2)
Let c(y) be the second derivative of -y**6/150 + y**5/50 + y**4/30 + 9*y**2/2 + 28*y. Let x(j) be the first derivative of c(j). Factor x(g).
-2*g*(g - 2)*(2*g + 1)/5
Find z, given that -13*z + 7331 + 4*z**3 - 7323 + z = 0.
-2, 1
Let b(y) be the second derivative of y**4/78 + y**3/39 - 12*y**2/13 - 114*y. Determine j, given that b(j) = 0.
-4, 3
Let c(j) be the third derivative of j**2 + 1/36*j**4 + 0*j + 0 + 1/126*j**5 + 1/21*j**3 + 1/1260*j**6. Factor c(s).
2*(s + 1)**2*(s + 3)/21
Let 2043*f**2 - 5*f**4 + f - 2063*f**2 - 25*f**3 - f = 0. What is f?
-4, -1, 0
Factor -58/15 - 56/15*m + 2/15*m**2.
2*(m - 29)*(m + 1)/15
Let w(u) = -u + 1. Let a = -63 + 64. Let c(n) = n**2 + 7*n - 6. Let d(j) = a*c(j) + 6*w(j). Factor d(h).
h*(h + 1)
Factor 2/9*w**2 - 7/9*w**4 + 0*w + 5/9*w**3 + 0.
-w**2*(w - 1)*(7*w + 2)/9
Let b(h) be the second derivative of h**6/90 - h**5/30 - h**4/3 - 7*h**3/9 - 5*h**2/6 + 4*h + 1. Factor b(k).
(k - 5)*(k + 1)**3/3
Let w(y) be the first derivative of -y**4/6 + 14*y**3/9 - 2*y**2 - 95. Find l, given that w(l) = 0.
0, 1, 6
Let k be 75/(-50)*4/18*78/(-13). Factor 6/11*f**k + 30/11 - 36/11*f.
6*(f - 5)*(f - 1)/11
Let a(w) be the first derivative of -5*w - 2*w**2 - 1/4*w**4 + 5 - 4/3*w**3. Let f(j) be the first derivative of a(j). Factor f(o).
-(o + 2)*(3*o + 2)
Let i = 3280 + -3118. Factor 24*z + 8/9 + i*z**2.
2*(27*z + 2)**2/9
Factor -34/5 + 1/5*q**4 - 63/5*q**2 - 83/5*q - 13/5*q**3.
(q - 17)*(q + 1)**2*(q + 2)/5
Let k(a) be the second derivative of 19/16*a**4 + 0 + 243/8*a**2 - 99/8*a**3 - 3/80*a**5 + 45*a. Let k(s) = 0. What is s?
1, 9
Let q = -2109 + 2111. Find y, given that 2/3*y**3 - 10/9*y**4 + 0 + 8/9*y + 8/3*y**q = 0.
-1, -2/5, 0, 2
Let b be ((-716)/(-10))/((54/30)/9). Suppose 1278 = 23*s + b. Suppose 12*a**5 - 100/3*a**3 + 48*a + 32/3 + s*a**2 - 24*a**4 = 0. Calculate a.
-1, -2/3, -1/3, 2
Let m = -58 + 60. Factor 643*i + m*i**2 - 643*i.
2*i**2
Solve -2/7*q**3 + 0 + 12/7*q**2 + 0*q = 0 for q.
0, 6
Let c(v) be the third derivative of -v**6/30 + 16*v**5/15 - 32*v**4/3 - 16*v**2 - 4. Determine h, given that c(h) = 0.
0, 8
Determine k so that 0 - 3/5*k**2 + 3/5*k = 0.
0, 1
Let o(w) be the second derivative of w**4/42 - 76*w**3/21 + 1444*w**2/7 - 3*w - 34. Factor o(d).
2*(d - 38)**2/7
Suppose 0 = 6*l - 0*l + 2*l. Let j(g) be the second derivative of l*g**2 - 1/6*g**4 + g**3 + 0 + g. What is v in j(v) = 0?
0, 3
Let t be 2/(-2)*(-45)/180. Let h = -7 - -9. Factor -3/4 + 3/4*c**h - 1/4*c + t*c**3.
(c - 1)*(c + 1)*(c + 3)/4
Find q such that 59*q**4 + 56*q**4 + 65*q**2 + 187*q - 217*q - 2 + 20*q**5 + 190*q**3 + 2 = 0.
-3, -2, -1, 0, 1/4
Let c(d) be the third derivative of -d**6/180 - 7*d**5/90 + 2*d**4/9 + 38*d**2 + 2*d. Find z, given that c(z) = 0.
-8, 0, 1
Let t = -163 + 491/3. Let m be 5/(-2)*8/(-30). Suppose 0 + m*q**3 - 4/3*q - t*q**2 = 0. Calculate q.
