 2
Factor -6/7*r**2 + 0 - 2/7*r**4 + 0*r + 8/7*r**3.
-2*r**2*(r - 3)*(r - 1)/7
Let p be ((-459)/(-340))/(6/4). Let f(k) be the second derivative of 1/2*k**4 - 4*k**2 + p*k**5 + 2*k + 0 - 8/3*k**3. Solve f(v) = 0.
-2/3, 1
Let 2*d**2 + 4/5 - 14/5*d = 0. Calculate d.
2/5, 1
Let r(b) be the third derivative of b**8/336 + 2*b**7/105 - b**6/20 - b**5/15 + 5*b**4/24 - 22*b**2 + 4*b. Factor r(f).
f*(f - 1)**2*(f + 1)*(f + 5)
Let b be (4/(12/9))/(1/(-3)). Let x = 19/2 + b. Factor 0 + 0*r + 1/2*r**3 - 1/2*r**2 + x*r**4 - 1/2*r**5.
-r**2*(r - 1)**2*(r + 1)/2
Let g(b) be the second derivative of b**6/75 + 9*b**5/50 - 10*b + 4. Factor g(z).
2*z**3*(z + 9)/5
Let j be 2 - 2 - (-3 + (-16)/(-12)). Solve -5/3 - j*f**2 - 10/3*f = 0.
-1
Factor -4 + 1/2*d**2 - d.
(d - 4)*(d + 2)/2
Let h(u) be the second derivative of -317*u**4/12 - 106*u**3 - 2*u**2 - 6*u - 2. Find w such that h(w) = 0.
-2, -2/317
Let q(g) be the first derivative of g**6/4 + 6*g**5/5 + 15*g**4/8 + g**3 + 75. Factor q(y).
3*y**2*(y + 1)**2*(y + 2)/2
Let s(z) be the second derivative of -z**7/126 + z**6/45 + z**5/20 - z**4/9 - 2*z**3/9 - z - 27. Factor s(w).
-w*(w - 2)**2*(w + 1)**2/3
Let i = 7 - 5. Let d = -72 - -76. Factor 17*q**3 + 12*q - 5*q**3 - q**d - 18*q**i - 3 - 3*q**4 + q**4.
-3*(q - 1)**4
Suppose 13*l = 7*l + 204. Let d = 36 - l. Factor -1/3*w**2 + d*w - 3.
-(w - 3)**2/3
Let n(m) be the second derivative of m**4/4 - 3*m**3/2 + 3*m**2 - 15*m - 1. Determine s, given that n(s) = 0.
1, 2
Let a(f) = -f**3 + 15*f**2 - 16*f + 34. Let s be a(14). Suppose 90*g = 93*g - s. Factor -8/3*z**g + 10/3*z - 2/3.
-2*(z - 1)*(4*z - 1)/3
Factor -845*b**4 - 3210*b**3 - 800*b**2 - 27*b - 33*b + 415*b**3.
-5*b*(b + 3)*(13*b + 2)**2
Let d(g) be the second derivative of -g**8/7560 - g**7/3780 + g**3/2 + 11*g. Let f(s) be the second derivative of d(s). Let f(j) = 0. Calculate j.
-1, 0
Let p(a) be the third derivative of a**7/210 - a**6/20 + a**5/12 - 9*a**2 - 4*a. Factor p(i).
i**2*(i - 5)*(i - 1)
Let g(h) = 3*h - 87. Let f be g(29). Let l(a) be the second derivative of 2*a + 1/60*a**4 + 0 + f*a**3 + 1/100*a**5 + 0*a**2. Factor l(t).
t**2*(t + 1)/5
Let j = 26 + -12. Let b be j/4 + (-4)/(-8). Factor 3*z**4 + z**4 + 0*z + 2*z**b + 9*z**3 - 3*z.
3*z*(z + 1)**2*(2*z - 1)
Let u(l) be the first derivative of -11*l + 0*l**3 + 0*l**5 - 1/60*l**4 - 12 + 1/150*l**6 + 0*l**2. Let c(f) be the first derivative of u(f). Solve c(t) = 0.
-1, 0, 1
Let q(i) = -i**3 + 16*i**2 + 6. Let v be q(16). Let o be (-102)/(-170) - v/10. Determine g so that -1/7*g**3 + o - 1/7*g + 2/7*g**2 = 0.
0, 1
Let i(x) be the third derivative of 0*x + 0 - 11/84*x**4 - 2/21*x**3 - 3/70*x**5 - 22*x**2. Factor i(y).
-2*(y + 1)*(9*y + 2)/7
Let f(r) be the first derivative of -r**6/360 + r**5/180 + 5*r**4/72 + r**3/6 - 11*r**2/2 - 4. Let w(q) be the second derivative of f(q). Factor w(d).
