t p be (5/3 - 1) + 48/9. Let d(i) be the first derivative of -7/8*i**p - 3/4*i**2 - 9 + 13/4*i**3 - 81/16*i**4 + 0*i + 69/20*i**5. Solve d(z) = 0 for z.
0, 2/7, 1
Let k(x) be the second derivative of 3*x**5/160 - 13*x**4/32 + 15*x**3/8 + 63*x. Find a, given that k(a) = 0.
0, 3, 10
Let y be (-76)/(-114) + (-7)/(-3). Let s(h) be the second derivative of 4/15*h**6 + 0 + 2/21*h**7 - 2*h + 0*h**2 + 0*h**y + 0*h**5 + 0*h**4. Factor s(w).
4*w**4*(w + 2)
Let d(m) be the second derivative of -4*m**4 - 17*m**3/2 - 3*m**2/2 + 2*m + 18. Find a, given that d(a) = 0.
-1, -1/16
Let h be ((-312)/1638)/((-24)/7). Let v(j) be the first derivative of 0*j**2 + 1/30*j**5 - 3 + 1/12*j**4 + 0*j + h*j**3. Factor v(c).
c**2*(c + 1)**2/6
Let d be (1/2)/(1/(-4)). Let i be (d/6)/(9/(-36)). Factor 8/3*h**3 - 2/3*h**2 - i*h + 0 + 2*h**4.
2*h*(h + 1)**2*(3*h - 2)/3
Let l(v) = 2*v**3 + 50*v**2 - 52*v + 4. Let d(y) = 2*y**3 + 51*y**2 - 53*y + 6. Let a(k) = -2*d(k) + 3*l(k). Factor a(c).
2*c*(c - 1)*(c + 25)
Let l(j) be the first derivative of j**3/3 + 19*j**2/2 + 60*j - 39. Determine h so that l(h) = 0.
-15, -4
Let f be (-3)/(-6)*(-10)/(-1). Factor 4*z**2 - f*z**3 + 14*z**2 + 12*z**2 - 60*z + 40.
-5*(z - 2)**3
Let z(n) be the first derivative of 50*n**6/21 + 76*n**5/7 - 36*n**4/7 - 272*n**3/21 - 32*n**2/7 - 89. Let z(x) = 0. What is x?
-4, -2/5, 0, 1
Let t(o) be the first derivative of 1/5*o**2 - 18 + 4/5*o - 2/15*o**3. Find q such that t(q) = 0.
-1, 2
Suppose 165*x = 177*x. Factor -1/3*i**3 + 1/3*i**5 - 1/3*i**2 + 1/3*i**4 + 0*i + x.
i**2*(i - 1)*(i + 1)**2/3
Let x(n) be the second derivative of -361*n**7/1400 - 19*n**6/40 + 9*n**5/25 - n**4/10 - 6*n**3 + 10*n. Let f(j) be the second derivative of x(j). Factor f(m).
-3*(m + 1)*(19*m - 2)**2/5
Let q(s) be the second derivative of -1/8*s**4 + 5/36*s**3 + 26*s + 1/180*s**6 + 0*s**2 + 1/40*s**5 + 0. Factor q(v).
v*(v - 1)**2*(v + 5)/6
Let q(o) be the second derivative of -2*o**6/75 + o**4/15 - 167*o. Factor q(j).
-4*j**2*(j - 1)*(j + 1)/5
Let h be 3 + -16 + 16/(-4). Let d = h + 19. Factor -6*i - 6 - 3/2*i**d.
-3*(i + 2)**2/2
Let r = 25548 - 434308/17. Find m such that 22/17*m**2 - r*m**3 - 12/17*m + 0 - 2/17*m**4 = 0.
-6, 0, 1
Factor 20*p**2 - 36*p + 52/3 - 4/3*p**3.
-4*(p - 13)*(p - 1)**2/3
Suppose -2*h = 3*h - 2*d + 10, -2*d = 4*h - 10. Suppose l - 2*l = -h*l. Let m + 9/2*m**2 + l = 0. Calculate m.
-2/9, 0
Let h(a) = -a**5 + 7*a**4 + 4*a**3 + 10*a**2 + 5*a + 5. Let z(d) = -d**5 + 6*d**4 + 3*d**3 + 8*d**2 + 4*d + 4. Let v(j) = -4*h(j) + 5*z(j). Factor v(p).
-p**3*(p - 1)**2
Let v(o) be the second derivative of -o**7/168 + 2*o**6/15 - 27*o**5/40 + 19*o**4/12 - 49*o**3/24 + 3*o**2/2 + 112*o. Factor v(q).
