culate i.
0, 12
Let k(d) be the first derivative of 3*d**5/5 - 6*d**4 + 8*d**3 + 48*d**2 - 144*d + 17. Determine t, given that k(t) = 0.
-2, 2, 6
Let v(u) be the second derivative of u**6/6 - 7*u**5/4 - 65*u**4/4 + 475*u**3/6 - 125*u**2 - 650*u. Let v(o) = 0. Calculate o.
-5, 1, 10
Let m = -156 - -242. Let a = 88 - m. Factor 0 - 1/2*o**4 + 0*o**3 + o + 3/2*o**a.
-o*(o - 2)*(o + 1)**2/2
Let d(u) be the second derivative of -u**6/24 + u**5/6 + 8*u**2 - 15*u. Let k(y) be the first derivative of d(y). Factor k(c).
-5*c**2*(c - 2)
Find p, given that -35*p**2 - 269*p + 8 + 7 + 169*p = 0.
-3, 1/7
Let h(n) = 7*n**3 + 13*n**2 + 7*n + 3. Let r(b) = -14*b**3 - 27*b**2 - 13*b - 5. Let u = 20 - 23. Let z(d) = u*r(d) - 5*h(d). Let z(y) = 0. Calculate y.
-2, -2/7, 0
Let v(h) = -h**3 - 5*h**2 + 4*h + 2. Let q be v(-6). Factor 39*l**2 - 3 - 14*l + 3*l**4 + 15 - 18*l**3 - 36*l + q*l.
3*(l - 2)**2*(l - 1)**2
Let p be 7/(14/(-4)) - -6. Suppose p - 12 = -j. Factor -5*i - 4*i**4 - 6*i**4 + 5*i**5 + j*i**2 + 2*i**2.
5*i*(i - 1)**3*(i + 1)
Let a be ((-1)/(-2))/(2/12). Factor 12*u**a - 10*u**3 + 2*u + 4*u**2 + 0*u**2.
2*u*(u + 1)**2
Let k = 4517/6774 + -1/6774. Determine d so that 4/3*d - k*d**2 + 0 = 0.
0, 2
Let v(a) be the first derivative of a**3/18 - a**2/12 - 28*a/3 + 107. Let v(x) = 0. Calculate x.
-7, 8
Let n be (-2)/7 + (-8)/56*-2. Let m(d) be the second derivative of 1/40*d**6 - 1/16*d**4 - 3/40*d**5 + 1/4*d**3 + 0 - 7*d + n*d**2. Factor m(t).
3*t*(t - 2)*(t - 1)*(t + 1)/4
Let l(w) be the second derivative of -6*w**7/7 - 4*w**6/15 + 27*w**5/5 + 8*w**4 + 8*w**3/3 - 43*w. Find i such that l(i) = 0.
-1, -2/9, 0, 2
Let w be (26/(-39))/((-6)/5931). Determine n, given that -675*n - 2 + w*n + 2*n**4 - 4 - 12*n**2 = 0.
-1, 3
Factor 1/2*z**2 - 19/2 - 9*z.
(z - 19)*(z + 1)/2
Let q = -5676/5 + 158941/140. Let x(f) be the third derivative of -11/56*f**4 + 3/14*f**3 + q*f**5 + 0*f + 0 - 1/56*f**6 + 4*f**2. Factor x(b).
-3*(b - 1)**2*(5*b - 3)/7
Let k(u) = -3*u**2 - 7*u - 1. Let p(z) = -z. Let j(n) = -k(n) + 3*p(n). Let q(i) = -4*i**2 - 4*i - 2. Let o(a) = -5*j(a) - 4*q(a). Let o(b) = 0. Calculate b.
1, 3
Suppose 39*v**3 + 14 + 20 - 38*v**3 - 10*v + 32*v**2 - 57*v = 0. Calculate v.
-34, 1
Let n(y) be the second derivative of -4*y**2 - 8*y + 6*y**3 + 0 - 7/3*y**4. Factor n(w).
-4*(w - 1)*(7*w - 2)
Let d be ((-1)/6*-5)/(235/188). Let w(s) be the first derivative of -3 - 1/2*s**4 + s**2 - d*s**3 + 2/5*s**5 + 0*s. Suppose w(j) = 0. Calculate j.
-1, 0, 1
Let j(x) be the first derivative of -16*x + 4/3*x**3 + 19 - 6*x**2. Determine i, given that j(i) = 0.
-1, 4
Suppose -x - 35 = -38. Let z(c) be the first derivative of 2/9*c + 0*c**2 - 5 - 2/27*c**x. Let z(k) = 0. What is k?
