - 6*s**5/25 + 11*s**4/20 - 2*s**3/15 - 6*s**2/5 + 8*s/5 + 250. Let h(y) = 0. What is y?
-1, 1, 2
Let h = -2078 + 6238/3. Let 1/6*g**2 - h*g + 7/6 = 0. What is g?
1, 7
Let b(v) be the first derivative of -2*v**5/5 + v**4/3 + v**3/18 - v**2/12 + 10. Factor b(u).
-u*(2*u - 1)**2*(3*u + 1)/6
Suppose -9*z - 13 = 32. Let s = 7 + z. Let 0 - 2*h**s + 1/3*h = 0. Calculate h.
0, 1/6
Let d = -71 - -65. Let v(x) = -8*x - 46. Let q be v(d). Factor -4/3*f - 10/3*f**q - 2/3*f**4 - 8/3*f**3 + 0.
-2*f*(f + 1)**2*(f + 2)/3
Let g(k) = k**2 + 13*k + 6. Let w(h) = 2*h**2 + 29*h + 14. Let f(u) = 9*g(u) - 4*w(u). Factor f(c).
(c - 1)*(c + 2)
Let o(d) be the third derivative of 1/13*d**3 - 2/195*d**5 + 1/78*d**4 + 0*d - 4*d**2 + 1/1365*d**7 - 1/390*d**6 + 0. Determine y so that o(y) = 0.
-1, 1, 3
Factor 7/3*k + 1 - 10/3*k**2.
-(k - 1)*(10*k + 3)/3
Let k(o) be the second derivative of -25*o**4/3 - 254*o**3/3 - 20*o**2 - 2*o + 41. Solve k(f) = 0 for f.
-5, -2/25
Let o(i) be the second derivative of -i**4/3 - 24*i**3 - 648*i**2 + 3*i - 10. Find z, given that o(z) = 0.
-18
Let w be 0 + -4 + 8 + -1. Factor -5*x**4 + 174*x**3 - 5*x**4 - 15*x**5 - 169*x**w.
-5*x**3*(x + 1)*(3*x - 1)
What is l in 16*l**4 + 0*l - 12*l**3 - 10681 - 16*l**2 - 4*l**5 + 10681 + 16*l = 0?
-1, 0, 1, 2
Let g = -2 + 7. Let s(q) = 2*q - 7. Let d be s(g). Factor 0*y**2 + 0 - 6/5*y**d + 0*y + 3/5*y**4.
3*y**3*(y - 2)/5
Let j(p) be the third derivative of -p**5/90 - p**4/12 - 39*p**2. Factor j(q).
-2*q*(q + 3)/3
Solve -152/5*h**3 - 248/5*h**4 + 316/5*h**2 - 14/5*h**5 - 68/5 + 166/5*h = 0 for h.
-17, -1, 2/7, 1
Let o(c) be the second derivative of 5*c**4/48 - 15*c**3/8 + 45*c**2/4 + 187*c. Find r, given that o(r) = 0.
3, 6
Factor -4*b**3 + 4 + 4*b**4 + 4*b - 2*b**4 + 4 + 2*b**4 - 12*b**2.
4*(b - 2)*(b - 1)*(b + 1)**2
Let z(i) be the first derivative of 2*i**3/45 - 3*i**2/5 + 28*i/15 + 31. Determine l so that z(l) = 0.
2, 7
Let b(f) be the second derivative of -f**4/12 - 2*f**3 + 32*f**2 + f - 91. Factor b(r).
-(r - 4)*(r + 16)
Let y(d) = 5*d**3 + 35*d**2 - 710*d + 665. Let j(f) = 7*f**3 + 52*f**2 - 1065*f + 998. Let o(p) = -5*j(p) + 8*y(p). Factor o(m).
5*(m - 6)*(m - 1)*(m + 11)
Let b(u) be the second derivative of -u**6/150 + u**5/100 + u**4/30 - 4*u - 9. Determine d, given that b(d) = 0.
-1, 0, 2
Let k(z) be the third derivative of z**7/630 - z**6/180 - 13*z**4/24 - 6*z**2. Let u(w) be the second derivative of k(w). Let u(s) = 0. What is s?
0, 1
Let z = -116 + 118. Suppose -5*y - 2 = 3*o, -4*y + z*o + 18 = y. Factor 1/2*m - 1/4 - 1/4*m**y.
-(m - 1)**2/4
Let l = 3445 - 3440. Factor 2/5*m**l + 0*m**3 + 0*m**2 + 0*m + 0*m**4 + 0.
2*m**5/5
Let 22/5*l**3 - 128/5*l + 64/5 - 2/5*l**5 - 8/5*l**4 + 52/5*l**2 = 0. Calculate l.
-4, 1, 2
Let s(a) = -a**2 - 20*a - 17. Let x be 4*6/8 - (4 + 18). Let o be s(x). Factor 3/5*d**3 + 2/5*d**4 - 3/5*d - 1/5 - 1/5*d**o.
