, 2
Let y(a) be the second derivative of -a**5/110 + 3*a**4/22 - 8*a**3/33 - 69*a. Factor y(j).
-2*j*(j - 8)*(j - 1)/11
Suppose 0 = -5*z + 25 - 5. Suppose -h + 2*y - y - 1 = 0, h - z*y = -13. Factor 0*p**2 - h*p**2 + 5*p**3 - 2*p**3.
3*p**2*(p - 1)
Let g = 9829 + -39267/4. Solve -g + 7/2*w - 1/4*w**2 = 0 for w.
7
Let c = 7213/12 - 601. Let t(q) be the first derivative of 8 - c*q**3 + 1/4*q**2 + 0*q. Solve t(l) = 0 for l.
0, 2
Let s(j) be the first derivative of -j**4/16 + 7*j**3/12 + j**2 - 11. Factor s(w).
-w*(w - 8)*(w + 1)/4
Let w = 2715 - 2705. Let d(l) be the second derivative of -5/36*l**4 - 1/18*l**2 + w*l - 2/45*l**5 + 0 + 4/27*l**3 + 8/135*l**6. Find u, given that d(u) = 0.
-1, 1/4, 1
Let w(y) be the first derivative of y**5/90 - 17*y**4/108 + 10*y**3/27 + 3*y**2 - 20. Let j(l) be the second derivative of w(l). What is g in j(g) = 0?
2/3, 5
Let p(u) be the second derivative of -u**7/6 + 17*u**6/10 + 91*u**5/10 + 7*u**4 - 20*u**3/3 - u - 71. What is y in p(y) = 0?
-2, -1, 0, 2/7, 10
Let x = 14 + 4. Suppose -4*m - 6 = -x. Determine v, given that -v**3 + v - 2*v**2 + 2*v**m + 0*v = 0.
0, 1
Suppose -16*o = -17 - 15. Let i(r) be the first derivative of 1/22*r**4 + 0*r + 1/11*r**o - 5 - 4/33*r**3. Factor i(c).
2*c*(c - 1)**2/11
Let q(a) be the third derivative of -a**6/24 - 7*a**5/6 - 5*a**4 - 125*a**2. Factor q(b).
-5*b*(b + 2)*(b + 12)
Let s(p) = 18*p**3 + 13*p**2 - 761*p - 743. Let a(i) = 3*i**3 + 2*i**2 - 127*i - 124. Let f(z) = -13*a(z) + 2*s(z). Suppose f(c) = 0. What is c?
-6, -1, 7
Suppose 2/7*v**2 + 186/7 + 188/7*v = 0. Calculate v.
-93, -1
Let n = -3 + 11. Factor b**2 + 28*b - 4*b**4 + 6*b**2 + 21*b**2 + n*b**3 - 12*b.
-4*b*(b - 4)*(b + 1)**2
Let y be 12/(-3) - -12 - 2. Let o(d) = -3*d**3 + 14*d**2 - 23*d. Let g(l) = l + 1. Let b(p) = y*g(p) + o(p). Find m, given that b(m) = 0.
2/3, 1, 3
Let k = 1325 + -1310. Solve -245/4*n**4 + 5/2 - 15/4*n + k*n**5 - 125/4*n**2 + 315/4*n**3 = 0.
-1/4, 1/3, 1, 2
Let d(t) be the third derivative of -t**6/30 + t**2 + 4*t. Factor d(f).
-4*f**3
Let l(n) be the first derivative of n**8/448 - n**6/160 - 33*n**2/2 - 25. Let b(h) be the second derivative of l(h). Let b(a) = 0. Calculate a.
-1, 0, 1
Suppose 4*h - 91 = -7. Suppose -5*j - 3*r + h = 0, 2*j - 8 = r - 2*r. Determine b so that j*b**2 + 2 - b + 1 - 5*b = 0.
1
Let r = -47 + 52. Factor -499*b**4 - 4*b**r - 3 + 3 + 503*b**4.
-4*b**4*(b - 1)
Suppose 20*p + 21*p = 123. Let y(k) be the second derivative of 3*k + k**2 + 0 - 1/20*k**5 + 1/6*k**p - 1/6*k**4. Factor y(l).
-(l - 1)*(l + 1)*(l + 2)
Let v(y) be the first derivative of 1/120*y**5 - 12 + 1/96*y**6 + 0*y**4 + 5/2*y**2 + 0*y + 0*y**3. Let i(w) be the second derivative of v(w). Factor i(x).
x**2*(5*x + 2)/4
Let q(z) be the third derivative of z**8/131040 + z**7/16380 + z**6/4680 + 2*z**5/15 - 2*z**2. Let i(l) be the third derivative of q(l). Solve i(k) = 0 for k.