-(d - 3)*(d + 1)**2/3
Let r(f) = -f**3 + 7*f**2 + 12*f - 80. Let o be r(7). Let l(t) be the second derivative of 0 + 1/6*t**2 - 1/36*t**o + 0*t**3 + 8*t. Suppose l(d) = 0. What is d?
-1, 1
Let n(r) = -4*r**3 + 244*r**2 + 3800*r + 9408. Let y(a) = 2*a**3 - 2*a**2 + 2*a. Let q(p) = -n(p) - 4*y(p). Factor q(l).
-4*(l + 3)*(l + 28)**2
Factor -1/2*f + 1/6*f**3 - 1/3*f**2 + 0.
f*(f - 3)*(f + 1)/6
Let b(l) be the first derivative of -l**7/1120 - l**6/96 - 7*l**5/160 - 3*l**4/32 - 31*l**3/3 + 43. Let k(g) be the third derivative of b(g). Factor k(d).
-3*(d + 1)**2*(d + 3)/4
Let m(k) = 26*k**3 + 150*k**2 + 172*k - 16. Let a(d) = 5*d**3 + 30*d**2 + 34*d - 3. Let s(w) = 16*a(w) - 3*m(w). Determine i so that s(i) = 0.
-14, -1, 0
Let a(v) = -6*v - 35. Let y be a(-14). Let c = y - 45. Factor 338/3*w**c + 0 + 78*w**3 - 32*w**2 + 8/3*w.
2*w*(w + 1)*(13*w - 2)**2/3
Let l(w) be the third derivative of -w**9/15120 - w**8/840 - w**7/140 - 31*w**5/60 - 25*w**2. Let p(n) be the third derivative of l(n). Factor p(j).
-4*j*(j + 3)**2
Let z be 4*(-6)/4 - 419442/(-6595). Factor -48/5*f + z + 2/5*f**2.
2*(f - 12)**2/5
Let v(l) be the third derivative of 1/42*l**4 + 0*l + 22*l**2 - 1/105*l**5 + 0 + 4/7*l**3. Factor v(k).
-4*(k - 3)*(k + 2)/7
Let v be 115/184 + (-129)/(-24) + -5. Factor -3/2*p**3 + v - 4*p**2 - 3/2*p.
-(p + 1)*(p + 2)*(3*p - 1)/2
Let x(c) = -c**3 + c**2 + c. Let h(g) = g**4 + 4*g**3 - 11*g**2 - 5*g. Let r(p) = h(p) + 5*x(p). Let r(s) = 0. What is s?
-2, 0, 3
Let r be (-459)/(-1020) - 3/15. Determine u so that r*u**4 + 0 + 3*u**2 + 2*u + 3/2*u**3 = 0.
-2, 0
Let r(c) = -8*c**2 - 2*c + 4. Let b be r(1). Let j be b + (4 - 0/2) + 4. Factor -v - 2/3 - 1/3*v**j.
-(v + 1)*(v + 2)/3
Let w be 4*2 + (-147 - -141). Let d(p) be the second derivative of 6/7*p**3 - 9*p + 0 + 4/7*p**w + 4/21*p**4. Determine a, given that d(a) = 0.
-2, -1/4
Let v(y) be the second derivative of y**4/24 - 5*y**3/6 + 9*y**2/4 - y + 44. Factor v(a).
(a - 9)*(a - 1)/2
Let n(h) be the third derivative of h**5/30 + h**4/6 + h**3/3 + 161*h**2. Factor n(y).
2*(y + 1)**2
Let o(c) be the first derivative of -20*c**3/3 - 726*c**2 + 584*c + 757. Solve o(v) = 0 for v.
-73, 2/5
Suppose -16*r + 15*r + 25 = 3*q, -r - q + 11 = 0. Let 2/7*k**5 + 4/21*k - 26/21*k**r + 0 - 22/21*k**2 + 38/21*k**3 = 0. Calculate k.
0, 1/3, 1, 2
Let s(i) be the second derivative of i**8/2940 + i**7/735 - i**6/630 - i**5/105 - i**3/2 + 10*i. Let w(a) be the second derivative of s(a). Factor w(l).
4*l*(l - 1)*(l + 1)*(l + 2)/7
Suppose -45*m - 25*m = -140. Factor 0*v + 0*v**4 - 1/5*v**5 + 1/5*v**3 + 0 + 0*v**m.
-v**3*(v - 1)*(v + 1)/5
Let l(m) be the third derivative of -m**8/112 + m**7/70 + m**6/5 - 2*m**5/5 - 2*m**4 + 8*m**3 + 2*m**2 + 24*m. Solve l(b) = 0 for b.
