)/9
Let q(i) be the second derivative of i**7/210 + i**6/150 - 24*i**5/25 - 33*i**4/5 - 20*i + 30. Factor q(n).
n**2*(n - 11)*(n + 6)**2/5
Let z(u) be the first derivative of -3/2*u**2 - 3*u - 9 + 3/4*u**3. Let z(s) = 0. Calculate s.
-2/3, 2
Factor -65/4*q - 3/2*q**2 + 11/4.
-(q + 11)*(6*q - 1)/4
Let k be (-19)/(-114) + (-488)/(-240). Let h(n) be the second derivative of 0 - 16*n - 2*n**3 + 0*n**2 - k*n**5 - 8/15*n**6 - 10/3*n**4. Factor h(w).
-4*w*(w + 1)**2*(4*w + 3)
Let t = -21 + 14. Let i(g) = g**3 + 8*g**2 + 5*g. Let l be i(t). Factor 4 - 9*f + l*f**2 - 27*f**2 - 10 + 10*f**2.
-3*(f + 1)*(f + 2)
Factor -1682*h**2 + 3337*h**2 + 8816 - 1660*h**2 - 645*h - 1866.
-5*(h - 10)*(h + 139)
Let k(z) = -21*z**4 + 28*z**3 + 139*z**2 - 485*z - 15. Let o(n) = 51*n**4 - 69*n**3 - 348*n**2 + 1212*n + 36. Let g(c) = -12*k(c) - 5*o(c). Factor g(t).
-3*t*(t - 4)**2*(t + 5)
Let o = 464 + -464. Let c(q) be the third derivative of o*q**4 - 1/120*q**5 + 0*q**3 + 0*q + 0 - 12*q**2. Determine g, given that c(g) = 0.
0
Let y(g) be the second derivative of g**4/24 + 2*g**3/3 + 4*g**2 + 881*g. Factor y(b).
(b + 4)**2/2
Let g(r) be the second derivative of 1 + 20*r + 3/40*r**5 + 1/8*r**4 - r**3 - 3*r**2. Factor g(f).
3*(f - 2)*(f + 1)*(f + 2)/2
Let p(a) be the second derivative of -a**5/10 - 387*a**4 - 599076*a**3 - 463684824*a**2 + 8*a + 200. Determine c so that p(c) = 0.
-774
Let q(l) be the third derivative of 65*l**2 + 11/4*l**4 + 0 + 1/70*l**7 + 4*l**3 + 0*l + 1/5*l**6 + 21/20*l**5. Factor q(c).
3*(c + 1)**2*(c + 2)*(c + 4)
Solve 43002*l**3 + 2*l**5 + 9135824*l**2 + 16300*l**3 - 34645976 + 984*l**4 + 103038*l**3 + 25346826*l = 0 for l.
-163, -4, 1
Factor -764/3*z - 72962 - 2/9*z**2.
-2*(z + 573)**2/9
Let f(h) be the second derivative of -h**5/40 + h**4/8 + 255*h**3/4 + 7425*h**2/4 - 790*h. Factor f(g).
-(g - 33)*(g + 15)**2/2
Let x = -2829 - -2829. Let a(h) be the third derivative of -20*h**2 - 1/9*h**3 - 1/12*h**4 + x + 0*h**5 + 1/45*h**6 + 0*h. What is p in a(p) = 0?
-1/2, 1
Let m(c) = -10*c**2 - 1846*c - 211606. Let f(l) = -28*l**2 - 5536*l - 634816. Let o(w) = 3*f(w) - 8*m(w). Factor o(k).
-4*(k + 230)**2
Let p(m) be the second derivative of m**7/210 + m**6/8 - 4*m**5/15 - 29*m**2 - 95*m. Let a(j) be the first derivative of p(j). Factor a(c).
c**2*(c - 1)*(c + 16)
Let x = 181159/17254 - -4/8627. Determine f so that 3*f + 0 - 29/2*f**2 + x*f**3 - 2*f**4 = 0.
0, 1/4, 2, 3
Let o(h) be the second derivative of -h**5/70 + 13*h**4/21 - 13*h**3/3 + 66*h**2/7 + h + 600. Factor o(u).
-2*(u - 22)*(u - 3)*(u - 1)/7
Let v = -1285 - -3413. Let t be 5544/v - 5/2. Factor 128/19 + t*q**2 + 32/19*q.
2*(q + 8)**2/19
Let c(w) be the second derivative of -w**4/12 + 127*w**3/6 - 63*w**2 + 1204*w. Suppose c(d) = 0. Calculate d.
