. Let i be 2/(2/(7/((-252)/(-9)))). Determine s so that i - z*s + 1/4*s**2 = 0.
1
Suppose 0 = 11*m + 1814 - 1847. Suppose 3/2 - 3/8*i**4 + 3*i - 15/8*i**m + 3/8*i**2 + 3/8*i**5 = 0. What is i?
-1, 2
Find z such that 5*z**5 - 30*z**2 - 45*z + 27*z**3 + 18*z**3 + 30*z**4 + 14*z**3 - 19*z**3 = 0.
-3, -1, 0, 1
Let d be (10 - 5)*6/10. Suppose 3*g - 9 = -d. Suppose 8*a**2 + a**2 - a**2 - 8 + 8*a - g*a**2 = 0. Calculate a.
-2, 2/3
Let g(s) be the second derivative of 0 + 0*s**5 + 0*s**2 + 0*s**3 + 11*s - 1/30*s**6 + 0*s**4. Factor g(u).
-u**4
Let q(a) be the third derivative of -a**8/448 + a**7/140 + a**6/20 - 9*a**5/40 + 9*a**4/32 - 441*a**2. Suppose q(l) = 0. Calculate l.
-3, 0, 1, 3
Let p = -14711/2 - -7609. Factor p + 3/2*j**2 - 39*j.
3*(j - 13)**2/2
Let u be -3*(66/(-9) + 2). Suppose 8*p - u = -0*p. Suppose 2/3*a + 1/3*a**p + 0 = 0. Calculate a.
-2, 0
Suppose 0 = -3*w + 3*g + 12, -g + 6 = -2*w - 6*g. Suppose -w*n + 6 = m + 4*m, 0 = 5*n + 10. Suppose -3/4*t**m + 3/4*t**3 - 3/4*t + 3/4 = 0. What is t?
-1, 1
Let f(d) be the third derivative of d**7/315 - d**6/180 - 2*d**5/45 + d**4/9 - 17*d**2. Find c, given that f(c) = 0.
-2, 0, 1, 2
Suppose 2*u + 1 = -4*c + 89, u - c - 32 = 0. Determine m so that 2*m**5 + 41*m**2 - 5*m**3 + 3*m**5 - 5*m**4 - u*m**2 = 0.
-1, 0, 1
Factor 24 - 46 - d**2 + 5*d + 22.
-d*(d - 5)
Let h(f) be the third derivative of f**6/60 - 149*f**5/90 + 119*f**4/18 + 32*f**3/3 - 4*f**2 + 53*f. Factor h(t).
2*(t - 48)*(t - 2)*(3*t + 1)/3
Let i be (8/6)/((-1)/(-39)). Factor 5*h**2 + i + 204*h - 174*h - 7.
5*(h + 3)**2
Determine j so that -6/5*j + 4/3*j**3 - 4/3*j**2 + 2/15*j**4 - 2/15*j**5 + 6/5 = 0.
-3, -1, 1, 3
Suppose -5*f = -3*q + 37, -3*f - 2 - 21 = -2*q. Let x be 7/4 - 6/q. Let 0*s + x - 1/4*s**2 = 0. What is s?
-1, 1
Let v(d) = -51*d**3 + 902*d**2 - 3190*d - 1541. Let h(b) = 280*b**3 - 4964*b**2 + 17544*b + 8476. Let i(l) = 5*h(l) + 28*v(l). What is f in i(f) = 0?
-3/7, 8
Let n(y) be the second derivative of -1/14*y**7 + 3/10*y**6 + 0 - 3/2*y**2 + 3/2*y**3 - 1/2*y**4 + 2*y - 3/10*y**5. Factor n(d).
-3*(d - 1)**4*(d + 1)
Let o(l) be the second derivative of -2*l**4/33 + 73*l**3/33 + 57*l**2/11 - 33*l. Solve o(x) = 0.
-3/4, 19
Let c(q) be the first derivative of 6*q**3 - 22*q**2 + 16*q + 130. Factor c(a).
2*(a - 2)*(9*a - 4)
Suppose 0 = n - 7 - 7. Let 80*b**3 + 8*b**4 + 13*b**4 - 30*b - 85*b**2 + n*b**4 = 0. What is b?
-3, -2/7, 0, 1
Let z(r) be the second derivative of -r**8/15680 + r**6/560 - r**5/140 - 7*r**4/12 + 6*r. Let u(b) be the third derivative of z(b). What is c in u(c) = 0?
-2, 1
Let s(o) be the third derivative of -5/36*o**4 - 27*o**2 + 0 + 0*o - 1/36*o**5 + 0*o**3. Factor s(b).
-5*b*(b + 2)/3
Let j(f) be the second derivative of f**7/21 + f**6/45 - 11*f**5/30 - f**4/2 + 4*f**3/9 + 4*f**2/3 + 77*f. Determine x so that j(x) = 0.
