0/(-200). Let r(s) be the second derivative of 1/6*s**7 - 5/12*s**4 + 1/6*s**y + 1/3*s**3 - 6*s + 0*s**2 - 9/20*s**5 + 0. Factor r(z).
z*(z - 1)*(z + 1)**2*(7*z - 2)
Let k(a) = 5*a**4 + 2*a**3 - 17*a**2 - 14*a - 3. Let g(i) = -14*i**4 - 4*i**3 + 50*i**2 + 40*i + 8. Let z(j) = 3*g(j) + 8*k(j). Factor z(f).
-2*f*(f - 4)*(f + 1)**2
Let o(y) = y**2 + 49*y + 364. Let u be o(-9). Let s(f) be the second derivative of 1/78*f**u + 7*f + 4/13*f**2 + 4/39*f**3 + 0. Factor s(k).
2*(k + 2)**2/13
Let p(t) be the third derivative of t**6/60 - 14*t**5/45 - 53*t**4/36 - 22*t**3/9 - 290*t**2. Factor p(b).
2*(b - 11)*(b + 1)*(3*b + 2)/3
Let t(l) = 3*l + 20. Let a be t(-8). Let y be (a + 3)*-3 - -20. Factor -20*m**2 - 3*m - 10*m - y*m + 10 - 2.
-4*(m + 2)*(5*m - 1)
Let l(n) be the second derivative of n**8/1176 + 2*n**7/735 - n**5/105 - n**4/84 - 7*n**2 + n. Let w(p) be the first derivative of l(p). What is d in w(d) = 0?
-1, 0, 1
Let f(q) = 6*q**3 + 5*q**2 - 24*q - 5. Let h(s) = 3*s**3 + 2*s**2 - 12*s - 2. Let z(a) = 2*f(a) - 5*h(a). Find o such that z(o) = 0.
-2, 0, 2
Let c(d) be the first derivative of 16/55*d**5 + 0*d - 16/11*d**2 - 1/33*d**6 - 12/11*d**4 + 64/33*d**3 - 10. Find n, given that c(n) = 0.
0, 2
Let h = 38 + -33. Let p(q) = -4*q**2 - 9*q + 5. Let i(n) = 4*n**2 + 8*n - 4. Let o(c) = h*i(c) + 4*p(c). Factor o(y).
4*y*(y + 1)
Factor -311469 - 19881/2*q - 423/4*q**2 - 3/8*q**3.
-3*(q + 94)**3/8
Let i = -7 - -10. Suppose -80*a = -86*a + 18. Suppose i - l**a - 2 - 1 = 0. Calculate l.
0
Suppose 8*m + 0*m = -120. Let w be 5 - 344/120 - (-2)/m. Solve 2/3*v**4 + 2/3*v**2 + 2*v - w*v**3 - 4/3 = 0 for v.
-1, 1, 2
Let y(d) be the third derivative of -11*d**5/120 + 7*d**4/24 - 197*d**2. Factor y(q).
-q*(11*q - 14)/2
Let j(p) be the first derivative of 5*p**3/3 - 85*p**2/2 + 80*p + 217. Factor j(h).
5*(h - 16)*(h - 1)
Suppose 1823*k**3 - 3*k**5 + 6*k**4 + 0*k**5 + 48*k - 96*k**2 - 1778*k**3 = 0. What is k?
-4, 0, 1, 4
Let b(l) = -l**2 - 10*l - 17. Let k be b(-7). Find y such that 36*y - y**3 - 56*y + 20*y**4 + 40*y**2 - 39*y**3 + k - 4*y**5 = 0.
1
Let g(d) be the second derivative of -d**6/30 - d**5/2 + 7*d**4/12 + 38*d**3/3 + 30*d**2 - 82*d. Suppose g(k) = 0. What is k?
-10, -2, -1, 3
Factor 11*a**4 - 1600*a + 1/2*a**5 - 460*a**2 + 8000 + 38*a**3.
(a - 4)**2*(a + 10)**3/2
Factor -152/3*p**2 + 3034/3*p - 5476/3 + 2/3*p**3.
2*(p - 37)**2*(p - 2)/3
Let q = 163 - 321/2. Let n(u) be the first derivative of -q*u**4 - 6*u**3 + 6 - 2/5*u**5 - 7*u**2 - 4*u. Let n(a) = 0. What is a?
-2, -1
Let c be -2*(-3)/(-2) + 15/5. Let j(f) be the second derivative of 0 + 3/20*f**5 + 0*f**3 - 10*f + 0*f**2 + c*f**4. Find a such that j(a) = 0.
0
Let u(m) be the third derivative of -m**7/1260 + m**6/240 + 17*m**5/360 - 13*m**4/48 + 5*m**3/9 - m**2 + 85. Factor u(g).