-1
Let v = -85 + 95. Let -14*y**2 - 16 - 11*y + v*y**2 + 31*y = 0. Calculate y.
1, 4
Let b(j) be the second derivative of j**5/110 - j**4/11 + 5*j**3/33 + 84*j. Factor b(t).
2*t*(t - 5)*(t - 1)/11
Suppose -2*k = 5*o + 92 + 460, 3*k - 327 = 3*o. Let a = o - -331/3. Determine b, given that a*b**3 - 1/3*b**5 + 0 + 1/3*b**2 + 0*b - 1/3*b**4 = 0.
-1, 0, 1
Let b(d) = d**3 - 13*d**2 + 17*d - 17. Let x(y) = -y**2 - y - 4. Let n(u) = -3*b(u) + 6*x(u). Factor n(h).
-3*(h - 9)*(h - 1)**2
Suppose -36*v = -37*v + 4. Let o(h) be the second derivative of h + 0*h**2 + 1/2*h**3 - 1/4*h**v + 0. Factor o(g).
-3*g*(g - 1)
Factor 176/3*w - 2/3*w**3 + 38/3*w**2 + 184/3.
-2*(w - 23)*(w + 2)**2/3
Let s(q) be the second derivative of -q**6/210 + q**5/28 - 3*q**4/28 + q**3/6 - q**2/7 - 30*q - 2. Factor s(v).
-(v - 2)*(v - 1)**3/7
Let a(f) = f + 10. Let k be a(8). Suppose -k + 28 = 5*q. Solve 0*m + 0 - 3/2*m**q - 9/2*m**3 - 3/2*m**5 - 9/2*m**4 = 0 for m.
-1, 0
Let k(j) = j**4 + 11*j**3 - 40*j**2 + 19*j. Let z(g) = -g**4 - 13*g**3 + 39*g**2 - 19*g. Let a(r) = 2*k(r) + 3*z(r). Let a(t) = 0. Calculate t.
-19, 0, 1
Let z(c) be the third derivative of c**8/1512 - c**7/315 + c**6/180 - c**5/270 - c**2. Suppose z(o) = 0. Calculate o.
0, 1
Let w(d) be the third derivative of 1/90*d**5 + 0 - 1/360*d**6 - 1/72*d**4 - 7*d**2 + 0*d**3 + 0*d. What is p in w(p) = 0?
0, 1
Let c = 9142/5 - 63859/35. Factor -c - 72/7*r - 48/7*r**2.
-3*(4*r + 3)**2/7
Let o be (16/(-208))/((-1)/4). Let u(f) = -f**3 + 18*f**2 - 16*f - 17. Let p be u(17). Factor o + p*t**2 - 6/13*t + 2/13*t**3.
2*(t - 1)**2*(t + 2)/13
Let m(b) = 107*b**3 - 145*b**2 - 359*b - 81. Let k(v) = 18*v**3 - 24*v**2 - 60*v - 14. Let c(f) = 26*k(f) - 4*m(f). Let c(h) = 0. Calculate h.
-1, -2/5, 5/2
Let u(q) be the second derivative of 1/2*q**2 + 1/5*q**5 + 0 + 5/8*q**4 + q + 1/2*q**3. Let t(c) be the first derivative of u(c). Factor t(w).
3*(w + 1)*(4*w + 1)
Let s(m) = m - 10. Let z be s(10). Suppose 4*w = -3*d - 10, -w - 4 = -z*w. Determine x, given that 0*x**2 - x**4 + x**2 - 1 + x**d = 0.
-1, 1
Let h(b) = -6*b**2 - 10*b - 4. Let s(c) be the first derivative of -13*c**3/3 - 21*c**2/2 - 8*c + 13. Let m(g) = -11*h(g) + 6*s(g). Factor m(a).
-4*(a + 1)*(3*a + 1)
Let z be (-63)/28 - 145/(-58). Factor z*d**4 + 3/4*d + 0 - 5/4*d**2 + 1/4*d**3.
d*(d - 1)**2*(d + 3)/4
Factor -2/7*q**2 + 24/7 + 2/7*q.
-2*(q - 4)*(q + 3)/7
Let l(g) be the second derivative of g**6/30 - 3*g**5/20 - g**4/12 + g**3/2 - 85*g. Solve l(r) = 0.
-1, 0, 1, 3
Factor 2/5*z**3 + 0 + 266/5*z**2 + 0*z.
2*z**2*(z + 133)/5
Let l(c) = 155*c**4 - 1715*c**3 + 3875*c**2 + 1525*c + 50. Let a(u) = 13*u**4 - 143*u**3 + 323*u**2 + 127*u + 4. Let i(s) = -25*a(s) + 2*l(s). Factor i(h).
