 - 1. Let d be p(3). Let m be -2*(d/7 - 0/(-3)). Determine q so that -4/7 + m*q**2 + 2/7*q = 0.
-2, 1
Let h(w) be the third derivative of -w**6/2160 + w**5/90 - w**4/12 - 14*w**3/3 - 43*w**2. Let m(p) be the first derivative of h(p). Factor m(a).
-(a - 6)*(a - 2)/6
Suppose 0 = w - v + 3, 0 = -w + 4*v - 6*v + 15. Suppose -3*i + 8*i = 0. Suppose 4/5*o**2 + 2/5*o**w + i + 2/5*o = 0. What is o?
-1, 0
Factor 4*u**5 - 12*u**3 - u**2 + 7*u**2 + 6*u**2 - 4*u**2.
4*u**2*(u - 1)**2*(u + 2)
Suppose -4*r = 4*w, -6*r + 5*w + 40 = -r. Solve n - 15*n**2 - 13*n + 5*n**r + 2*n = 0 for n.
-1, 0, 2
Let v(b) be the first derivative of 2*b**3/15 - 2*b**2 - 22*b/5 + 82. Factor v(n).
2*(n - 11)*(n + 1)/5
Let s = 1603 + -1600. Factor 0*a**4 + 0*a - 4/13*a**2 - 6/13*a**s + 2/13*a**5 + 0.
2*a**2*(a - 2)*(a + 1)**2/13
Let v(h) = h**2 - 76*h - 81. Let r(o) = 3*o**2 - 153*o - 163. Let q(z) = 4*r(z) - 7*v(z). Factor q(i).
5*(i - 17)*(i + 1)
Let -6/7*g**3 + 18/7 + 6/7*g - 18/7*g**2 = 0. Calculate g.
-3, -1, 1
Let j = -539/12 + 45. Let o(s) be the second derivative of -2*s + 2*s**2 + 0 + j*s**4 + 2/3*s**3. Factor o(l).
(l + 2)**2
Let z(s) be the first derivative of 2*s**5/25 + 2*s**4/5 - 2*s**3/5 - 14*s**2/5 - 16*s/5 - 43. Factor z(t).
2*(t - 2)*(t + 1)**2*(t + 4)/5
Let c(p) = 4*p**4 + 4*p**3 + 17*p**2 + 17*p + 9. Let l(b) = 15*b**4 + 17*b**3 + 68*b**2 + 68*b + 35. Let s(i) = 22*c(i) - 6*l(i). What is y in s(y) = 0?
-3, -2, -1
Let z(l) be the second derivative of l**6/90 + 2*l**5/15 - l**4/36 - 4*l**3/9 - 94*l - 1. Solve z(u) = 0 for u.
-8, -1, 0, 1
Let p = -28/23 + 820/69. Let r = -10 + p. Suppose -r*y**2 + 0*y - y**3 + 5/3*y**4 + 0 = 0. Calculate y.
-2/5, 0, 1
Let s(x) = x**3 + 9*x**2 - 8*x + 23. Let d = 172 - 182. Let w be s(d). Find a, given that -12/7 + 12/7*a**2 + 4/7*a**w - 4/7*a = 0.
-3, -1, 1
Determine n so that -13*n + 9*n**2 - 3*n**4 - 11*n + 24 - 12*n - 3*n**2 + 9*n**3 = 0.
-2, 1, 2
Let w(v) = 31*v**4 - 102*v**3 + 78*v**2 - 17*v + 7. Let x(p) = p**4 - p**3 - 2*p**2 - 3*p + 1. Let f(c) = -2*w(c) + 14*x(c). Suppose f(t) = 0. Calculate t.
-1/24, 0, 2
Let c be -2*(-21)/11 - (-2)/11. Factor -35*y - 9*y - 28*y + 307 + c*y**2 + 17.
4*(y - 9)**2
Let c(q) be the first derivative of q**4/9 + 412*q**3/9 + 21218*q**2/3 + 4370908*q/9 + 448. Find j, given that c(j) = 0.
-103
Let j(n) = -77*n**3 - 306*n**2 - 13*n. Let d(l) = -l**3 - 2*l**2 + l. Let q(a) = 3*d(a) - j(a). Factor q(t).
2*t*(t + 4)*(37*t + 2)
Let n(o) be the third derivative of o**5/330 - 7*o**4/44 - 3*o**2 + 18. Factor n(v).
2*v*(v - 21)/11
Let v(u) be the first derivative of -49*u**6/8 - 357*u**5/20 - 27*u**4/8 + 11*u**3 - 3*u**2 - 117. Determine s, given that v(s) = 0.
-2, -1, 0, 2/7
Suppose 0 = 2*t + r + 1, -3*t = -2*r - 2. Let q be t + 0 - (-12)/6. Determine v, given that 3/4*v**q - 3/4*v**4 + 0*v + 0*v**3 + 0 = 0.