(d - 1)*(d + 1)**2*(2*d + 1)/5
Let u = 8 - 8. Suppose -4*d - a + 17 = 0, -2*a + u*a + 7 = -d. Let 20*f + 6*f**2 + f**3 + 4 + 11*f**2 + 3*f**d = 0. Calculate f.
-2, -1/4
Let c(f) be the second derivative of f**9/9072 - f**8/5040 - f**7/1260 + 7*f**3/6 + 15*f. Let m(s) be the second derivative of c(s). Factor m(a).
a**3*(a - 2)*(a + 1)/3
Let d(r) = 6*r - 28. Let q be d(6). Solve -43*l**2 - 44*l**3 + 0*l + 10*l**5 + 15*l**2 + q + 20*l**4 + 28*l + 6*l**5 = 0 for l.
-2, -1, -1/4, 1
Factor 15*p - 19 + 66 + 3*p**2 + 5*p**2 - 42 + 7*p**2 + 5*p**3.
5*(p + 1)**3
Let g(p) = -2*p**2. Let v(c) = c**2 + 14*c - 4. Let k be v(-14). Let t(q) = 4 - 4*q**2 - 4 - q. Let y(d) = k*t(d) + 9*g(d). Factor y(h).
-2*h*(h - 2)
Let b = -3/3358 - -1685/6716. Let b*a + 0 + 1/2*a**2 + 1/4*a**3 = 0. Calculate a.
-1, 0
Let i(q) be the third derivative of q**6/200 - q**5/25 + q**4/10 + 55*q**2. Suppose i(v) = 0. What is v?
0, 2
Let p(s) = s + 11. Let j be p(-9). Factor -8*m**3 + 9*m**3 - j*m - 9*m**3 + 6*m + 4*m**5.
4*m*(m - 1)**2*(m + 1)**2
Let a = 6 - 6. Suppose a = 4*c - 6*c. Let c*g**2 - 2*g - 4*g**2 + 2*g**2 = 0. What is g?
-1, 0
Let m(a) be the second derivative of -a**4/18 + 26*a**3/3 - 507*a**2 + 112*a. Let m(z) = 0. Calculate z.
39
Let f(l) be the second derivative of l**6/90 + l**5/20 - l**4/36 - l**3/6 - 3*l + 9. Factor f(b).
b*(b - 1)*(b + 1)*(b + 3)/3
Let c(b) = b**2 + 123*b - 1019. Let a(t) = 2*t**2 + 122*t - 1018. Let n(f) = -5*a(f) + 6*c(f). Factor n(u).
-4*(u - 16)**2
Let o(a) = -9*a**3 + 5*a**2 + 23*a + 31. Let x(z) = 8*z**3 - 4*z**2 - 22*z - 30. Let r(w) = -6*o(w) - 7*x(w). Factor r(t).
-2*(t - 3)*(t + 2)**2
Let r(n) be the third derivative of n**6/360 - n**5/30 - n**4/8 + 7*n**3/9 - 10*n**2 + 5. Determine m so that r(m) = 0.
-2, 1, 7
Let h be -30*(1 + (-25)/15). What is i in 10*i**2 + 11*i**2 + 8*i**2 - 25*i**2 - h*i = 0?
0, 5
Let d(n) be the second derivative of 7*n**6/120 - 3*n**5/8 - 13*n**4/48 + 11*n**3/2 - 9*n**2/2 + 2*n - 50. Factor d(y).
(y - 3)**2*(y + 2)*(7*y - 2)/4
Let p(t) be the second derivative of t**7/168 - 13*t**6/120 + t**5/8 + t**4/2 + 101*t + 2. What is o in p(o) = 0?
-1, 0, 2, 12
Let j(w) = -185*w**3 - 390*w**2 + 415*w + 85. Let l(i) = -46*i**3 - 97*i**2 + 104*i + 21. Let y(r) = 6*j(r) - 25*l(r). Suppose y(p) = 0. Calculate p.
-3, -1/8, 1
Let p(v) be the second derivative of 4*v**4/9 + 58*v**3/9 - 16*v**2 - 4*v + 1. Factor p(h).
4*(h + 8)*(4*h - 3)/3
Let f = -14831/3 - -4944. Factor f*p**2 + 1/3*p + 0.
p*(p + 1)/3
Let t(o) be the first derivative of o**7/231 + o**6/165 - o**5/55 - 6*o + 8. Let q(p) be the first derivative of t(p). Factor q(r).
2*r**3*(r - 1)*(r + 2)/11
Let v(s) = -4*s**2 + 6*s - 6. Let w be v(2). Let y be -4 + (-36)/w + (-72)/(-105). Factor -y*x + 4/7 - 2/7*x**2.
-2*(x - 1)*(x + 2)/7
Let l(v) be the second derivative of 2/5*v**2 + 13*v + 1/60*v**4 - 2/15*v**3 + 0. Determine y so that l(y) = 0.
2
Let g(t) 