-5*h*(h - 5)**2*(3*h + 1)
Let q be -3*(0 - (0 - (-16)/12)). Solve 12*g + 21*g + 24*g**3 - 4*g**q - 30*g - 36*g**2 + 13*g = 0 for g.
0, 1, 4
Solve -2*h**4 - 1/3*h**5 + 0 - 4*h**3 + 0*h - 8/3*h**2 = 0 for h.
-2, 0
Suppose 0 = -5*u - 5, -2*t - u = 4 - 11. Let g(k) be the second derivative of 0*k**2 + k + 0 + 1/20*k**5 - 1/6*k**3 + 0*k**t. Solve g(i) = 0.
-1, 0, 1
Let q(p) = -p**4 - p**3 - p**2 + p + 1. Suppose -3*k + 90 = -9*k. Let w = k + 17. Let h(z) = -3*z**4 + z**2 - 2*z - 2. Let u(o) = w*h(o) - 4*q(o). Factor u(b).
-2*(b - 2)**2*(b + 1)**2
Let n(r) be the second derivative of r**5/14 - 46*r**4/21 + 12*r**3/7 - 114*r. Determine a so that n(a) = 0.
0, 2/5, 18
Let p(x) be the second derivative of -21*x**5/40 - 19*x**4/48 + 7*x**3/8 + 5*x**2/4 + 12*x - 11. Solve p(n) = 0.
-2/3, -1/2, 5/7
Factor -1/3*h**2 - 100/3 - 20/3*h.
-(h + 10)**2/3
Let d be (-1)/(-10) - (-279)/810. Let b(u) be the second derivative of -2*u**4 + 109/30*u**5 + 2*u - 14/5*u**6 + 0 + 0*u**2 + d*u**3 + 7/9*u**7. Factor b(k).
2*k*(k - 1)**2*(7*k - 2)**2/3
Let q be 5/(-20) + (-1970)/(-8). Let w be q/66 + -1 + -2. What is a in -18/11*a**4 + 0 + 12/11*a**3 + w*a**5 - 2/11*a**2 + 0*a = 0?
0, 1/4, 1
Factor -5408*v - 2/3*v**3 - 104*v**2 - 281216/3.
-2*(v + 52)**3/3
Let k(s) = 7*s**2 + 16*s + 13. Let v be k(-1). Let l(t) be the second derivative of -7/6*t**3 + 10*t - 3/20*t**5 - 2/3*t**v - t**2 + 0. Factor l(y).
-(y + 1)**2*(3*y + 2)
Let m(g) = 3*g**2 + g - 6. Let h(j) be the first derivative of 13*j**3/3 + 5*j**2/2 - 24*j - 9. Let f(i) = -2*h(i) + 9*m(i). Factor f(o).
(o - 3)*(o + 2)
What is k in -34/25*k**3 + 4/25*k**2 + 0*k + 0 + 6/5*k**4 = 0?
0, 2/15, 1
Let g(b) be the third derivative of b**8/1680 - b**7/8400 - b**6/1200 + b**5/10 - 13*b**2. Let m(k) be the third derivative of g(k). Let m(j) = 0. Calculate j.
-1/5, 1/4
Let x = -8 - -10. Determine a so that -5*a**4 + 4*a**4 - x*a + 116*a**3 - 114*a**3 + 1 = 0.
-1, 1
Let o(d) = -d**2 + 42*d - 430. Let x be o(24). Factor 0 - 8/5*a**x + 4/5*a + 4/5*a**3.
4*a*(a - 1)**2/5
Suppose f - 4 = -f. Let z be 3/9 + f/6. Factor -z*g**2 - 2/3*g**4 - 4/3*g**3 + 0 + 0*g.
-2*g**2*(g + 1)**2/3
Determine t, given that 0 + 5/2*t**2 + 25/4*t + 1/4*t**3 = 0.
-5, 0
Let s(y) be the second derivative of -y**7/189 - y**6/27 - y**5/45 + 7*y**4/27 + y**3/9 - y**2 - 712*y. Suppose s(w) = 0. What is w?
-3, -1, 1
Let c(j) be the third derivative of -j**5/90 - j**4/4 - 20*j**3/9 - 176*j**2. Suppose c(s) = 0. What is s?
-5, -4
Let p = 70 + -75. Let y(q) = -q**2 - 4*q + 7. Let b be y(p). Factor 5/3*f**b - 7/3*f + 2/3.
(f - 1)*(5*f - 2)/3
Let m = 590/21 + -164/7. Let v(n) be the second derivative of 49/24*n**4 + 5*n 