-(q - 12)*(q - 1)**4/4
Solve -72 + 23*v**4 + 66*v + 0*v**3 - 10*v**3 + 0*v**2 + 21*v**2 - 26*v**4 - 2*v**3 = 0.
-4, -3, 1, 2
Let w = -12 - -122. Let z be -2 - ((-18)/99 + (-244)/w). Factor z*d - 1/5*d**2 - 1/5.
-(d - 1)**2/5
Let s(y) be the first derivative of -8/3*y - 4 - 1/3*y**2 + 8/9*y**3 + 1/6*y**4. What is z in s(z) = 0?
-4, -1, 1
Let y(i) = 4*i**3 - 55*i**2 - 60*i + 125. Let g(t) = t**3 - 19*t**2 - 20*t + 42. Let w(o) = -7*g(o) + 2*y(o). Factor w(h).
(h - 1)*(h + 2)*(h + 22)
Let k be (8/14)/(-1)*21/(-6). Suppose -3*f - f = -k*f. Factor f*a**2 + 2/9*a**3 - 2/9*a + 0.
2*a*(a - 1)*(a + 1)/9
Let z(u) be the second derivative of -u**4/54 + 274*u**3/27 - 18769*u**2/9 + 204*u. Find c, given that z(c) = 0.
137
Let t(a) = -a**2 + 537*a + 1622. Let u be t(-3). Solve -8/7*i**3 + 4/7 + u*i - 10/7*i**2 = 0 for i.
-2, -1/4, 1
Let z(b) be the first derivative of -b**6/2 - 18*b**5/5 - 6*b**4 + 6*b**3 + 27*b**2/2 - 959. Let z(h) = 0. What is h?
-3, -1, 0, 1
Suppose -4*l + 4*j = -4, 4*l + 23*j = 21*j + 16. Suppose -5*k + 11 = -a, 2*k = 3*a + 2*a + 9. Factor 2/5*p**l + 4/5*p**k - 2/5*p - 4/5.
2*(p - 1)*(p + 1)*(p + 2)/5
Suppose -4*z + 3*m = -63, -3*z - 3*m + 8 = -13. Factor -42*c**2 + 12 + 3*c**3 - z*c + 23*c**2 + 16*c**2.
3*(c - 2)*(c - 1)*(c + 2)
Let i(z) be the first derivative of -9*z**6/2 - 117*z**5/10 - 69*z**4/8 - z**3/2 + 3*z**2/4 - 76. Suppose i(o) = 0. Calculate o.
-1, -1/3, 0, 1/6
Let u(t) be the second derivative of -t**8/336 - t**7/84 - 5*t**3/2 + 14*t. Let f(v) be the second derivative of u(v). Factor f(o).
-5*o**3*(o + 2)
Let s(h) be the second derivative of -h**7/462 + 7*h**6/165 + 3*h**5/220 - 10*h**4/33 - 14*h**3/33 + 187*h. Determine w so that s(w) = 0.
-1, 0, 2, 14
Let h(o) be the second derivative of o**6/135 - 4*o**5/45 + 5*o**4/54 + 50*o**3/27 + 19*o. Factor h(k).
2*k*(k - 5)**2*(k + 2)/9
Let f(b) be the second derivative of b**7/20160 - b**5/240 + 17*b**4/12 + 25*b. Let v(k) be the third derivative of f(k). Factor v(r).
(r - 2)*(r + 2)/8
Let q(b) be the first derivative of -4*b**5/45 - b**4/4 + 10*b**3/27 + b**2/6 + 101. Let q(j) = 0. What is j?
-3, -1/4, 0, 1
Let -4*g**2 - 42*g - 10 + 6 + 50*g = 0. What is g?
1
Let d(v) be the first derivative of v**4/28 - v**3/7 + 3*v**2/14 - 11*v + 3. Let u(k) be the first derivative of d(k). Find y such that u(y) = 0.
1
Let g = 1482 - 1480. Let l = -3188/11 - -290. Factor -14/11*f**g + l - 8/11*f**3 - 4/11*f.
-2*(f + 1)**2*(4*f - 1)/11
Let c(j) be the second derivative of j**4/12 - j**3/2 - 4*j**2 + 6*j. Let u be c(5). Factor 1/3*p**u + 4/3 - 4/3*p.
(p - 2)**2/3
Let u(x) = 32*x**3 - 275*x**2 + 691*x + 320. Let f(t) = -28*t**3 + 274*t**2 - 690*t - 320. Let c(o) = -3*f(o) - 2*u(o). Factor c(d).
4*(d - 10)*(d - 4)*(5*d + 2)
Let c(n) = -2*n**3 + 29*n**2 - 13*n - 12. Let s be c(14). Factor -32*l + 21*l**2 + 12 + 6*l**2 - s*l**2 - l**2 - 4*l**4.