-(g - 5)*(g - 1)**2*(g + 4)/6
Let y = -14 - -16. Factor 2*q**2 + 6*q + 2*q**2 - q**2 - 7 - y.
3*(q - 1)*(q + 3)
Let z(g) be the first derivative of -g**6/10 - 24*g**5/25 + 9*g**4/5 + 22*g**3/5 - 129*g**2/10 + 54*g/5 - 233. Suppose z(r) = 0. Calculate r.
-9, -2, 1
Let v = 1717/45 - 208/5. Let x = v - -11/3. Solve -x*j**2 + 0 + 2/9*j = 0 for j.
0, 1
Let f(k) be the third derivative of k**5/300 - 17*k**4/60 + 11*k**3/10 - 80*k**2 + 3. Factor f(p).
(p - 33)*(p - 1)/5
Factor -24/5*n + 3/5*n**3 + 0 + 34/5*n**2.
n*(n + 12)*(3*n - 2)/5
Let p(s) be the third derivative of 0*s**5 + 1/270*s**6 - 1/54*s**4 + 0*s + 0 - 1/27*s**3 - s**2 + 1/945*s**7. Suppose p(j) = 0. Calculate j.
-1, 1
Factor -10*u - 2*u**4 + 20*u**4 + 140*u**3 - 39*u + 256*u**2 - 15*u.
2*u*(u + 4)**2*(9*u - 2)
Let x(p) be the first derivative of p**4/18 - 28*p**2/9 - 32*p/3 - 832. Factor x(s).
2*(s - 6)*(s + 2)*(s + 4)/9
Let x(g) be the second derivative of g**6/75 + g**5/50 - g**4/30 - g**3/15 - 13*g - 1. Factor x(n).
2*n*(n - 1)*(n + 1)**2/5
Let q be 2 + (-4)/(-4) + 0. Suppose -q + 9 = 3*g. Factor g*d**2 + 5*d**2 + 8 + 4 - 12*d - 4*d**2.
3*(d - 2)**2
Let s = 383/2370 + 2/395. Let o(z) be the second derivative of -z**2 - 8*z + 0 + s*z**4 + 0*z**3. Factor o(i).
2*(i - 1)*(i + 1)
Factor 0 - 39/5*i**2 + 36/5*i + 3/5*i**3.
3*i*(i - 12)*(i - 1)/5
Let a(k) = 6*k**2 + 20*k - 106. Let v(r) = -2*r**2 - 6*r + 35. Let j(f) = 3*a(f) + 10*v(f). Factor j(l).
-2*(l - 4)*(l + 4)
Let p(y) be the third derivative of 0 - 1/180*y**6 + 19*y**2 + 0*y + 1/45*y**5 + 0*y**3 + 1/12*y**4. Determine w, given that p(w) = 0.
-1, 0, 3
Let n = -20 + 23. Suppose 3*z + 2*z + 5*i - 90 = 0, 54 = n*z - 5*i. Find m such that -8*m**2 + 30*m - z*m - 2 - 2*m = 0.
1/4, 1
Let i be (-110)/132*(-5)/(100/6). Determine j so that -3/4*j + i*j**2 + 1/2 = 0.
1, 2
Let i(d) be the first derivative of 7/6*d**2 + 1/12*d**4 - d + 8 - 5/9*d**3. Determine g, given that i(g) = 0.
1, 3
Let o be ((-50)/(-4))/(1/10). Let p = -121 + o. Let -1/4*f + 0 + 1/4*f**p + 1/4*f**3 - 1/4*f**2 = 0. Calculate f.
-1, 0, 1
Let r(n) be the first derivative of -7*n**6/4 - 276*n**5/5 - 4629*n**4/8 - 2215*n**3 - 3399*n**2 - 1452*n + 271. Determine w, given that r(w) = 0.
-11, -2, -2/7
Let r(h) = 4*h**2 + 27*h - 7. Let w be r(-7). Suppose 9*d - 3*d = w. Solve 0 - 2/3*s**3 + d*s + 1/3*s**2 = 0.
0, 1/2
Let g(d) = d**2. Let x(b) = -b**3 - 2*b**2 - 12*b + 21. Let i(u) = -4*g(u) + x(u). Let m(q) be the first derivative of i(q). Determine k so that m(k) = 0.
-2
Let q(b) = b**2 + 4*b + 7. Suppose -29 + 14 = 5*x. Let t be q(x). Find g, given that -12*g + g**3 + 14*g**3 + 5*g**5 - 8*g + 25*g**t - 25*g**2 = 0.
