
-1, 1, 2
Suppose 7*p = -2*p. Determine o, given that p - 2/3*o**3 - 1/3*o**2 - 1/3*o**4 + 0*o = 0.
-1, 0
Factor 0 - 2/3*q**5 - 2/3*q**2 + 2/3*q**3 + 2/3*q**4 + 0*q.
-2*q**2*(q - 1)**2*(q + 1)/3
Suppose 0 = -5*i - 2*u - 277, 2*i - u + 108 = u. Let x be ((-2)/(-5))/((-44)/i). Suppose 1/2*j**3 + x*j**5 + 0*j - j**4 + 0 + 0*j**2 = 0. What is j?
0, 1
Let j(i) be the first derivative of -i**6/4 + 9*i**4/8 + i**3 - 6. Factor j(d).
-3*d**2*(d - 2)*(d + 1)**2/2
Suppose 10 - 20 = -5*r. What is d in 0*d - 2/7*d**r + 0 - 2/7*d**3 = 0?
-1, 0
Let p(t) = -95*t**4 + 325*t**3 - 815*t**2 + 685*t - 275. Let i(l) = 8*l**4 - 27*l**3 + 68*l**2 - 57*l + 23. Let u(d) = -35*i(d) - 3*p(d). Factor u(o).
5*(o - 2)**2*(o - 1)**2
Let s(w) be the second derivative of 9/80*w**5 - 1/8*w**4 + 0 - 1/40*w**6 + 0*w**3 + 0*w**2 - 2*w. Factor s(q).
-3*q**2*(q - 2)*(q - 1)/4
Let q(x) be the third derivative of -1/120*x**6 + 0*x**3 + 0*x + 1/30*x**5 - 1/24*x**4 + 0 + x**2. Determine i so that q(i) = 0.
0, 1
Let c(p) be the first derivative of -p**6/30 + p**5/10 - p**4/12 + p - 3. Let j(v) be the first derivative of c(v). Factor j(m).
-m**2*(m - 1)**2
Let i(q) be the third derivative of q**5/140 - 2*q**3/7 + 5*q**2. Solve i(z) = 0 for z.
-2, 2
Let n = -2 - -5. Let a(i) = -i**3 + 3*i**2 + 3*i - 3. Let b be a(n). Solve b*f**2 + 6*f**3 - 4*f**3 + 2*f + 6*f + 2 - 2*f = 0 for f.
-1
Let f(s) be the second derivative of -s**7/70 - 4*s**6/25 - 27*s**5/50 - 4*s**4/5 - s**3/2 + 19*s. Let f(z) = 0. Calculate z.
-5, -1, 0
Let h(k) be the first derivative of k**4 - 8*k**2 + 21. Solve h(t) = 0.
-2, 0, 2
Let q = 2 - 2. Suppose -4*s + q*s = -20. Let 1/2*y**s - y**3 + y**2 - 1/2*y**4 + 1/2*y - 1/2 = 0. What is y?
-1, 1
Let r(w) be the third derivative of w**8/16800 + w**7/6300 + w**4/12 + 2*w**2. Let a(q) be the second derivative of r(q). Determine z so that a(z) = 0.
-1, 0
Let j(l) = -2*l. Let o be j(-1). Let b = 13 + -7. Factor 6 + k**o - b - 2*k.
k*(k - 2)
Suppose 4*o = o + 6. Solve 6*a + 3*a**3 - 3*a**o + 7*a**2 - a**3 - 4*a = 0 for a.
-1, 0
Factor -1 + 4*s - 11*s**2 - 6*s + 10*s**2.
-(s + 1)**2
Let f be (3 - 2)/1 + 7. Let l = f + -6. Factor l*r**2 - r**2 + 0*r**2 + r - 2.
(r - 1)*(r + 2)
Let g(j) be the third derivative of j**6/24 - j**5/12 - 25*j**4/24 - 5*j**3/2 - 2*j**2. Factor g(c).
5*(c - 3)*(c + 1)**2
Suppose 3*x - 4*x = 76. Let p = 230/3 + x. Let 5/3*y + p*y**2 - 2/3 - 5/3*y**3 = 0. What is y?
-1, 2/5, 1
Suppose -25 - 8 = 5*a + c, -c - 3 = 0. Let b = 10 + a. Solve -2/5*i + 0 + 4/5*i**3 - 2/5*i**5 + 0*i**2 + 0*i**b = 0 for i.
-1, 0, 1
Let b(s) = -3*s**2 - 6*s + 6. Let h(m) = -9*m + 7. Let x(r) = r**2 - 10*r + 7. Let n(y) = -3*h(y) + 2*x(y). Let q(z) = 5*b(z) + 6*n(z). Factor q(d).