-4*(l - 1)**3*(l + 3)
Let t(j) = j**3 + 4*j**2 + j - 3. Let x be t(-2). Determine m, given that -3*m**x - 6*m**2 - m**2 + 10*m**2 = 0.
0, 1
Let m(w) be the third derivative of w**8/1344 + w**7/280 + w**6/240 + 4*w**5/15 - 22*w**2. Let q(d) be the third derivative of m(d). Let q(j) = 0. Calculate j.
-1, -1/5
Factor 21/2*f**2 + 0 - 3/2*f**3 + 12*f.
-3*f*(f - 8)*(f + 1)/2
Let j(d) be the third derivative of -d**6/240 + d**5/24 - 7*d**4/48 + d**3/4 + 3*d**2 - 2*d. Suppose j(z) = 0. What is z?
1, 3
Let y(k) = -28*k**2 + 24*k - 18. Let z(g) = -15*g**2 + 12*g - 9. Let b(v) = -6*y(v) + 11*z(v). Factor b(a).
3*(a - 3)*(a - 1)
Let r(w) be the first derivative of -3*w**4/14 + 8*w**3/21 + w**2/7 - 4*w/7 + 178. Factor r(d).
-2*(d - 1)**2*(3*d + 2)/7
Let a(i) be the third derivative of -i**5/60 + i**4/3 - 2*i**3/3 + i**2. Let b be a(7). Factor -5*v**3 - 9*v**2 + 4*v**3 + 2*v**3 - 4*v**b.
-3*v**2*(v + 3)
Factor -3/2*x**3 - 823875/2 - 38025/2*x - 585/2*x**2.
-3*(x + 65)**3/2
Let d(z) = -4*z**5 - 34*z**2 - 6*z. Let f(j) = -7*j**5 + j**4 - j**3 - 66*j**2 - 13*j. Let u(t) = -11*d(t) + 6*f(t). Factor u(k).
2*k*(k - 2)*(k + 1)**2*(k + 3)
Find u such that -12321/4 + 3307/2*u**2 - 4773/4*u - 69/4*u**4 - 1/4*u**5 - 501/2*u**3 = 0.
-37, -1, 3
Let d(p) be the second derivative of -p**4/54 + 8*p**3/27 - 7*p**2/9 + 504*p. Let d(j) = 0. What is j?
1, 7
Let v(z) be the second derivative of -z**5/2 - 15*z**4/4 - 10*z**3 - 10*z**2 - 20*z. Determine g, given that v(g) = 0.
-2, -1/2
Let g be (-5)/2*12/(-15). Let x(k) = -16*k + 83. Let q be x(5). Find s, given that g*s**2 + 0 - 4/3*s - 2/3*s**q = 0.
0, 1, 2
Let a(p) be the third derivative of -p**9/12096 - p**8/4032 + p**7/504 - 2*p**5/15 + 3*p**2. Let u(v) be the third derivative of a(v). Factor u(q).
-5*q*(q - 1)*(q + 2)
Let k(p) = -4*p**2 - 87*p - 83. Let o(l) = l**2 + 29*l + 28. Let t(r) = -2*k(r) - 7*o(r). Let t(c) = 0. Calculate c.
-1, 30
Let n(i) = 5*i**2 - 4. Let g(m) = m**3 - 40*m**2 + m + 34. Let p(q) = 6*g(q) + 51*n(q). Factor p(h).
3*h*(h + 2)*(2*h + 1)
Find j such that 33124/5 + 4/5*j**2 + 728/5*j = 0.
-91
Let v = 193/1332 - 5/148. Let r(s) be the second derivative of -1/45*s**6 - v*s**3 - 8*s + 0*s**2 - 1/6*s**4 + 0 - 1/10*s**5. Solve r(k) = 0 for k.
-1, 0
Let w(s) = s**3 + 14*s**2 - 15*s + 3. Let c be w(-15). Let z(x) be the first derivative of x**c - x**2 + 7 - 1/4*x**4 + 0*x. Solve z(u) = 0 for u.
0, 1, 2
Let f(c) be the first derivative of 7*c**6/9 + 158*c**5/15 + 89*c**4/2 + 490*c**3/9 + 50*c**2/3 - 262. Determine z, given that f(z) = 0.
-5, -1, -2/7, 0
What is p in -2/19*p**2 - 1152/19 + 96/19*p = 0?
24
Let y(g) be the third derivative of -g**5/240 - 7*g**4/24 + 87*g**2. Factor y(d).
-d*(d + 28)/4
Suppose