-1, 2/3, 2
Let p(v) = -14*v**3 - 26*v**2 - 20*v + 8. Let m(c) = -5*c**3 - 9*c**2 - 7*c + 3. Let o(g) = 8*m(g) - 3*p(g). Factor o(h).
2*h*(h + 1)*(h + 2)
Let l be (8/(-60))/((-8)/30). Let y(c) be the first derivative of 7 - 2/3*c**3 + l*c**4 - c**2 + 2*c. Factor y(s).
2*(s - 1)**2*(s + 1)
Suppose 258 - 290 = -8*c. Let h(g) be the third derivative of 0 + 5*g**2 + 0*g - 1/200*g**6 + 1/15*g**3 - 7/300*g**5 + 1/40*g**c + 1/210*g**7. Factor h(p).
(p - 1)**2*(p + 1)*(5*p + 2)/5
Suppose 111*z = 103*z + 24. Find r such that 0 - 6/7*r**2 + 0*r + 4/7*r**z = 0.
0, 3/2
Let s = -11117 + 11119. Determine f, given that -2/9*f**5 - 4/9 - 32/9*f**s - 4/3*f**4 - 2*f - 28/9*f**3 = 0.
-2, -1
Let t(c) be the third derivative of 0*c**3 + 0 - 1/150*c**5 + 1/200*c**6 - 1/1050*c**7 + 0*c**4 + 0*c - 6*c**2. Factor t(y).
-y**2*(y - 2)*(y - 1)/5
Suppose 2*t + i - 153 = 88, t - 118 = 2*i. Let s be 2/15 - (-344)/t. Factor -4*a**2 - 8*a + 2*a - a**5 - 6*a**s - 6*a - 4*a**4 + 11*a.
-a*(a + 1)**4
Let b(z) be the first derivative of z**6/15 - 116*z**5/25 + 419*z**4/5 + 352*z**3/15 - 2639*z**2/5 + 3364*z/5 + 373. Solve b(q) = 0.
-2, 1, 29
Factor 0 - 119/4*h - 1/4*h**2.
-h*(h + 119)/4
Let t = 5 + -7. Let v = t - -5. Factor -u**3 - u**3 - 2 + 3 + u**v - u**2 + u.
-(u - 1)*(u + 1)**2
Let v(y) be the second derivative of -y**6/10 + 3*y**5/10 - 72*y. Factor v(x).
-3*x**3*(x - 2)
Let q(c) be the second derivative of c**8/2240 - c**6/80 + c**5/20 + c**4 - 17*c. Let f(x) be the third derivative of q(x). Let f(r) = 0. What is r?
-2, 1
Solve -t**2 + 5 - 7 - 2 + 9*t - 4 = 0.
1, 8
Let g(u) be the first derivative of u**4/28 + 23*u**3/21 + 43*u**2/14 + 3*u + 23. Factor g(t).
(t + 1)**2*(t + 21)/7
Solve 5 + 5*u**3 + 55 + 39*u + 35*u**2 + 11*u + 30*u = 0 for u.
-3, -2
Let g = -209/49 - -872/147. Suppose g*y + 1/3*y**2 - 2 = 0. Calculate y.
-6, 1
Let o(y) be the second derivative of 20/9*y**6 - 40/63*y**7 + 16*y + 0 + 25/18*y**4 - 11/4*y**5 - 5/18*y**3 + 0*y**2. Determine g, given that o(g) = 0.
0, 1/4, 1
Let y(o) be the second derivative of -o**8/420 - o**7/105 + o**6/30 - 4*o**3/3 + 23*o. Let k(d) be the second derivative of y(d). Factor k(g).
-4*g**2*(g - 1)*(g + 3)
Let w(t) be the second derivative of t**8/1792 - t**7/1008 - 7*t**6/576 - t**5/48 - t**4/6 + 13*t. Let g(z) be the third derivative of w(z). Factor g(p).
5*(p - 2)*(p + 1)*(3*p + 1)/4
Let 5*t + 10*t + 13*t + 24*t**2 - 12 - 32*t**2 = 0. Calculate t.
1/2, 3
Let s(w) be the second derivative of w**5/60 - w**4/4 - 5*w**3/9 + 130*w. Find y such that s(y) = 0.
-1, 0, 10
Let k(w) be the third derivative of -1/120*w**5 - 1/48*w**4 + 1/6*w**3 + w**2 + 0 + 0*w. Let k(t) = 0. What is t?
-2, 1
Factor -13/5*b - 4*b**4 + 9/5*b**5 + 2/5 + 4/5*b**3 + 18/5*b**2.