-3*(d - 2)**2
Suppose 5*v - 10 = 0, -b + 4*v - 5 - 3 = 0. Let z(g) be the second derivative of g + b + 0*g**3 + 0*g**4 - 1/10*g**5 - 1/15*g**6 + 0*g**2. Factor z(q).
-2*q**3*(q + 1)
Let p = -27 + 31. Let c(b) be the third derivative of 2/105*b**6 + 1/105*b**5 + 0*b + 2*b**2 + 1/21*b**3 - 5/84*b**p + 0. Solve c(g) = 0 for g.
-1, 1/4, 1/2
Let n(z) = z - 6. Let v be n(5). Let g be v/2*(6 + -6). Find r, given that -2/9*r**2 + 0*r + g + 2/9*r**3 = 0.
0, 1
Suppose 0 = 5*k - 8 - 2. Let o(t) be the third derivative of 1/210*t**5 - 2/21*t**3 - t**k - 1/84*t**4 + 0 + 0*t. Factor o(i).
2*(i - 2)*(i + 1)/7
Determine r, given that 2/7*r**2 - 12/7 + 2/7*r = 0.
-3, 2
Factor 8/9*a**2 + 2/9*a**5 - 16/9*a + 0 - 10/9*a**4 + 4/3*a**3.
2*a*(a - 2)**3*(a + 1)/9
Let i(h) be the first derivative of h**6/240 - h**5/60 + h**4/48 - 3*h**2/2 - 1. Let l(j) be the second derivative of i(j). Factor l(t).
t*(t - 1)**2/2
Let a be (12/20)/(2/(-10)). Let b be (a/(-14))/((-84)/(-98)). Factor 1/2 + b*o - 1/4*o**2.
-(o - 2)*(o + 1)/4
Let i(w) be the second derivative of -w**6/150 - 3*w**5/100 - w**4/30 - w. Factor i(m).
-m**2*(m + 1)*(m + 2)/5
Let d(y) be the third derivative of -y**5/30 + y**3/3 - 6*y**2. Find l such that d(l) = 0.
-1, 1
Suppose 3*a + 3*m = 7*m, a - 4*m + 8 = 0. Let x(y) = -5*y - 2*y**2 + y**2 - a*y. Let v(h) = 2*h. Let t(j) = -11*v(j) - 2*x(j). Determine s so that t(s) = 0.
0, 2
Let a(p) be the first derivative of 0*p**2 - 2 + 0*p - 1/1440*p**6 + 0*p**5 + p**3 + 1/96*p**4. Let z(i) be the third derivative of a(i). Factor z(m).
-(m - 1)*(m + 1)/4
Suppose 3*c - 15 = -3. Let k be -1 + -3 + (9 - 2). Determine l so that -6*l**k + 2*l**5 + 34*l**4 - 4*l**2 - 34*l**c = 0.
-1, 0, 2
Suppose b - 7 - 13 = 0. Suppose -2*m**3 + 11 - b + 10 - m**2 - m + 3*m**3 = 0. What is m?
-1, 1
Factor -16*z**2 - 196*z - 25*z**2 - 40*z**2 - 4*z**3 + 25*z**2.
-4*z*(z + 7)**2
Suppose -2*u - 5*u**3 - 5*u**2 - u**4 - 9*u**3 + 10*u**3 = 0. What is u?
-2, -1, 0
Let k be (-42)/(-24) - (-2)/8. Suppose -k = o - 2*o. Factor -1/3 + 2*n - 3*n**o.
-(3*n - 1)**2/3
Let x(m) be the second derivative of m**4/12 + m**3/3 - 4*m**2 + 24*m - 2. Factor x(o).
(o - 2)*(o + 4)
Suppose -13*c + 8*c = 22*c. Let c*g - 2 + 1/2*g**2 = 0. What is g?
-2, 2
Suppose -10 = 2*o, -y - o = -0*o + 1. Determine k, given that -1/2*k - 1/4*k**2 - 5/4*k**y + 2*k**3 + 0 = 0.
-2/5, 0, 1
Let n(o) be the second derivative of -o**5/30 + o**4/18 - 8*o. Solve n(d) = 0 for d.
0, 1
Let n(u) be the second derivative of 3*u**5/40 + u**4/4 + u**3/4 + 28*u. Determine c, given that n(c) = 0.
-1, 0
Let g(y) be the second derivative of y**4/60 - y**3/15 + 14*y. Factor g(i).
i*(i - 2)/5
Let w(q) = q**3 + 6*q**2 + 2*q - 7. Let h be w(-5). Let c be (-27)/(-18)*h/6. Let -35*n + n**2 + n**c + 33*n = 0. What is n?
0, 1
Let j(t) = -t**3 - 19*t**2 + t + 24. Let i(f) = 2*f**3 + 29*f**2 - 2*f - 36. Let l(a) = -5*i(a) - 7*j(a). Factor l(k).