-1, 0, 1
Let n(c) be the second derivative of -c**6/10 - 3*c**5/20 + 3*c**4/4 + 5*c**3/2 + 3*c**2 - 85*c. Solve n(h) = 0 for h.
-1, 2
Let f(a) be the third derivative of -a**7/285 - 3*a**6/380 + 2*a**5/95 + a**4/57 - 558*a**2. Suppose f(o) = 0. What is o?
-2, -2/7, 0, 1
Let d(h) be the first derivative of -h**5/10 - 13*h**4/8 - 23*h**3/3 - 3*h**2 + 36*h + 58. What is j in d(j) = 0?
-6, -2, 1
Let k = -639 - -641. Let w(q) be the third derivative of 0*q - 5*q**k - 1/6*q**4 - 1/60*q**6 + 0*q**3 + 0 - 1/10*q**5. Find a, given that w(a) = 0.
-2, -1, 0
Determine s, given that 4*s**4 - 10*s**3 + 51*s - 51*s + 42*s**3 - 72*s + 36*s**2 = 0.
-6, -3, 0, 1
Factor -4*r**2 + 108*r**2 + 4*r**4 + 64*r + 9*r**3 + 19*r**3 + 16*r**3.
4*r*(r + 1)*(r + 2)*(r + 8)
Suppose -178874 - c**2 + 178874 - 8*c = 0. Calculate c.
-8, 0
Suppose -8/11 + 8/11*u - 2/11*u**3 + 2/11*u**2 = 0. Calculate u.
-2, 1, 2
Let p(h) be the third derivative of h**7/735 + 13*h**6/420 + 2*h**5/35 - 3*h**2. Factor p(b).
2*b**2*(b + 1)*(b + 12)/7
Let i(v) be the second derivative of -v**6/60 - 3*v**5/10 - 3*v**4/8 + 11*v**3/6 + 51*v. Factor i(x).
-x*(x - 1)*(x + 2)*(x + 11)/2
Let p(y) = 11*y**4 - 64*y**3 - 156*y**2 + 11*y + 213. Let u(z) = -4*z**4 + 32*z**3 + 78*z**2 - 6*z - 106. Let b(x) = 4*p(x) + 10*u(x). Factor b(d).
4*(d - 1)*(d + 2)**2*(d + 13)
Let k(h) = h**2 + 7*h + 6. Let t be k(-5). Let p be ((2 + t)/(-2 + 0))/2. Factor n + p*n**3 + 3/2*n**2 + 0.
n*(n + 1)*(n + 2)/2
Let p(s) = -8*s**2 + 1480*s - 27380. Let i(o) = -3*o**2 + 592*o - 10952. Let b(r) = -12*i(r) + 5*p(r). Let b(z) = 0. What is z?
37
Solve 10/7*y**4 - 24/7*y**2 + 2/7*y**5 - 16/7*y**3 + 0 + 0*y = 0.
-6, -1, 0, 2
Suppose 4*c = -f - 20, -4*c = 5 + 15. Let m(a) = a**2 - 9*a + 3. Let w be m(f). What is d in -2*d**2 - 2/5*d**w - 16/5*d - 8/5 = 0?
-2, -1
Factor y**2 - 22*y - 12 + 12 + 20*y.
y*(y - 2)
Let w = -3302 + 3305. Factor 0 + 20/3*n**2 - 8/3*n + 4/3*n**4 - 16/3*n**w.
4*n*(n - 2)*(n - 1)**2/3
Let c = 3 + -149/50. Let v(m) be the second derivative of c*m**5 + 0*m**2 + 0 - 5*m + 0*m**3 + 1/15*m**4. Find k such that v(k) = 0.
-2, 0
Let q(x) be the third derivative of x**5/12 + 25*x**4/24 + 5*x**3 + 71*x**2. Find o, given that q(o) = 0.
-3, -2
Let c(p) be the second derivative of 4*p**7/63 - 2*p**6/3 + 51*p**5/40 - 55*p**4/72 + p**3/6 - 27*p - 2. Solve c(a) = 0.
0, 1/4, 1, 6
Let q(h) be the third derivative of h**8/20160 + h**7/2520 - h**5/60 + 11*h**2. Let g(x) be the third derivative of q(x). Find f such that g(f) = 0.
-2, 0
Let a be (1 + -1)/((-7)/7) - -2. Suppose a*d - 7*d = 4*y - 17, -14 = -5*y + d. Factor 2*v**y + 52/7*v**2 + 40/7*v - 16/7.
2*(v + 2)**2*(7*v - 2)/7
Let s(u) be the third derivative of 0*u**3 - 1/720*u**6 + 1/120*u**5 - 10*u**2 + 0*u - 1/72*u**4 + 0. Find x, given that s(x) = 0.