-1, 0, 2
Suppose 682 = -27*c + 28*c. Let j = c + -6128/9. Let -2/3*o**3 + 2/9 - 2/9*o - j*o**2 = 0. Calculate o.
-1, 1/3
Let s(w) be the second derivative of 0 + 5/12*w**4 + 0*w**2 + 23*w + 5/3*w**3. Let s(k) = 0. Calculate k.
-2, 0
Let t(j) be the first derivative of 9*j**5/5 + 15*j**4 + 48*j**3 + 72*j**2 + 48*j + 12. Factor t(v).
3*(v + 2)**3*(3*v + 2)
Factor -11/6*a + 2 - 1/6*a**2.
-(a - 1)*(a + 12)/6
Let f be (-2 + -3 - 8)*-1. Suppose f = -o + 4*n, -4*o + 8 = 2*n - 3*n. Factor 1/3*r**o + 0*r**2 + 0*r + 0.
r**3/3
Suppose 2 = 2*h + 2*y, -3*y - 18 = 33*h - 37*h. Suppose 4/7*w - 1/7*w**4 + 4/7 - 3/7*w**2 - 4/7*w**h = 0. Calculate w.
-2, -1, 1
Determine w, given that -7 - 130/3*w**2 - 85/3*w - 1/3*w**5 - 25/3*w**4 - 30*w**3 = 0.
-21, -1
Factor -8*s**4 + 616*s + 4*s**4 + 16*s**2 + 8*s**3 - 648*s.
-4*s*(s - 2)**2*(s + 2)
Let j(i) be the third derivative of -1/9*i**3 - 1/27*i**4 - 1/270*i**5 + 0*i + 4*i**2 + 0. Factor j(v).
-2*(v + 1)*(v + 3)/9
Find f, given that -10/11*f + 2/11*f**3 - 4/11*f**2 + 12/11 = 0.
-2, 1, 3
Let k = 16 + -23. Let v be ((0 - 4)/1)/k. Factor 0 - v*g**3 - 6/7*g - 2*g**2.
-2*g*(g + 3)*(2*g + 1)/7
Let i = 35 + -9. Let v be (4 + (-3)/1)*i. Factor 6*h**4 - 51*h**3 - 8*h + 10*h**3 - 36*h**2 - v*h**4 - 7*h**3.
-4*h*(h + 1)**2*(5*h + 2)
Let c(i) = -i**4 + 2*i**2 - i - 1. Let l(y) = -3*y**4 - 5*y**3 + 6*y**2 + 2*y + 2. Let n(a) = 2*c(a) + l(a). Factor n(m).
-5*m**2*(m - 1)*(m + 2)
Let l(u) = -117*u + 471. Let f be l(4). Let h(p) be the second derivative of -1/18*p**f + 8*p + 1/36*p**4 + 0*p**2 + 0. Find k, given that h(k) = 0.
0, 1
Let y(a) be the third derivative of -a**6/165 + 43*a**5/330 + a**4/12 - 23*a**2 - 6. Factor y(m).
-2*m*(m - 11)*(4*m + 1)/11
Let j(o) = 15*o**2 + 18*o + 3. Let d(s) = -7*s**2 - 2*s**2 + 10*s**2 + 1 + 0. Let w(z) = 18*d(z) - j(z). Let w(u) = 0. What is u?
1, 5
Let s = 10 - 5. Let c(l) = -l**2 + 1. Let r(o) = -o**3 - 3*o**2 + 4. Let n(f) = s*r(f) - 20*c(f). What is v in n(v) = 0?
0, 1
Let t = -2/683 + 115435/2732. Let q = -42 + t. Factor -1/2*y**2 + q + 0*y**3 + 1/4*y**4 + 0*y.
(y - 1)**2*(y + 1)**2/4
Let q = -237372/43 - -5520. Let j = q - -177/172. Factor -3/4*m**2 + 0 + j*m**3 + 3/4*m**4 - 3/4*m.
3*m*(m - 1)*(m + 1)**2/4
Let w(m) be the first derivative of 15*m**6/2 + 33*m**5 + 115*m**4/2 + 50*m**3 + 45*m**2/2 + 5*m + 50. Factor w(y).
5*(y + 1)**3*(3*y + 1)**2
Let k(c) be the first derivative of -c**6/6 - 3*c**5/2 + 55*c**4/12 + 50*c**3 - 250*c**2 - 2*c - 19. Let l(w) be the first derivative of k(w). Solve l(p) = 0.
-5, 2
Factor -10/9*g + 0 - 4/3*g**2 - 2/9*g**3.
-2*g*(g + 1)*(g + 5)/9
Find y such that 2/9*y**2 - 70/9*y - 8 = 0.