-1, 1
Let n(r) be the third derivative of -3*r**7/1400 + 2*r**6/225 - r**5/120 - r**4/60 + 5*r**3/2 - 8*r**2. Let h(y) be the first derivative of n(y). Factor h(d).
-(d - 1)**2*(9*d + 2)/5
Let r(h) = 61*h**2 + 1272*h - 373. Let a(g) = -30*g**2 - 636*g + 186. Let o(p) = 5*a(p) + 2*r(p). Determine z so that o(z) = 0.
-23, 2/7
Let q(u) = u**2 - u + 1. Let w(f) = -6*f**2 - 10. Let i(v) = 18*v**2 + v + 30. Let k(o) = 4*i(o) + 11*w(o). Let h(y) = 2*k(y) - 28*q(y). Factor h(j).
-4*(j - 2)*(4*j - 1)
Let x be ((-15)/54)/((-25)/15)*30. Suppose 4*n + 12 = -3*d, -7*n - x*d = -2*n + 20. Factor 3/7*h**4 + 0*h**2 - 3/7*h**3 + 0 + n*h.
3*h**3*(h - 1)/7
Suppose -4*k - 15 + 23 = 0. Suppose -4*l**4 - l**k + 8*l**3 - l**2 + 2*l**2 = 0. What is l?
0, 2
What is w in 167*w**2 + 58*w**2 - 10*w**3 - 50*w**2 + 268*w + 443 - 128 + 452*w = 0?
-3, -1/2, 21
Let u(i) = i**2 + 10*i. Let r = -73 - -75. Let f(z) = -9*z. Let a(y) = r*f(y) + 3*u(y). Factor a(t).
3*t*(t + 4)
Let y(o) be the second derivative of -5*o**5/14 - 9*o**4/14 - 2*o**3/21 + 51*o + 2. Determine t so that y(t) = 0.
-1, -2/25, 0
Let d be (2/(-3))/(8/(-2)). Let c(t) be the second derivative of 5*t - d*t**3 + 0 + 1/100*t**5 - 1/150*t**6 + 1/20*t**4 + 1/5*t**2. Factor c(k).
-(k - 1)**3*(k + 2)/5
Let k(u) be the second derivative of u**4/96 - u**3/24 - u**2/2 + u - 1. Factor k(s).
(s - 4)*(s + 2)/8
Let v(n) be the second derivative of 0 - 1/80*n**5 - 1/16*n**4 - 7*n + 3/8*n**3 + 1/2*n**2. Let w(m) be the first derivative of v(m). Find k such that w(k) = 0.
-3, 1
Let g(y) be the third derivative of y**6/6 - 14*y**5/5 + 17*y**4/2 - 28*y**3/3 + 37*y**2. Suppose g(k) = 0. Calculate k.
2/5, 1, 7
Let f(i) = 6*i**2 - 9*i. Let u(y) = -7*y**2 + 10*y + 1. Let v = -8 - -17. Let s = 6 - v. Let h(p) = s*u(p) - 4*f(p). Factor h(m).
-3*(m - 1)**2
Factor -24*b**2 + 8*b**4 + 2*b**5 + 16*b**2 - 4*b**5 + 6*b**5 - 4*b**3.
4*b**2*(b - 1)*(b + 1)*(b + 2)
Let t(i) = i**2 + 4*i + 8. Let u be t(-2). Factor 44*d**2 + d - 4 - 4*d + u*d**3 - d - 40*d**2.
4*(d - 1)*(d + 1)**2
Let n(k) be the second derivative of -k**6/165 + 3*k**5/110 + 3*k**4/22 + 5*k**3/33 - 9*k. Factor n(v).
-2*v*(v - 5)*(v + 1)**2/11
Let j(m) be the third derivative of 0 + 3/200*m**6 - 1/10*m**3 - 7/100*m**5 + 0*m + 1/8*m**4 + 21*m**2. What is z in j(z) = 0?
1/3, 1
Let q = 11 + -13. Let t be 5 + q + 0/(-3). Factor 2*d**5 + 4*d - d - 6*d**t + d**5 + 0*d.
3*d*(d - 1)**2*(d + 1)**2
Let u be (2 - (-8)/(-3))*(-50)/150. Factor -8/9*a**2 + u*a**3 + 0 + 0*a.
2*a**2*(a - 4)/9
Let n(p) be the third derivative of -p**7/1680 + 3*p**6/64 - 9*p**5/10 - 9*p**4 + 12*p**2 - 4*p. Find m, given that n(m) = 0.
-3, 0, 24
Let z(w) be the first derivative of w**7/840 + w**6/180 + w**5/120 - 8*w**3/3 - 1. Let b(r) be the third derivative of z(r). Let b(n) = 0. Calculate n.
-1, 0
Factor -5/3*i**4 + 110/3*i**3 + 0*i + 0 - 605/3*i**2.