(b - 1)**3*(b + 1)*(9*b - 2)/5
Let m(h) be the third derivative of -7*h**2 + 0*h**4 + 1/300*h**5 + 0 - 1/30*h**3 + 0*h. Factor m(g).
(g - 1)*(g + 1)/5
Let i(p) be the third derivative of 1/21*p**5 - 14*p**2 + 2/21*p**3 - 1/84*p**6 + 3/28*p**4 + 0 - 1/294*p**8 - 4/245*p**7 + 0*p. Suppose i(y) = 0. Calculate y.
-2, -1, -1/2, 1
Solve 8/3 - 2/9*b - 2/9*b**2 = 0.
-4, 3
Let a(i) = 5. Let v(m) = -m + 1. Let n(x) = -a(x) + 3*v(x). Let b be n(-1). Factor -3*d**2 - 7 - d + 10*d + b.
-3*(d - 2)*(d - 1)
Suppose -j + 0 = 2*p + 1, -3*j - 15 = 0. Suppose -y + 3 = 3*v + p*y, 5*v + y = 17. Let -5*r**4 - 10*r**3 - v*r + 15 - 10 + 14*r = 0. What is r?
-1, 1
Suppose o - 4*o = -3*x + 15, x = -3*o + 5. Determine z so that 16*z**2 + 16*z + o*z**4 + z**3 + 3*z**5 + 2*z**3 - 4*z**4 - 19*z**3 = 0.
-2, -2/3, 0, 2
Let d be (0 + (-6)/21)/((-12)/21). Let m(p) be the first derivative of 0*p - 2*p**3 + 7 + 0*p**2 + d*p**6 + 6/5*p**5 - 3/4*p**4. Suppose m(r) = 0. What is r?
-2, -1, 0, 1
Let -12*j**2 + 293*j + 905*j - 4*j**2 + 4*j**2 - 400 + 18*j**2 = 0. What is j?
-200, 1/3
Let m(b) = -48*b**2 - 68*b + 24. Let f(k) = 19*k**2 + 27*k - 10. Let u(x) = 12*f(x) + 5*m(x). Factor u(j).
-4*j*(3*j + 4)
Factor -2*d**3 + 3 - 66*d**5 - 6*d**4 - 2*d**3 + 64*d**5 - 3.
-2*d**3*(d + 1)*(d + 2)
Let w(c) be the first derivative of -c**7/126 - c**6/90 + c**5/30 - 24*c - 1. Let s(h) be the first derivative of w(h). Factor s(f).
-f**3*(f - 1)*(f + 2)/3
Let p(y) = y - 19. Let k be p(-18). Let z be -4 + 1 - 4/36*k. Determine l so that 0 + 8/3*l**4 + z*l**5 + 2*l**3 + 4/9*l**2 + 0*l = 0.
-1, -2/5, 0
Solve 0 - 12/7*b**2 + 8/7*b**3 + 0*b - 1/7*b**5 + 5/7*b**4 = 0 for b.
-2, 0, 1, 6
Let w(u) be the third derivative of u**5/60 - 5*u**4/3 + 200*u**3/3 - 78*u**2 + 2*u. Factor w(j).
(j - 20)**2
Let u(f) = -765*f - 3056. Let w be u(-4). Suppose w*y**4 + 0 - 120/7*y**3 - 24/7*y + 116/7*y**2 = 0. What is y?
0, 2/7, 1, 3
Let -16/5 + 6*v**2 + 14/5*v**3 - 108/5*v = 0. Calculate v.
-4, -1/7, 2
Let 21*m**4 + 362 + 50*m**2 + 153*m**4 - 2*m**5 - 440*m**2 - 146 + 204*m - 195*m**3 - 7*m**5 = 0. Calculate m.
-1, -2/3, 1, 2, 18
Find n such that 9/5*n - 1/5*n**2 + 22/5 = 0.
-2, 11
Let i(m) = m**5 - m**3 - m - 1. Let w = -79 + 78. Let d(b) = 5*b**5 - b**4 - 6*b**3 - 4*b - 4. Let s(x) = w*d(x) + 4*i(x). Factor s(n).
-n**3*(n - 2)*(n + 1)
Let q = 651 + -39059/60. Let t(l) be the third derivative of -q*l**6 + 1/12*l**4 - 2/15*l**5 + 10*l**2 + 0*l**3 + 0*l + 4/105*l**7 + 0. Factor t(s).
2*s*(s - 1)*(s + 1)*(4*s - 1)
Let z be (-10)/(4 + 1)*2/(-4). Let g be (20/15 - z)*12/7. Factor -g*f - 2/7*f**2 + 0 + 2/7*f**3.
2*f*(f - 2)*(f + 1)/7
Determine u, given that 1258 - 2497 - 5*u**2 + 5*u + 1389 = 0.
-5, 6
Let i = 956 + -95