-1, 36
Let j(r) be the second derivative of -r**6/75 + r**4/10 + 2*r**3/15 - 91*r. Find z, given that j(z) = 0.
-1, 0, 2
Let q(s) be the first derivative of 5*s**3/3 + 105*s**2 + 205*s - 14. Factor q(x).
5*(x + 1)*(x + 41)
Let x(d) be the second derivative of -1/16*d**6 + 5/2*d**2 + 0*d**3 + 6*d - 3/10*d**5 + 0 - 1/4*d**4. Let u(c) be the first derivative of x(c). Factor u(p).
-3*p*(p + 2)*(5*p + 2)/2
Let a be (-5 - (-3 + -2))/(1/(-1)). Let v(b) be the second derivative of -1/24*b**3 - 1/24*b**4 + 0*b**2 - 1/80*b**5 + 3*b + a. Factor v(k).
-k*(k + 1)**2/4
Let q(m) = -m**5 + 4*m**4 + 21*m**3 - 14*m**2. Let p(u) = -u**5 + 3*u**4 + 22*u**3 - 16*u**2. Let w(l) = -5*p(l) + 4*q(l). Find y, given that w(y) = 0.
-6, 0, 1, 4
Let u be 3/(-8)*(16/(-3) - -4). Factor u*b**2 + 0*b**4 + 0*b - 3/4*b**3 + 0 + 1/4*b**5.
b**2*(b - 1)**2*(b + 2)/4
Let q be (0 - 4/10)/((-16)/80). Factor 1/8*t - 1/8 - 1/8*t**3 + 1/8*t**q.
-(t - 1)**2*(t + 1)/8
Factor -37*n**2 - 54*n - 35*n + 12*n**2 + 15 + 19*n.
-5*(n + 3)*(5*n - 1)
Let k = 4543 + -4543. Factor -2/3*n + k - n**2 - 1/3*n**3.
-n*(n + 1)*(n + 2)/3
Suppose o + l - 3*l = 6, -4*o = 4*l. Determine i so that -4*i**o - 50 + 0*i**2 + 20*i + 2*i**2 = 0.
5
Suppose 10*p + 55*p = -7*p + 864. Suppose 3/2*y**3 - 21/2*y**2 + 24 + p*y = 0. Calculate y.
-1, 4
Let c(z) be the first derivative of 1/240*z**5 + 1 + 0*z**3 + 0*z + 3*z**2 + 0*z**4. Let a(u) be the second derivative of c(u). Factor a(l).
l**2/4
Let t(f) = -f**2 - 2*f + 57. Let g be t(0). Suppose -4*j = 5*k - 108, -2*k + g = k + 5*j. Factor 21/2*n**2 - k*n + 6.
3*(n - 2)*(7*n - 2)/2
Let m(g) be the third derivative of 0 - 2*g + 1/240*g**5 - 3*g**2 - 1/8*g**4 + 3/2*g**3. Factor m(j).
(j - 6)**2/4
Let c(s) be the second derivative of 5*s**4/12 - 2*s**3/3 - 2*s**2 - s. Let v(n) = 4*n**2 - 4*n - 4. Let f(o) = 5*c(o) - 6*v(o). Let f(p) = 0. What is p?
-2
Factor 12 - 52 + 49*l + 130*l**2 + 55*l + 19126*l**3 - 19140*l**3.
-2*(l - 10)*(l + 1)*(7*l - 2)
Let n = -8 - -5. Let h be (n/9)/(4/(-36)). Factor -l**3 + 2*l**5 + 5*l**3 + 8*l**4 + 2*l**3 + 4*l**2 + 4*l**h.
2*l**2*(l + 1)**2*(l + 2)
Let q(d) be the second derivative of 0*d**4 - 1/220*d**5 + 0 + 1/22*d**3 + 1/11*d**2 - 14*d. Find p, given that q(p) = 0.
-1, 2
Let o = 137 - 132. Suppose -2*b = 2*v - 2 - 0, -2 = -4*b - o*v. Factor -1/3*a**b + 2/3*a**2 + 0 - 1/3*a.
-a*(a - 1)**2/3
Let j(u) be the second derivative of -u**6/30 - u**5/20 + u**4/12 + u**3/6 - 297*u + 1. Suppose j(y) = 0. What is y?
-1, 0, 1
Factor 0 - 592/3*h**3 + 314*h**2 - 120*h - 32/3*h**4.
-2*h*(h + 20)*(4*h - 3)**2/3
Factor 5/4*w**2 - 45 + 25/4*w.
5*(w - 4)*(w + 9)/4
Let o = -3995/12 + 1333/4. Factor -o*u**2 - 4/3*u + 0.
-u*(u + 4)/3
Let s = 118 + -233. Let v = 691/6 + s. Let 0 - v*t**2 - 1/3*t = 0. Calculate t.
-2, 0
Let i(k) = 