y(z) be the second derivative of -1/20*z**5 + 1/9*z**4 - 1/18*z**3 + 0 + 0*z**2 + 6*z. Suppose y(a) = 0. What is a?
0, 1/3, 1
Let y(a) be the third derivative of a**8/5040 + a**7/1260 + a**5/30 + 10*a**3/3 - 31*a**2 + 1. Let r(g) be the third derivative of y(g). Factor r(q).
4*q*(q + 1)
Let i(m) = -15*m + 122. Let w be i(8). Let b(c) be the first derivative of 4/3*c**3 + 6 - 2*c**w + 0*c. Factor b(l).
4*l*(l - 1)
Let n(k) be the first derivative of -5*k**3/3 + 5*k**2 + 175*k - 101. Factor n(o).
-5*(o - 7)*(o + 5)
Suppose 3*b - 3*h = 2*h - 31, -11 = -2*b - 3*h. Let j be (15/b)/((-13)/26). Solve p**5 - 4*p + 10*p**3 + j - 30*p**2 - 6*p**5 - p + 15*p**4 = 0 for p.
-1, 1, 3
Let j(p) = -9*p**2 + 3*p - 2. Let c(q) be the second derivative of q**4/3 - q**3/6 + q**2/2 - 10*q. Let y(d) = -7*c(d) - 3*j(d). Find s, given that y(s) = 0.
-1
Factor 4/5*f**4 + 0 + 8/5*f**2 - 2/5*f - 2*f**3.
2*f*(f - 1)**2*(2*f - 1)/5
Let z be 216/16 + ((-3)/2 - -1). Suppose 8*k + 19*k**4 - 2*k + 9*k**4 - 18*k**3 + 18*k**5 - 9*k**2 - z*k**4 = 0. What is k?
-1, 0, 1/2, 2/3
Let p(z) = 3*z**4 - z**3. Let o(m) = 40*m**4 + 28*m**3 - 16*m**2. Let r(v) = o(v) - 20*p(v). Solve r(t) = 0 for t.
0, 2/5, 2
Let l(j) be the second derivative of -3*j**7/14 + 19*j**6/10 - 117*j**5/20 + 29*j**4/4 - 3*j**3 + 378*j. Let l(t) = 0. What is t?
0, 1/3, 1, 2, 3
Let o(k) be the first derivative of 0*k + 5/14*k**4 - 2/7*k**3 - 24 - 2/7*k**2. Let o(j) = 0. Calculate j.
-2/5, 0, 1
Let s(p) be the first derivative of 3*p**4/16 - 4*p**3/3 - 33*p**2/8 - 7*p/2 + 86. Factor s(g).
(g - 7)*(g + 1)*(3*g + 2)/4
Let p(l) = -l**4 + 1. Let v(k) = -26*k**3 + k**2 - 4*k**3 - 18 - 2*k**5 + 32*k + 8*k**4 + 9*k**2. Let h(w) = 6*p(w) - v(w). Determine r so that h(r) = 0.
-1, 1, 2, 3
Let o(i) be the second derivative of i**5/10 - i**4/2 - 3*i**3 + 27*i**2 + 4*i + 31. Find d, given that o(d) = 0.
-3, 3
Factor -6/19*n**2 - 2/19*n**4 + 0*n + 10/19*n**3 + 0 - 2/19*n**5.
-2*n**2*(n - 1)**2*(n + 3)/19
Let g(x) be the second derivative of 0*x**2 - 5/3*x**3 + 0 - 1/4*x**5 - 5/4*x**4 + 15*x. Factor g(k).
-5*k*(k + 1)*(k + 2)
Let g(u) = u - 1. Let d(k) = 2*k**2 + 29*k - 5. Let p(w) = -d(w) + 5*g(w). Factor p(c).
-2*c*(c + 12)
Let a(p) be the first derivative of -30 + 4/7*p**3 + 0*p - 3/7*p**4 + 4/35*p**5 - 2/7*p**2. Determine x so that a(x) = 0.
0, 1
Suppose 201 = 11*g + 201. Factor 0*t + g - 2/3*t**2.
-2*t**2/3
Let t(x) = -115*x**3 - 65*x**2 + 1305*x + 2425. Let j(f) = -14*f**3 - 8*f**2 + 163*f + 303. Let y(p) = -25*j(p) + 3*t(p). Find m such that y(m) = 0.
-5, -2, 6
Let r(o) be the third derivative of o**6/160 - o**5/80 - 2*o**2 + 21*o. Let r(s) = 0. What is s?
0, 1
Let b = -175799/120 + 1465. Let i(f) be the third derivative of 0*f + 1/3*f**3 + 5*f**2 + b*f**5 + 1/12*f**4 + 0. Factor i(y).