-5*i**2*(i - 11)**2/3
Let g(i) be the second derivative of -3*i**5/20 - 13*i**4/4 - 2*i - 17. Find j, given that g(j) = 0.
-13, 0
Let f be (9 + (-19)/2)*-4. Let w(i) be the first derivative of 0*i**3 - 3/2*i**2 + 5 + 1/4*i**4 - f*i. Factor w(a).
(a - 2)*(a + 1)**2
Let w(q) = -q**3 - q**2 - q. Let i(a) = 6*a**3 + 12*a**2 + 3*a. Let d(t) = -i(t) - 3*w(t). Factor d(n).
-3*n**2*(n + 3)
Suppose -7 = -2*n - p, -4*n + 13 = -n - p. Let a(y) be the second derivative of 0 - 4*y - y**2 - 2/3*y**3 + 1/2*y**n. Factor a(r).
2*(r - 1)*(3*r + 1)
Let h(v) be the first derivative of 3*v**5/10 - 11*v**4/4 + 20*v**3/3 - 13*v**2/2 + 5*v/2 + 15. Factor h(q).
(q - 5)*(q - 1)**2*(3*q - 1)/2
Let r(s) be the first derivative of 2*s**3/51 + 27*s**2/17 - 207. Let r(o) = 0. What is o?
-27, 0
Suppose 0 - 40/3*y + 4/3*y**3 - 4*y**2 = 0. Calculate y.
-2, 0, 5
Let d(v) be the second derivative of -v**4/78 - 38*v**3/39 - 37*v**2/13 + 94*v. Factor d(m).
-2*(m + 1)*(m + 37)/13
Let b be (0 + -1)*(-2 + -2). Factor 41*h**3 - 13*h**b - 50*h**2 - 4*h - 2 + 5*h**2 + 23*h.
-(h - 1)**3*(13*h - 2)
Let h(v) be the third derivative of -1 - 16/3*v**3 + 7/3*v**4 - 2/15*v**6 + 2/105*v**7 + 0*v - 1/5*v**5 - 5*v**2. What is r in h(r) = 0?
-2, 1, 4
Let l(u) = -u**3 + u**2 + u - 1. Let g(x) = 10*x**3 - 19*x**2 + 29. Let a(q) = -2*g(q) - 22*l(q). Suppose a(z) = 0. Calculate z.
-9, -1, 2
Let t(r) be the first derivative of r**4/22 + 38*r**3/33 + 120*r**2/11 + 504*r/11 - 262. Determine o, given that t(o) = 0.
-7, -6
Suppose 5415 = 6*l + 5415. Factor -2/15*o**3 + l*o - 4/5*o**2 + 0.
-2*o**2*(o + 6)/15
Let k(c) be the third derivative of -17*c**7/210 - 23*c**6/160 + 67*c**5/240 + 23*c**4/32 + c**3/24 - 2*c**2 + 33*c. What is v in k(v) = 0?
-1, -1/68, 1
Suppose 0 = 2*c - 5*f + 47, -2*f + 77 = -3*c - 10. Let t = 33 + c. Factor -2/3*n**t + 8/3*n**3 + 0*n + 0.
2*n**2*(4*n - 1)/3
Let y(n) be the second derivative of 23*n + 1/18*n**4 + 0*n**3 - 1/20*n**5 + 0 + 0*n**2 + 1/90*n**6. Factor y(l).
l**2*(l - 2)*(l - 1)/3
Suppose 0 = -3*s + 2*c - 15 + 6, 0 = -4*s + 4*c - 12. Let p be ((-6 + 3)/s)/3. Factor 0*q**2 + 0 + 1/3*q**3 - p*q.
q*(q - 1)*(q + 1)/3
Let f(i) be the first derivative of i**4/26 + 34*i**3/39 + 7*i**2 + 294*i/13 - 164. Factor f(w).
2*(w + 3)*(w + 7)**2/13
Factor 2 + g + 1 + 2 - g**3 + g**2 - 6.
-(g - 1)**2*(g + 1)
Let p be (6/21)/(5 - 207/42). Let 3*s**2 - p*s**2 - 8*s**4 + 5*s**2 + 9*s**4 - 4*s**3 = 0. What is s?
0, 2
Let d(t) be the second derivative of t**4/36 + 121*t**3/9 + 14641*t**2/6 - t + 51. Factor d(o).
(o + 121)**2/3
Suppose -2 = -5*r - k, -4*r + 10 = 2*k + 3*k. Suppose -2*a + 15 - 11 = r. Factor 1/4 - 3/4*w + 3/4*w**a - 1/4*w**3.
-(w - 1)**3/4
Let i(c) be the first de