0, 1, 2
Factor -1/2*t**2 + 0 - 12*t.
-t*(t + 24)/2
Let t be (-5372)/(-23970) + (-6)/(-141). Factor 0 - 2/15*v**5 + t*v**4 - 4/15*v**2 + 0*v**3 + 2/15*v.
-2*v*(v - 1)**3*(v + 1)/15
Let x = 1/731 + 1455/5117. Let i(c) be the first derivative of x*c**3 + 2/7*c - 4/7*c**2 - 3. Factor i(v).
2*(v - 1)*(3*v - 1)/7
Suppose -3 = 224*g - 225*g. Let n(i) be the first derivative of 4 + i**3 - g*i - 3/4*i**4 + 3/2*i**2. Factor n(a).
-3*(a - 1)**2*(a + 1)
Let x(h) = 9*h**4 + 6*h**3 - 3*h + 3. Let w(o) = o**5 + 18*o**4 + 12*o**3 - 5*o + 5. Let c be (5/4)/((-10)/(-40)). Let n(i) = c*x(i) - 3*w(i). Factor n(a).
-3*a**3*(a + 1)*(a + 2)
Let j(r) be the second derivative of r**6/420 + r**5/105 - r**4/84 - 2*r**3/21 + 15*r**2/2 + 13*r. Let n(l) be the first derivative of j(l). Factor n(m).
2*(m - 1)*(m + 1)*(m + 2)/7
Let g = -1633/3 - -11455/21. Find q, given that -2/7*q**5 + g + 2/7*q**3 + 6/7*q**4 - 2*q**2 + 0*q = 0.
-1, 1, 2
Suppose 0 = 15*f + 4*f - 38. Let g be 2/((-15)/(-6) + 0). Determine l, given that 2/5*l**5 + 4/5*l**f - 2/5*l + 0*l**3 - g*l**4 + 0 = 0.
-1, 0, 1
Let g(m) be the second derivative of 0*m**6 + 0 - 31*m + 5/4*m**5 - 5/42*m**7 + 0*m**2 - 10/3*m**3 + 0*m**4. Solve g(w) = 0.
-2, -1, 0, 1, 2
Let 2*t - 6 + 6 + t + t**2 + 0*t = 0. Calculate t.
-3, 0
Let y(j) be the first derivative of -15*j**4 + 199*j**3/5 - 147*j**2/5 - 3*j/5 + 248. Factor y(f).
-3*(f - 1)**2*(100*f + 1)/5
Let n = 52 - 43. Let m be ((-3)/(-5))/(n/6). Factor 6/5*y**5 + 0 + 0*y**2 + 0*y + m*y**3 - 8/5*y**4.
2*y**3*(y - 1)*(3*y - 1)/5
Let o(h) = 5*h**4 - 17*h**3 - 36*h**2 + 20*h + 19. Let j(w) = 10*w**4 - 33*w**3 - 74*w**2 + 40*w + 36. Let b(t) = -3*j(t) + 7*o(t). Factor b(k).
5*(k - 5)*(k - 1)*(k + 1)**2
Let n be 5/(-5) + -2*1. Let a be (-2)/5*(-13 - n). What is x in 0*x**2 + 3*x**3 - 2*x**a + x**3 + 3*x**2 - 5*x**2 = 0?
0, 1
Let v be (-16)/6*(-6)/4. Factor -118 - 12*s + 118 + 4*s**v + 12*s**3 - 4*s**2.
4*s*(s - 1)*(s + 1)*(s + 3)
Let k(v) = 2*v**2 - 8*v + 10. Let o be k(4). Factor 4 - 10*a**2 - a**2 - o*a - 8*a**2 + 5*a**2.
-2*(a + 1)*(7*a - 2)
Solve -6*u**2 - 2752*u + 2*u**2 + 4424*u - 174724 = 0 for u.
209
Let u be 24/(4/2) - 1. Let v = 15 - u. What is x in -v*x**2 + 4 - 6*x + 2 + 4 - 6 = 0?
-2, 1/2
Let t = 313/3 - 6259/60. Let u(c) be the third derivative of -c**2 - t*c**5 + 0*c**3 + 0*c**4 - 1/80*c**6 - 1/420*c**7 + 0 + 0*c. Factor u(n).
-n**2*(n + 1)*(n + 2)/2
Suppose -6*i = 2*i. Suppose -36*w + 32*w + 12 = i. Solve -h**2 + 3/2*h**5 + 0 + 0*h - 3/2*h**w + h**4 = 0 for h.
-1, -2/3, 0, 1
Suppose 4*q - 4*s + 15 = 3, -q - 5*s = -27. Let f be 4/1 + 16/(-8). Determine k so that 7*k + 1 + 0*k**f - 6*k + k**q + k = 0.
-1
Let i(