(y + 2)**2/2
Factor 18*s**2 + 11*s**2 - 16*s - 29*s**2 + 64 + s**2.
(s - 8)**2
Let s(d) be the third derivative of -d**7/168 + d**6/18 - 5*d**5/24 + 5*d**4/12 - 3*d**3 + 7*d**2. Let i(u) be the first derivative of s(u). Factor i(x).
-5*(x - 2)*(x - 1)**2
Factor 2/5*i**3 - 2/5*i**2 - 4/5*i + 0.
2*i*(i - 2)*(i + 1)/5
Let x be (7*4/210)/(4/5). Factor -1/6*v**2 + 1/6*v**4 - 1/6*v**3 + 0 + x*v.
v*(v - 1)**2*(v + 1)/6
Let o(h) be the first derivative of -2*h**6/9 - 4*h**5/15 + 13*h**4/3 + 4*h**3/9 - 8*h**2 - 399. Let o(p) = 0. Calculate p.
-4, -1, 0, 1, 3
Let o = 37 - 34. Find p such that 3*p**3 - p**3 + o*p**2 - 10*p - 11*p + 22*p = 0.
-1, -1/2, 0
Let g = -511 - -518. Let p(a) be the second derivative of 3*a + 0 - 2*a**3 + 0*a**2 + 1/14*a**g + 2/5*a**6 - a**4 + 9/20*a**5. Factor p(r).
3*r*(r - 1)*(r + 1)*(r + 2)**2
Suppose -2/5*m**2 - 168/5 - 34*m = 0. What is m?
-84, -1
Find v such that 33/5*v + 0 - 3/5*v**2 = 0.
0, 11
Let c = -145 + 148. Factor 1/6*q**c - 2/3 - 5/6*q**2 + 4/3*q.
(q - 2)**2*(q - 1)/6
Suppose -654 = -4*i - 2*i. Suppose -4*l**4 + i*l**2 - l**4 - 10 - 5*l + 5*l**3 - 94*l**2 = 0. What is l?
-1, 1, 2
Suppose -4*r + 30 = -3*g, -2*g + 0*r - 41 = -5*r. Find q, given that 4*q + 26/3*q**g - 10/3*q**3 + 0 = 0.
-2/5, 0, 3
Let y be 2 + 1 + -4 + (-20)/(-5). Let j(a) be the second derivative of 6*a**2 - 3/4*a**5 - y*a - 13/4*a**4 + 0 - 2*a**3. Find d, given that j(d) = 0.
-2, -1, 2/5
Let f(d) be the third derivative of -d**5/75 - d**4/10 - 4*d**3/15 + 59*d**2. Factor f(w).
-4*(w + 1)*(w + 2)/5
Let j be (564/60 + -9)/(14/20). Find y, given that 10/7*y**3 + 0 + j*y**2 + 0*y = 0.
-2/5, 0
Suppose 0 = 6*p - 21 - 621. Let t = p - 107. Let t - 1/2*r**3 - 3/2*r**2 - r = 0. Calculate r.
-2, -1, 0
Let r(c) = c**2 - 15*c. Let w(u) = 3*u**2 - 42*u. Let v(s) = 8*r(s) - 3*w(s). Factor v(d).
-d*(d - 6)
Determine p so that -2608*p**5 + p**2 + 2607*p**5 + 4*p**4 + p**2 - 5*p**3 = 0.
0, 1, 2
Let c(g) = -2*g**3 - 12*g**2 + 2. Let x be c(-6). What is z in -2*z**x + 1 - 1 - 117*z + 119*z = 0?
0, 1
Let b(x) be the first derivative of -x**3/3 + 5*x**2/2 + 88. Factor b(j).
-j*(j - 5)
Factor 2/9*w**3 + 0*w + 0 - 4/3*w**2.
2*w**2*(w - 6)/9
Let l(r) be the third derivative of -r**5/30 + 20*r**4/3 + 2*r**2 - 31. Let l(z) = 0. Calculate z.
0, 80
Let j(k) = k**2 + 159*k + 5939. Let c(a) = -a - 2. Let v(i) = -10*c(i) - 2*j(i). What is d in v(d) = 0?
-77
Let a be 13/4 + 39/52. Let -43*u - 13*u + 0*u**2 - 44 - a*u**2 + 8*u = 0. What is u?
-11, -1
Factor -6/7*d**3 - 2/7*d**4 + 0 + 16/7*d + 12/7*d**2.
-2*d*(d - 2)*(d + 1)*(d + 4)/7
Let z be (-1)/6 - (1 - (-38)/(-12)). Let k be 2 - (-18)/(-12)*z/(-3). Determine i so that 14/5*i**5 + 54/5*i**k + 0 + 26/5*i**2 + 4/5*i + 46/5*i**4 = 0.
