1)
Solve 2/13*u**4 + 2/13*u**3 + 0 - 2/13*u**2 - 2/13*u = 0 for u.
-1, 0, 1
Let z(m) be the second derivative of m**5/5 - 7*m**4/3 - 16*m**3/3 + 9*m - 5. Factor z(r).
4*r*(r - 8)*(r + 1)
Let n(y) be the first derivative of -y**4/6 + 2*y**3/3 + 3*y**2 - 7*y - 15. Let h(w) be the first derivative of n(w). Factor h(z).
-2*(z - 3)*(z + 1)
Let h = 14726 + -103080/7. Factor -4/7 + 4/7*c**2 - h*c**3 + 2/7*c.
-2*(c - 2)*(c - 1)*(c + 1)/7
Let w(y) = -20*y**2 + 265*y + 525. Let n(q) = -25*q**2 + 263*q + 524. Let l(j) = -5*n(j) + 6*w(j). Determine h, given that l(h) = 0.
-53, -2
Let j(f) = 4*f**3 + 67*f**2 - 1723*f + 13824. Let v(q) = q**3 - q**2 + q. Let i(x) = -j(x) + 5*v(x). Factor i(m).
(m - 24)**3
Let r(f) be the first derivative of 4*f**3/5 - 5*f**2/2 + 2*f/5 - 50. Factor r(a).
(a - 2)*(12*a - 1)/5
Let x(q) be the third derivative of -q**8/4032 + q**7/1008 + 31*q**5/60 + 20*q**2. Let w(l) be the third derivative of x(l). Suppose w(i) = 0. Calculate i.
0, 1
Factor -1/3*x**2 - 14/3*x - 49/3.
-(x + 7)**2/3
Let r(o) be the first derivative of 0*o**3 + 0*o - 7 + 1/2*o**4 + 0*o**2 + 1/5*o**5. Suppose r(t) = 0. What is t?
-2, 0
Let x be 2 + 6 - (-2072)/(-280). Let m(o) be the first derivative of 0*o + x*o**5 + 8*o**3 + 6*o**2 + 15/4*o**4 - 10. Factor m(q).
3*q*(q + 1)*(q + 2)**2
Factor -39/2*p - 9*p**2 + 1/2*p**3 - 10.
(p - 20)*(p + 1)**2/2
Let t(x) be the second derivative of 0 - 1/30*x**5 - 1/9*x**4 + 0*x**2 + 6*x + 0*x**3. Factor t(i).
-2*i**2*(i + 2)/3
Factor -7*g + 9*g + 15 - 13 - g**3 + g.
-(g - 2)*(g + 1)**2
Let m = -26 - -32. Suppose 0 = w - 4, 0 = 5*u - m*w + 3*w + 2. Solve u*r + 2*r**3 + 2*r**3 + 2*r - 6*r**2 - 2*r**3 = 0.
0, 1, 2
Let t = 117 + -142. Let s(o) = -60*o**3 + 1225*o**2 - 6025*o. Let j(x) = 5*x**3 - 102*x**2 + 502*x. Let n(h) = t*j(h) - 2*s(h). Determine i so that n(i) = 0.
0, 10
Let j be (-1)/2*-6 + 112 + -109. Let o(q) be the third derivative of 0 + 2*q**2 - 5/84*q**4 + 2/105*q**5 - 1/420*q**j + 0*q + 2/21*q**3. Factor o(r).
-2*(r - 2)*(r - 1)**2/7
Let z(h) = h**3 - 4*h**2 - 6*h + 7. Let q be z(5). Let -19*f + f**3 + q*f**3 + 37*f - 21*f**2 = 0. What is f?
0, 1, 6
Let p(y) = y - 2. Let s be p(3). Let c be 5 + 2/s*-1. Factor -4*q**2 + 6*q + q**c - 2 - 4*q + 3*q.
(q - 2)*(q - 1)**2
Factor 11*j**4 - 64*j**2 + j**4 + 4*j**5 + 47 - 20 + 37 - 16*j**3.
4*(j - 2)*(j - 1)*(j + 2)**3
Let u(g) be the second derivative of -g**5/30 - g**4/9 + g**3 + 6*g**2 + 3*g + 36. Suppose u(p) = 0. Calculate p.
-3, -2, 3
Let c(l) be the second derivative of 0*l**5 - 3/10*l**6 - 1/14*l**7 + 0*l**3 + l**4 + 0*l**2 - 10*l + 0. Factor c(o).
-3*o**2*(o - 1)*(o + 2)**2
Let d = 832 + -91519/110. Let p(j) be the second derivative of 1/22*j**4 + d*j**5 + 0 + 0*j**2 - 4*j + 2/33*j**3. Suppose p(x) = 0. Calculate x.
