1 - 1)/((-1)/(-2 - -1)). Suppose 4/9*d - 10/9*d**2 + j = 0. What is d?
0, 2/5
Let k(f) be the second derivative of -f**4/60 + f**3/15 - f**2/10 - 2*f. Factor k(n).
-(n - 1)**2/5
Let m(g) = g**3 - 3*g**2 + 4*g - 4. Let a be m(3). Suppose -6*b = -4 - a. Determine c so that -4/5 - b*c**2 + 14/5*c = 0.
2/5, 1
Let k(a) = -6*a**4 - 21*a**3 - 33*a**2 - 18*a. Let f(s) = -5*s**4 - 20*s**3 - 33*s**2 - 18*s. Let b(q) = -3*f(q) + 2*k(q). Factor b(d).
3*d*(d + 1)*(d + 2)*(d + 3)
Let y = 149 - 103. Let x be y/14 - (-4)/(-14). Factor 2 - x*r**2 + 0 - 2 - 2*r.
-r*(3*r + 2)
Let v be 4/2 - (-1 + 1). Let s(g) be the third derivative of 0*g - 1/240*g**5 + 1/96*g**4 + v*g**2 + 1/12*g**3 + 0. Find w, given that s(w) = 0.
-1, 2
Let d be ((-14)/(-3))/((-4)/6). Let i(m) = -m - 4. Let k be i(d). Let a**5 + 2*a**2 + 5*a**4 + k*a**3 + 2*a**2 - 2*a**4 - 3*a**2 = 0. What is a?
-1, 0
Let k(h) be the second derivative of 0 + 1/9*h**2 + 5/18*h**4 + 2*h - 13/90*h**5 + 4/135*h**6 - 7/27*h**3. Find i, given that k(i) = 0.
1/4, 1
Let a(t) be the second derivative of -t**4/30 + t**3/15 + 6*t**2/5 + 16*t. Suppose a(q) = 0. What is q?
-2, 3
Let o = 177/4 + -44. Factor 0 + 1/4*u**2 + o*u**3 + 0*u.
u**2*(u + 1)/4
Let y(x) be the second derivative of -x**6/480 - x**5/80 - x**4/32 - x**3/24 - x**2/2 + 3*x. Let h(a) be the first derivative of y(a). Factor h(m).
-(m + 1)**3/4
Suppose -7 = -5*b + 3. Suppose 0 = b*s - 3*s + 4. Factor -l**2 - l**5 + l**3 + l**s + 4*l**3 - 4*l**3.
-l**2*(l - 1)**2*(l + 1)
Let a be -2 - 1 - (1/(-1) + -7). Let l(u) be the second derivative of 1/50*u**a - 1/15*u**3 + 0 + 0*u**2 + 0*u**4 + 3*u. Factor l(n).
2*n*(n - 1)*(n + 1)/5
Let g(b) be the second derivative of 1/240*b**5 - 1/160*b**6 + 1/32*b**4 - 1/24*b**3 - 3/2*b**2 + 0 - b. Let m(w) be the first derivative of g(w). Factor m(r).
-(r - 1)*(r + 1)*(3*r - 1)/4
Let m = 60 - 58. Suppose 1 = 5*b + 3*n - 3, -n = 2. Factor 1/2*f**m + b - 2*f.
(f - 2)**2/2
Let l(n) be the first derivative of 0*n + 1/6*n**2 + 1/6*n**3 - 1 + 1/24*n**4. Let l(q) = 0. Calculate q.
-2, -1, 0
Factor -3/2*g + 0*g**2 + 1 + 1/2*g**3.
(g - 1)**2*(g + 2)/2
Let l(a) be the second derivative of -7*a**5/30 + 2*a**4/3 - a**3/3 - 2*a**2/3 - 19*a. Determine k, given that l(k) = 0.
-2/7, 1
Let d(n) be the third derivative of n**5/90 - n**4/12 + 2*n**3/9 - 20*n**2. Factor d(z).
2*(z - 2)*(z - 1)/3
Let c = -22 - -22. Let l(w) be the third derivative of 1/120*w**5 + 0 + c*w - 1/16*w**4 - w**2 + 1/6*w**3. Find z, given that l(z) = 0.
1, 2
Let i be -1 + 1 + (4 - -3) + -5. Let q(t) be the third derivative of 1/36*t**4 + 0*t + 0 - 1/18*t**3 + t**i - 1/180*t**5. Let q(c) = 0. What is c?
1
Let y = 118/9 + -772/63. Suppose -y*z - 2/7 - 2/7*z**3 - 6/7*z**2 = 0. What is z?
-1
Factor 14/3*a + 6*a**2 + 2/3*a**4 + 10/3*a**3 + 4/3.
2*(a + 1)**3*(a + 2)/3
Let m(f) be the second derivative of -3*f - 1/6*f**4 + 1/3*f**3 + 1/15*f**6 - 1/10*f**5 + 0*f**2 + 0. Factor m(p).
2*p*(p - 1)**2*(p + 1)
Let t = -11 + -9. Let b be t/45*6/(-4). Factor -b*f**4 - 2/3*f - 2/3*f**5 + 4/3*f**2 + 4/3*f**3 - 2/3.
-2*(f - 1)**2*(f + 1)**3/3
Let p(s) = -s + 6. Let h be p(6). Suppose -b + h = -5. What is n in -3/2*n**3 + 0 - 1/4*n**b - n**4 - 1/4*n - n**2 = 0?
-1, 0
Factor 32/5 + 16*n + 66/5*n**2 + 4*n**3 + 2/5*n**4.
2*(n + 1)**2*(n + 4)**2/5
Let j(y) = y**3 + 15*y**2 + 20*y + 84. Let q be j(-14). Find c, given that 1/3*c**3 - 1/3*c + q + 0*c**2 = 0.