-3*(k - 1)*(k + 1)*(k + 4)
Find b, given that -40*b**2 - 15*b**3 - 35*b - 13 + 1 + 2 = 0.
-1, -2/3
Factor 0 + 4/19*n**2 + 0*n - 6/19*n**3 + 2/19*n**4.
2*n**2*(n - 2)*(n - 1)/19
Let g(t) = -t - 10. Let i be g(-13). Let s be (86/4 - i) + -2. Determine n so that -s*n**4 - 15*n**2 - 9/2*n - 1/2 - 23*n**3 - 9/2*n**5 = 0.
-1, -1/3
Let o(p) be the second derivative of -p**6/105 - p**5/70 + p**4/21 + 5*p. Factor o(m).
-2*m**2*(m - 1)*(m + 2)/7
Factor 3/8 - 3/8*q**2 - 3/4*q**3 + 3/4*q.
-3*(q - 1)*(q + 1)*(2*q + 1)/8
Let c(t) be the second derivative of t**5/110 - 2*t**4/33 + 4*t**3/33 + 9*t. What is p in c(p) = 0?
0, 2
Let p(i) = -36*i**2 + 2*i + 18. Let w(d) = d**3 - d**2 + d + 1. Let l(c) = p(c) - 10*w(c). Factor l(a).
-2*(a + 1)*(a + 2)*(5*a - 2)
Determine t so that -t**4 - 3*t**4 + 3089*t**5 - 3091*t**5 - 2*t**3 = 0.
-1, 0
Let c(x) = -x**4 + x**3 + 10*x**2 + 8*x - 9. Let v(t) = t**2 + t - 1. Suppose w = -2*f + 35, f + 3*w - 9 = 6. Let j(b) = f*v(b) - 2*c(b). Factor j(d).
2*d*(d - 1)**2*(d + 1)
Determine p, given that 14/3*p**3 - 10/3*p**2 - 4/3*p + 0 = 0.
-2/7, 0, 1
Let j = -2424 - -581761/240. Let h(g) be the third derivative of -1/96*g**4 + 0 - j*g**5 + 0*g**3 + 0*g - 2*g**2. Factor h(v).
-v*(v + 1)/4
Let v(q) = -44*q**4 + 33*q**3 - 9*q**2. Let n = 6 + -10. Let h(z) = -45*z**4 + 32*z**3 - 8*z**2. Let x(w) = n*v(w) + 5*h(w). Factor x(j).
-j**2*(7*j - 2)**2
Let l(v) = 7*v**4 + 7*v**3 - 7*v**2 + 3*v - 5. Let m(q) = 6*q**4 + 6*q**3 - 6*q**2 + 2*q - 4. Suppose 3*i + i + 20 = 0. Let k(j) = i*m(j) + 4*l(j). Factor k(p).
-2*p*(p - 1)*(p + 1)**2
Let r(o) be the first derivative of -2*o**3 + o**2 + 4*o - 6. Factor r(t).
-2*(t - 1)*(3*t + 2)
Suppose 0 = -4*h - 5*x + 4, 14 = -2*h + 2*x + 34. Find w, given that 0 + 8*w**3 + h*w**2 + 10/3*w**4 + 4/3*w = 0.
-1, -2/5, 0
Let i(l) be the second derivative of l**4/6 + 10*l**3/3 + 9*l**2 + 54*l. Factor i(o).
2*(o + 1)*(o + 9)
Determine h so that -2/5*h**5 + 4/5*h**2 - 6/5*h**4 + 6/5*h - 4/5*h**3 + 2/5 = 0.
-1, 1
Let n(y) be the first derivative of -y**6/2 + 6*y**5/5 + 3*y**4/4 - 2*y**3 + 44. Suppose n(o) = 0. Calculate o.
-1, 0, 1, 2
Let b(g) be the second derivative of -5*g**7/42 - g**6/6 + g**5/2 + 4*g. Let b(f) = 0. Calculate f.
-2, 0, 1
Factor 9/2*w**2 + 9/2*w**3 + 3/2*w**4 + 0 + 3/2*w.
3*w*(w + 1)**3/2
Let p be (-3)/15 - 208/(-40). Let w(h) be the second derivative of 0*h**p + 0 + 0*h**3 - 1/16*h**4 + 1/40*h**6 + h + 0*h**2. Factor w(g).
3*g**2*(g - 1)*(g + 1)/4
Let t = -2765/4 + 692. Factor 0 + 3/4*u**3 + 3/2*u**2 + t*u.
3*u*(u + 1)**2/4
Let r be (-20)/6*18/(-12). Suppose -3 - r = -4*q. Factor -3*d + 6*d + q*d**2 - 2 - d - 2*d**3.
-2*(d - 1)**2*(d + 1)
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