-2, -1, 0
Let a(t) be the third derivative of -t**5/180 + 19*t**4/72 + 10*t**3/9 + 197*t**2. Factor a(f).
-(f - 20)*(f + 1)/3
Find h such that -9 + 9 + 4*h - h + 2*h + 25*h**2 - 20 = 0.
-1, 4/5
Find x, given that -45/4*x - 27/4*x**4 + 51/2*x**2 + 21/2*x**3 - 75/4 + 3/4*x**5 = 0.
-1, 1, 5
Suppose 0 = -3*j - 15 + 21. Suppose b = 5*b + j*b. Factor b*q + 2/3*q**3 + 2*q**2 - 8/3.
2*(q - 1)*(q + 2)**2/3
Factor 48*f**3 + 38*f - 34*f**2 + 4 - 56*f**3 - 6*f + 6.
-2*(f - 1)*(f + 5)*(4*f + 1)
Let m(i) be the first derivative of 3*i**5/20 - i**4 + 2*i**3 + i + 6. Let q(s) be the first derivative of m(s). Factor q(r).
3*r*(r - 2)**2
Let f = -4/369 - 5491/4059. Let v = 67/33 + f. Factor v*t**2 + 1/3*t**3 - 1/3*t - 2/3.
(t - 1)*(t + 1)*(t + 2)/3
Let m(v) be the first derivative of 21 + 5*v**2 - 2*v**3 + 1/6*v**4 - 14/3*v. Factor m(g).
2*(g - 7)*(g - 1)**2/3
Factor b**2 + 115*b + 251 + 3*b**2 + 125*b - 15.
4*(b + 1)*(b + 59)
Let b = -26091 - -26093. Solve 2/3*f**b + 0 + 1/3*f**3 + 1/3*f = 0.
-1, 0
Let u(i) be the first derivative of -i**5/15 - i**4/3 + 7*i**3/9 + 17*i**2/3 + 8*i + 30. What is l in u(l) = 0?
-4, -2, -1, 3
Let j(s) be the third derivative of 0 + 1/21*s**4 - 50*s - 1/420*s**5 + 3/14*s**3 - 2*s**2. Let j(l) = 0. Calculate l.
-1, 9
Let v(y) be the second derivative of -3*y**5/40 + 7*y**4/24 - y**3/3 + 38*y + 2. Factor v(h).
-h*(h - 1)*(3*h - 4)/2
Let k = 2054/2555 + -2/511. Suppose -4/5 - k*a + 1/5*a**3 + 1/5*a**2 = 0. What is a?
-2, -1, 2
Find x such that -9*x - 288*x**2 + 6*x + 19 + 21 - 16*x**4 - 9*x + 88*x + 188*x**3 = 0.
-1/4, 1, 10
Let r(g) be the second derivative of g**7/105 + g**6/20 + g**5/30 - g**4/4 - 2*g**3/3 - 13*g**2/2 + 14*g. Let n(w) be the first derivative of r(w). Factor n(t).
2*(t - 1)*(t + 1)**2*(t + 2)
Let g(f) be the second derivative of -f**7/105 - 4*f**6/75 + 27*f**5/50 - 19*f**4/15 + 16*f**3/15 + 43*f. Let g(p) = 0. Calculate p.
-8, 0, 1, 2
Let x(a) be the third derivative of -6*a**2 + 0 + 0*a**3 - 1/480*a**5 + 0*a + 1/1680*a**7 + 0*a**4 - 1/2688*a**8 + 1/960*a**6. Determine m so that x(m) = 0.
-1, 0, 1
Let o be ((-7)/(-448))/(5/2). Let h(b) be the third derivative of -1/120*b**5 + 0*b**4 + 0*b**7 - 1/1344*b**8 + 0*b + 0*b**3 + 0 + o*b**6 - 2*b**2. Factor h(s).
-s**2*(s - 1)**2*(s + 2)/4
Let u be (-1 - (-100)/8) + -3. Let i be 4/48 + 1140/144. What is w in 2 - i*w - 5/2*w**3 + u*w**2 = 0?
2/5, 1, 2
Solve 28*u - 34 + 34 - 40*u - 10*u**3 - 108*u - 245*u**2 = 0 for u.
-24, -1/2, 0
Let w = 38 + -36. Factor -4*l**3 - 2466*l**2 + 5*l**4 - 3*l**4 + 2464*l**w + 4*l.
2*l*(l - 2)*(l - 1)*(l + 1)
Suppose 0 = -9*n + 16 + 2. Solve -161 + 33*v + 11*v - n*v**2 - 81 = 0 for v.
11
Suppose -4*f + 0*v = v - 80, -5*v = -4*f + 56. Let r = -17 + f. Let 0 + 2/3*j**r + 0*j = 0. Calculate j.