1, 126
Let d(r) be the first derivative of -7/13*r**2 + 6/13*r + 1/39*r**6 + 127 + 3/13*r**4 - 2/13*r**5 + 4/39*r**3. Let d(o) = 0. What is o?
-1, 1, 3
Factor -2/13*y**3 - 148/13 - 80/13*y**2 - 226/13*y.
-2*(y + 1)*(y + 2)*(y + 37)/13
Let i(j) = 2*j**3 - 17*j**2 - 34*j - 6. Let n(m) = -7*m**3 + 52*m**2 + 99*m + 16. Let y(b) = -8*i(b) - 3*n(b). Factor y(q).
5*q*(q - 5)*(q + 1)
Let o(p) be the third derivative of -3 + 1/30*p**6 - 1/6*p**4 + 0*p + 2/105*p**7 - 1/15*p**5 + 7*p**2 + 0*p**3. Let o(n) = 0. What is n?
-1, 0, 1
Factor 8/3*v**2 + 178/3*v - 2/3*v**3 + 56.
-2*(v - 12)*(v + 1)*(v + 7)/3
Factor -58*p**3 - 4*p**4 + 82*p**3 + 93*p**3 + 27*p**3 + 68*p**3.
-4*p**3*(p - 53)
Let p(i) be the third derivative of 15*i**8/112 - i**7/2 - 7*i**6/12 + 23*i**5/6 + 25*i**4/24 - 125*i**3/6 + 15*i**2 + 11*i. Solve p(x) = 0.
-1, 1, 5/3
Factor 57*o - 65*o - 2*o**2 + o**2 - 91*o.
-o*(o + 99)
Let z = -522 + 519. Let v(o) = o**2 + 5*o + 4. Let b(f) = -f**2 + f + 2. Let x(h) = z*b(h) - v(h). Find k, given that x(k) = 0.
-1, 5
Let u(a) = -5*a**2 + 655*a + 20. Let s(q) = 9*q - 1. Let n(w) = -20*s(w) - u(w). Let n(f) = 0. What is f?
0, 167
Let g(y) be the first derivative of 51*y**4/4 + 47*y**3 - 6*y**2 - 180*y + 2964. Factor g(j).
3*(j - 1)*(j + 2)*(17*j + 30)
Let i(r) be the third derivative of -r**5/20 + 7*r**4/4 - 12*r**3 + 129*r**2 - 7*r. Factor i(x).
-3*(x - 12)*(x - 2)
Factor 1488*l**2 + 3180 - 2*l**3 - 3180 + 5*l**3.
3*l**2*(l + 496)
Let x = 4360 + -4360. Let s(d) be the first derivative of d**4 + 0*d**2 - 9 + x*d - 1/5*d**5 + 0*d**3. Suppose s(b) = 0. Calculate b.
0, 4
Let x(q) be the first derivative of 2*q**3/39 + 1134*q**2/13 + 2266*q/13 + 6732. Suppose x(b) = 0. What is b?
-1133, -1
Let z(t) be the second derivative of -t**8/5040 + 4*t**7/945 - t**6/45 + 47*t**4/4 + 29*t + 1. Let o(j) be the third derivative of z(j). Factor o(n).
-4*n*(n - 6)*(n - 2)/3
Let k(g) = 3*g**3 + 2548*g**2 + 720801*g + 67995559. Let j(d) = -d**2 + 2. Let q(w) = j(w) + k(w). Factor q(f).
3*(f + 283)**3
Let y(t) be the third derivative of -t**6/300 + 467*t**5/150 + 39*t**4/5 + 4*t**2 + 16. Factor y(u).
-2*u*(u - 468)*(u + 1)/5
Let i = 421278 + -421276. Solve -20/11*n**4 + 24/11*n + 2/11*n**5 + 0 + 58/11*n**3 - 64/11*n**i = 0.
0, 1, 2, 6
What is x in 0 - 11/7*x**2 + 5/7*x**4 - 2/7*x - 4/7*x**3 = 0?
-1, -1/5, 0, 2
Let w(s) = -2*s**2 + 80*s + 2. Let m be w(40). Suppose -6*i - 5*l + 35 = -i, -m*i - 1 = -l. Solve 4 - 38/3*q - 14/3*q**i = 0 for q.
-3, 2/7
Let x(u) be the third derivative of -u**5/30 + 10*u**4/3 - 112*u**3 - 70*u**2 - u + 24. Factor x(v).
-2*(v - 28)*(v - 12)
Let d = 92 - 149. Let q be (29 + -25)/(d/(-9)). Factor -18/19 - 2/19*w**2 + q*w.