-4, -1, 0, 1
Let q(m) be the second derivative of m**7/210 + 7*m**6/30 + 71*m**5/20 + 173*m**4/12 + 80*m**3/3 + 128*m**2/5 - 78*m. Determine l so that q(l) = 0.
-16, -1
Let v = 10250 - 20497/2. Factor -v + 1/2*d**2 + d.
(d - 1)*(d + 3)/2
Let 3420*m + 5*m**4 + 988 + 756 + 190*m**3 + 10 + 1985*m**2 - 134 = 0. What is m?
-18, -1
Let c = 189 + -942/5. Let k be 11/330*12*(-1 + (-9)/(-6)). Factor 0*h**2 - c*h + k*h**3 - 2/5.
(h - 2)*(h + 1)**2/5
Suppose -5*q = x - 11, 4*q + q = 3*x + 7. Let n be (q - 3)*(0 - 2). Factor -239*i + 3*i**3 + 6*i**n + 239*i.
3*i**2*(i + 2)
Let z = -1823 + 12773/7. Find g such that 8/7 + z*g + 0*g**2 - 4/7*g**3 = 0.
-1, 2
Factor -10*b - 82*b - 3*b**2 + 491 - 16*b - 11.
-3*(b - 4)*(b + 40)
Let u(v) be the first derivative of v**4 - 28*v**3 + 112*v**2 - 144*v - 178. Determine c, given that u(c) = 0.
1, 2, 18
Let l be -4 + 3 - (-7 - -2). Factor -12 + 76 - l*k**2 - 48*k + 4*k**3 + 4*k**2.
4*(k - 2)**2*(k + 4)
Let r be 3844/155 - (16 + 1). Factor -18/5*w**3 + 3/5*w**4 - 36/5*w + 12/5 + r*w**2.
3*(w - 2)**2*(w - 1)**2/5
Let f be (-12)/(-2)*(3 + -1). Suppose 13*h - f*h = 4. Factor -11*i**5 - 3*i**3 + i**4 + 11*i**h + 2*i**5.
-3*i**3*(i - 1)*(3*i - 1)
Let b(p) = 18*p**2 + p + 1. Let q be b(-1). Let t be (q/8)/((-12)/(-32)). Factor 63*k**3 - k**4 - t*k**4 - 39*k**2 + 3*k + 6*k + 12*k**5 - 38*k**4.
3*k*(k - 1)**3*(4*k - 3)
Let v(b) be the second derivative of 0 + 0*b**2 - 1/24*b**4 - 1/24*b**3 - 1/80*b**5 - 7*b. Factor v(o).
-o*(o + 1)**2/4
Let z(s) be the third derivative of s**8/504 - 13*s**7/315 + 2*s**6/9 - 2*s**5/5 - 2*s**2 + 29*s. Factor z(v).
2*v**2*(v - 9)*(v - 2)**2/3
Let q(x) be the third derivative of -x**7/1260 - x**6/360 + x**4/72 + x**3/36 + 3*x**2 - 2. Factor q(p).
-(p - 1)*(p + 1)**3/6
Let s(y) be the second derivative of -3*y**4/28 + 35*y**3/2 - 243*y**2/7 - 119*y + 2. Determine t, given that s(t) = 0.
2/3, 81
Let n(k) be the third derivative of k**7/140 + 19*k**6/360 + 11*k**5/90 + k**4/18 + 33*k**2 + 2. Suppose n(f) = 0. What is f?
-2, -2/9, 0
Let l(c) be the second derivative of c**9/52920 + c**8/3920 + c**7/735 + c**6/315 + 17*c**4/12 + 24*c. Let d(v) be the third derivative of l(v). Factor d(x).
2*x*(x + 2)**3/7
Let z(j) be the third derivative of -j**6/105 - 26*j**5/35 - 507*j**4/28 - 2*j**2 + 15*j. Factor z(t).
-2*t*(2*t + 39)**2/7
Let y = -32 + 36. Factor 5*o**4 - 5 + y*o**4 - 10*o + 8*o**3 + 2*o**3 - 4*o**4.
5*(o - 1)*(o + 1)**3
Let 0 - 5/2*w**3 + 1/10*w**4 + 169/10*w + 143/10*w**2 = 0. Calculate w.
-1, 0, 13
Let m(k) = -k**4 - k**2 - k. Let u(f) = 4*f + 0 - 8 - 20*f - 3*f**3 + 15*f**3. Let d(n) = -4*m(n) + u(n). Suppose d(p) = 0. Calculate p.
-2, -1, 1
Let j(t) be the first derivative of t**5/120 - t**4/24 - t**3/4 + t**2 - 11. Let s(r) be the second derivative of j(r). Factor s(u).
(u - 3)*(u + 1)/2
Let d(l)