0
Let a = 3665 + -69593/19. Suppose -2/19*u**3 - a*u - 16/19*u**2 - 36/19 = 0. Calculate u.
-3, -2
Suppose 0 = -4*k + 5*b + 39, -5*b = 4*k - 9 - 0. Suppose 6*v = -k*v + 24. What is n in 3/7*n + 2/7*n**v + 1/7 = 0?
-1, -1/2
Let t(v) be the first derivative of -2/3*v**3 - 9 - 4*v + 3*v**2. Factor t(u).
-2*(u - 2)*(u - 1)
Let m be 1/((-6)/(-735)*14). Let r(a) be the first derivative of -15*a**3 + 0*a + 6 - m*a**4 - 5*a**2. Suppose r(b) = 0. What is b?
-1, -2/7, 0
Suppose 0 = 3*k - 5*g - 11, -5*g + 79 = 4*k + 76. Find t such that -2*t - 4/7 + 4/7*t**k + 2*t**3 = 0.
-1, -2/7, 1
Let n = -40 - -44. Let t(c) be the third derivative of -4*c**2 + 0*c + 1/40*c**6 + 0*c**3 + 1/70*c**7 + 0 - 1/112*c**8 - 1/20*c**5 + 0*c**n. Factor t(l).
-3*l**2*(l - 1)**2*(l + 1)
Suppose -2*t = -8, -4*s - 48 + 64 = 4*t. Factor s + 0*z + 144/5*z**3 - 24*z**4 + 28/5*z**5 - 32/5*z**2.
4*z**2*(z - 2)**2*(7*z - 2)/5
Let w be 1*(1 + (1 - 4)). Let j be (-2)/(-12)*w*15/(-10). Factor 1 - 1/2*v - j*v**2.
-(v - 1)*(v + 2)/2
Factor 0 + 8/3*o**3 + 0*o - 4/3*o**5 + 0*o**2 - 4/3*o**4.
-4*o**3*(o - 1)*(o + 2)/3
Let q(l) = -8*l**4 - 200*l**3 + 2052*l**2 + 11652*l + 12. Let n(u) = u**4 + u - 1. Let s(z) = 12*n(z) + q(z). Factor s(h).
4*h*(h - 27)**2*(h + 4)
Let l(c) be the first derivative of -4*c**3/21 + 4*c**2/7 + 9. Determine p so that l(p) = 0.
0, 2
Suppose 2*c - 8 = -3*v, 0*v + 8 = -5*v + 2*c. Factor 1/5*y**3 + 2/5*y**2 + 1/5*y + v.
y*(y + 1)**2/5
Let q(i) = 2*i**2 + 7*i - 1. Let r be q(-6). Suppose 21*o - 14*o = 14. Let -27*a - 9*a**o + 8 - 6 - r - a**3 = 0. What is a?
-3
Factor 2/5*p**3 + 14/5*p**2 - 16/5*p + 0.
2*p*(p - 1)*(p + 8)/5
Let d(s) = s**3 - 5*s**2 + 18. Let n(m) = 2*m**3 - 9*m**2 + 39. Let o(w) = 13*d(w) - 6*n(w). Solve o(b) = 0.
0, 11
Let g(n) be the second derivative of n**5/30 + 5*n**4/6 - 16*n**3/9 + 110*n. Factor g(y).
2*y*(y - 1)*(y + 16)/3
Suppose -213 = -67*i - 12. Factor 11/7*r + 3/7*r**4 + 2/7 + 13/7*r**i + 19/7*r**2.
(r + 1)**2*(r + 2)*(3*r + 1)/7
Let b = 7751/27 + -287. Let y(n) be the first derivative of 3 - 4/9*n + b*n**3 - 1/9*n**2. Find t such that y(t) = 0.
-1, 2
Let a(g) be the third derivative of 1/36*g**4 + 0*g**5 - 1/180*g**6 + 0*g**3 + 0 - 29*g**2 + 0*g. Solve a(y) = 0.
-1, 0, 1
Let g = -109 - -114. Let f(d) = -d**2 + 5*d + 3. Let a be f(g). Find h, given that -3/4*h**2 - 9/4 + a*h = 0.
1, 3
Solve 3/4*i**2 + 33/4 + 9*i = 0 for i.
-11, -1
Let d = 34609/19788 - -5/4947. What is h in 0*h + 1/4*h**3 + d*h**2 + 0 = 0?
-7, 0
Suppose -8 = -g - 3*g. Suppose 0 = -o - 3*m + g*m + 6, 5*m - 5 = 0. Find p such that 4*p**2 + 5 - 5 + 1 - o*p**2 = 0.
-1, 1
Let b(c) be the third derivative of 5*c**8/336 - 13*c**7/42 + 67*c**6/24 - 57*c**5/4 + 45*c**4 - 90*c**3 + 2*c**2 + 12*c. Determine v so