-2, 1, 2
Let y(u) = -2*u**2 - 2*u + 4. Let m = -17 + 20. Let n(o) = 11*o - 6*o - 9 - m*o**2 + 7*o**2. Let f(i) = 4*n(i) + 10*y(i). Suppose f(d) = 0. Calculate d.
-1, 1
Factor 4*a**2 - 2/3*a**4 + 2/3*a**3 + 0 + 0*a.
-2*a**2*(a - 3)*(a + 2)/3
Let s(g) be the first derivative of 0*g**2 + 1/15*g**5 + 2/9*g**3 + 17 - 1/4*g**4 + 0*g. Factor s(a).
a**2*(a - 2)*(a - 1)/3
Let w(g) be the first derivative of 5/8*g**4 + 1/4*g - 11 + 3/20*g**5 + g**3 + 3/4*g**2. Factor w(k).
(k + 1)**3*(3*k + 1)/4
Let u(i) be the third derivative of 0*i + 0*i**3 + 0 + 1/8*i**4 + 19*i**2 - 1/10*i**5. Factor u(r).
-3*r*(2*r - 1)
Let d(i) be the second derivative of -i**3/6 + 7*i**2 - 2*i. Let k be d(12). Factor 7*a**2 - a**5 + 0*a**k - 7*a**2 + a**3.
-a**3*(a - 1)*(a + 1)
Determine l so that -7/3*l**2 - 8/3 - 14/3*l - 1/3*l**3 = 0.
-4, -2, -1
Suppose 12*s**3 + 14*s**4 - 6*s**2 - 5*s**2 + 3*s**2 - 4*s**4 + 4 - 9*s - 6*s**2 - 3*s**5 = 0. Calculate s.
-1, 1/3, 1, 4
Let q(w) be the second derivative of -w**4/12 - 7*w**3/6 + 12*w. Let x(k) = -k**2 - 8*k. Let v(b) = -6*q(b) + 5*x(b). Factor v(u).
u*(u + 2)
Suppose 3*p + 3 = 0, -m + 6*m + 3*p - 32 = 0. Factor -3*b - 2*b - 2*b**3 + m*b + b**5 - b.
b*(b - 1)**2*(b + 1)**2
Let b(x) be the third derivative of 7*x**8/6 + x**7/2 - 313*x**6/120 - 14*x**5/5 - 2*x**4/3 + 2*x**2 + 27*x. What is f in b(f) = 0?
-4/7, -1/8, 0, 1
Let x be (-553)/(-231)*3*1 + -7. Factor -4/11*s**3 + x*s**2 + 2/11*s + 0.
-2*s*(s - 1)*(2*s + 1)/11
Let m(t) be the second derivative of 0*t**2 - 1/5*t**3 + 1/30*t**4 + 2*t + 0. Factor m(a).
2*a*(a - 3)/5
Let u(i) be the third derivative of -1/108*i**6 - 4/27*i**3 - 4/27*i**4 + 0*i + 2*i**2 + 0 - 17/270*i**5. Factor u(v).
-2*(v + 1)*(v + 2)*(5*v + 2)/9
Let f(h) be the first derivative of h**4/6 + 10*h**3/9 - 25*h**2/3 - 250*h/3 - 832. Find a, given that f(a) = 0.
-5, 5
Suppose -46*b + 83*b = 111. Let o(c) be the third derivative of -1/90*c**4 - 7*c**2 + 0 - 1/450*c**5 + 1/15*c**b + 0*c. Factor o(w).
-2*(w - 1)*(w + 3)/15
Let m = -4361 - -4363. Factor -1/2*k**m - 9/2 - 3*k.
-(k + 3)**2/2
Let k(j) be the second derivative of j**4/4 + 5*j**3/2 + 9*j**2 - j + 18. Factor k(w).
3*(w + 2)*(w + 3)
Let h be 1 - 2/2 - -1 - -6. Factor 12*d**3 + h*d + 8*d**2 + 8*d - 27*d + 8*d.
4*d*(d + 1)*(3*d - 1)
Let g(k) be the third derivative of -k**6/900 - 2*k**5/25 - 23*k**4/60 - 34*k**3/45 + 284*k**2 - 2*k. Factor g(n).
-2*(n + 1)**2*(n + 34)/15
Let v(i) be the third derivative of -2/3*i**4 + 17*i**2 + 0*i + 2/3*i**3 - 2/15*i**6 + 0 + 2/105*i**7 + 2/5*i**5. Factor v(b).
4*(b - 1)**4
Let h = 67 - 63. Suppose -h + 0 + t**2 + 3*t**2 = 0. Calculate t.
-1, 1
Factor -1/3*f**3 + 0*f + 0*f**2 - 1/6*