-2*(w - 3)**2/19
Let b(d) = 1759*d + 5280. Let w be b(-3). Suppose -14/5*o**5 + 48/5*o**w + 0 - 128/5*o**2 + 32/5*o + 32/5*o**4 = 0. Calculate o.
-2, 0, 2/7, 2
Let o(g) be the second derivative of g**7/63 + 11*g**6/45 + 13*g**5/10 + 61*g**4/18 + 44*g**3/9 + 4*g**2 + 297*g. Find u such that o(u) = 0.
-6, -2, -1
Let j(z) = 954*z + 9546. Let i be j(-10). Let h(s) be the third derivative of 0 - 2/75*s**5 - 1/60*s**4 + 0*s + 1/300*s**i + 4/15*s**3 - 45*s**2. Factor h(o).
2*(o - 4)*(o - 1)*(o + 1)/5
Let c(u) be the first derivative of -u**4/24 + u**2 + 96*u - 49. Let m(b) be the first derivative of c(b). Let m(g) = 0. Calculate g.
-2, 2
Let n(x) = 23*x**2 + 146*x + 203. Let w be n(-2). Factor -2448/5*g**w - 136/5*g - 2592/5*g**4 - 8/5 - 866/5*g**2.
-2*(4*g + 1)**2*(9*g + 2)**2/5
Suppose 3*z - 18 = -3. Let k(v) = 5*v**2 - 10*v - 2. Let g(s) = 10*s**2 - 20*s - 5. Let q = 132 + -134. Let o(b) = q*g(b) + z*k(b). Factor o(u).
5*u*(u - 2)
Let a(u) be the first derivative of -u**6 - 158*u**5/15 - 9*u**4 + 32*u**3/9 - 2681. What is k in a(k) = 0?
-8, -1, 0, 2/9
Let t be ((-3)/39)/(17/34) + 4/26. Let r(a) be the second derivative of -2/69*a**3 + 0 + t*a**2 + 1/138*a**4 + 1/230*a**5 + 16*a. What is i in r(i) = 0?
-2, 0, 1
Let v(j) = -j**3 + 92*j**2 + 393*j + 8927. Let h be v(97). Factor -1/2*n**h - 99/2*n**2 - 3267/2*n - 35937/2.
-(n + 33)**3/2
Let g be (17 - 19)*(1 - 0). Let z(f) = f + 4. Let u be z(g). Factor b**3 - 2*b**3 + 4*b + b**u - 2*b.
-b*(b - 2)*(b + 1)
Let l = 1337 + -2671/2. Let j(a) be the third derivative of -l*a**4 - 10/3*a**3 + 12*a**2 + 1/30*a**6 + 0*a + 0 - 1/5*a**5. Factor j(g).
4*(g - 5)*(g + 1)**2
Let x(y) be the first derivative of y**6/33 - 12*y**5/55 + y**4/2 - 4*y**3/11 + 79. Determine w so that x(w) = 0.
0, 1, 2, 3
Let r(d) be the third derivative of d**8/6720 - d**7/1680 - d**5/20 - 4*d**3 + 7*d**2. Let o(t) be the third derivative of r(t). Factor o(p).
3*p*(p - 1)
Let d(u) = -u**2 + 4566*u + 1736831. Let y(m) = 4566*m + 1736964. Let r(s) = -3*d(s) + 4*y(s). What is x in r(x) = 0?
-761
Let b(h) be the third derivative of -h**7/105 - h**6/10 + 19*h**5/30 + 2*h**4 - 621*h**2 + 2. Find u such that b(u) = 0.
-8, -1, 0, 3
Let i(m) be the third derivative of m**7/4200 + m**6/450 - m**5/50 - 313*m**3/6 + 322*m**2. Let l(b) be the first derivative of i(b). Factor l(o).
o*(o - 2)*(o + 6)/5
Let i(u) be the first derivative of -u**4/4 + 224*u**3 - 75264*u**2 + 11239424*u - 1132. Determine t, given that i(t) = 0.
224
What is z in -2*z**2 + 39254*z - 77733*z + 38845*z + 1116 = 0?
-3, 186
Let w = -1/13239 - -39724/92673. Let u(q) be the first derivative of -w*q - 3/7*q**2 - 1/7*q**3 + 37. Suppose u(f) = 0. Calculate f.
-1
Let q be 39136/44028*((-18)/4)/(-1). Determine o, given that 592/5*o**2 - 288/5 - 6/5*o**5 - 672/5*o + 32/5*o**3 - 10*o**q = 0