-1, -2/7, 0
Let y(n) be the third derivative of n**8/13440 - n**7/672 + n**6/120 - 17*n**5/30 - 39*n**2. Let g(o) be the third derivative of y(o). Let g(c) = 0. What is c?
1, 4
Let r(v) be the first derivative of -v**7/105 + v**5/10 - v**4/6 + 23*v**2/2 + 5. Let s(q) be the second derivative of r(q). Factor s(n).
-2*n*(n - 1)**2*(n + 2)
Let v(p) = -3*p**3 + 7*p**2 + 4*p. Let s(h) = -h**3 + h. Let y(i) = -4*s(i) + v(i). Let j be y(-7). Factor -3*b**4 + 3*b**4 + 6*b**3 + 3*b**4 - 6*b + j - 3.
3*(b - 1)*(b + 1)**3
Let t be (0 - (-48)/27) + 4/18. Let j be 30/(-120) + (-11)/(-12). Factor -j*s**t - 4/3*s - 2/3.
-2*(s + 1)**2/3
Suppose 5*q - q = -3*j + 415, 0 = 5*j - 4*q - 681. Let v = -132 + j. Suppose 4/7*o**3 - 2/7 - 2/7*o - 2/7*o**v + 4/7*o**2 - 2/7*o**4 = 0. What is o?
-1, 1
Let z(f) be the second derivative of 14*f + 3/50*f**6 + 6/5*f**2 - 7/20*f**4 + 0 + 0*f**3 - 1/70*f**7 + 3/100*f**5. Suppose z(g) = 0. Calculate g.
-1, 1, 2
Suppose k = 5*o - 3*k + 16, 16 = 5*o + 4*k. Factor 0*x**2 + 1/4*x**5 + 0*x + o - 3/4*x**4 + 1/2*x**3.
x**3*(x - 2)*(x - 1)/4
Factor 45*i + 15/4*i**3 + 11 + 181/4*i**2.
(i + 11)*(3*i + 2)*(5*i + 2)/4
Let k(t) be the third derivative of t**7/490 + t**6/140 - 3*t**5/140 - t**4/7 - 2*t**3/7 - 35*t**2 - 1. Solve k(y) = 0 for y.
-2, -1, 2
Let l(k) be the second derivative of -k**7/10080 + k**5/480 + k**4/6 + 7*k. Let b(c) be the third derivative of l(c). Determine j, given that b(j) = 0.
-1, 1
Suppose 0*u - 400 = -4*u + y, u = -5*y + 121. Factor n**2 + 4*n**2 - 81*n + 0*n**2 + 15 + u*n.
5*(n + 1)*(n + 3)
Let z be (2/(-20))/((-175)/(-60) - 3). Let a be (-14)/(-5) - 4/2. Factor a*m**3 + 1/5 + z*m + 9/5*m**2.
(m + 1)**2*(4*m + 1)/5
Suppose -4 + 2 = -2*s. Suppose 0 = o + s - 3. Determine q so that -2*q**o - 4 + 2*q + 4 = 0.
0, 1
Let d be 2*((-1)/(-3))/((-2)/(-6)). Factor 4*g**2 - 8*g**d + 341 + 8*g - 325 - 2*g**3.
-2*(g - 2)*(g + 2)**2
Factor -4/5*i - 6*i**2 + 0.
-2*i*(15*i + 2)/5
Find w, given that 0 + 291/4*w**3 + 135/4*w**2 - 243/2*w + 57/4*w**4 + 3/4*w**5 = 0.
-9, -2, 0, 1
Factor -40*q + 30*q + q**3 + 1 + 9*q - q**2.
(q - 1)**2*(q + 1)
Let m be 2/(-26) - 1470/(-1365). Factor -3/2*x + m + 1/2*x**2.
(x - 2)*(x - 1)/2
Let g(w) be the second derivative of -w**6/75 + 3*w**5/50 - 4*w**3/15 + 16*w. Suppose g(n) = 0. What is n?
-1, 0, 2
Let c be (-1)/8 - -1*1/8. Suppose 23 = -2*h - 5*i, -3*i + 20 = -5*h - 8*i. Let -h + c - 4*g**2 + 17 = 0. What is g?
-2, 2
Let m(y) be the second derivative of -5*y**4/42 + 2*y**3 - 16*y**2/7 - 10*y + 1. Determine b so that m(b) = 0.
2/5, 8
Let l(h) be the third derivative of -h**7/1050 + h**6/600 + h**5/50 - h**4/30 - 4*h**3/15 - 28*h**2 - 1. Solve l(q) = 0 for q.
-2, -1, 2
Let c(v) = -v**2 + v + 24. Let i(w) = -4*w**2 + 5*w + 97. Let u(g) = 9*c(g) - 2*i(g)