-1, 0, 1
Let h(q) = 2*q**3 - 10*q**2 + 11*q. Let u(f) = f. Let z(c) = 2*h(c) - 22*u(c). Factor z(l).
4*l**2*(l - 5)
Let i(y) be the first derivative of y**3/15 - y**2/10 + 1. Factor i(m).
m*(m - 1)/5
Let r be 3/((-7)/(-2) - 2). Suppose -2*u - 5*c = -u + 18, 4*u = -r*c. What is t in -2/9*t**u + 2/9*t**5 - 2/9*t**3 + 0 + 2/9*t**4 + 0*t = 0?
-1, 0, 1
Let m(u) = -4*u**4 + 49*u**3 - 36*u**2 - u - 7. Let o(s) = -s**4 - s**3 - s + 1. Let b(h) = 4*m(h) + 28*o(h). Factor b(p).
-4*p*(p - 2)**2*(11*p + 2)
Let f(t) be the second derivative of t**5/130 - t**4/26 + t**3/13 - t**2/13 + 20*t. Factor f(h).
2*(h - 1)**3/13
Let u(c) be the third derivative of -c**8/28 + 2*c**7/105 + c**6/10 - c**5/15 - 12*c**2. Suppose u(w) = 0. Calculate w.
-1, 0, 1/3, 1
Let f(p) be the third derivative of p**6/40 - p**5/60 + 2*p**2. Factor f(d).
d**2*(3*d - 1)
Suppose 4*w - 27 = 5*i - 5, 0 = -4*w + 2*i + 16. Factor 0*o + 3*o + 6*o**2 + 2*o**3 + o**w.
3*o*(o + 1)**2
Suppose 27/2*h - 3/2*h**3 - 15/2 - 9/2*h**2 = 0. Calculate h.
-5, 1
Suppose -2*k**5 - k**5 + 15*k**4 - 15*k + 15*k - 27*k**2 - 9*k**3 = 0. What is k?
-1, 0, 3
Suppose 5*w = -h - 8, 6 = w - 4*w. Suppose q - 4 = -h. Factor q - m**2 - 3 + 0*m**2 - 2*m.
-(m + 1)**2
Suppose -5*v + 51 = -4*n, 4*v - 12 = -0*v - 4*n. Let k = 11 - v. Solve 3*z**4 + 0*z**4 - 2*z**4 - 1 - 2*z**k + 2*z**2 = 0 for z.
-1, 1
Let h(z) be the second derivative of 3*z**5/20 - 8*z**4/3 + 95*z**3/6 - 25*z**2 + 13*z. Factor h(g).
(g - 5)**2*(3*g - 2)
Let z be 23/(-230)*2/(-3). Let i(u) be the third derivative of 1/60*u**6 + 0*u - 2*u**2 + 0 + 0*u**4 + 0*u**3 - z*u**5. Determine q so that i(q) = 0.
0, 2
Find j, given that 2*j + 2/3*j**3 + 2/3 + 2*j**2 = 0.
-1
Let y(c) be the second derivative of c**4/8 - 7*c**3/2 + 147*c**2/4 - 15*c. Factor y(r).
3*(r - 7)**2/2
Solve 13*k**2 + 14*k + 17*k**2 - 32*k**2 - 12 = 0 for k.
1, 6
Suppose 33 = 5*v - b, 5*v - 4*b = b + 45. Let s(d) be the third derivative of 0*d + 1/60*d**v + 0 + 0*d**3 + 2*d**2 + 1/15*d**5 + 1/12*d**4. Solve s(i) = 0.
-1, 0
Let z(f) be the third derivative of f**8/112 + f**7/50 - 3*f**6/200 - 7*f**5/100 - f**4/20 + 5*f**2. Suppose z(m) = 0. Calculate m.
-1, -2/5, 0, 1
Let q(i) = -1019*i**4 - 1331*i**3 - 331*i**2 - 29*i. Let x(o) = 1528*o**4 + 1996*o**3 + 497*o**2 + 43*o. Let a(j) = -7*q(j) - 5*x(j). Let a(b) = 0. What is b?
-1, -2/13, 0
Let s(w) be the first derivative of w**6/540 - w**3 - 1. Let r(g) be the third derivative of s(g). Determine n so that r(n) = 0.
0
Let 2*j**3 + 0 + 0*j + 3/4*j**2 - 15/4*j**4 + j**5 = 0. What is j?
-1/4, 0, 1, 3
Let n(b) = -4*b**3 + b**2 + 5. Let q(t) = 2*t - 2 + 2*t**3 - 2*t. Let c be -2 + 2 + -4 + 2. Let f(i) = c*n(i) - 5*q(i). Factor f(z).
-2*z**2*(z + 1)
Let d(t) be the third derivative of 0 + 0*t + 1/72*t**4 + 0*t**3 + 1/90*t**5 + 1/360*t**6 - t**2. Determine s, given that d(s) = 0.
-1, 0
Suppose 2*l - l = p, 4*l = 2*p + 6. Suppose -2*t + p = -1. Factor 2*w - 6*w**4 - 2*w**3 - 2*w**4 + 10*w**2 - t*w**2.
-2*w*(w - 1)*(w + 1)*(4*w + 1)
Suppose -3*q - 4 = -3*j + 17, 2*j - 11 = 5*q. Suppose 2*b + 2 = j. Determine i, given that -4*i**3 + 0*i**3 + i**5 + b*i**3 = 0.
-1, 0, 1
Let o = 1443 + -1441. Factor 0 - 2*y**o - 4/7*y.
-2*y*(7*y + 2)/7
Suppose -3*v + 3*o + 6 + 12 = 0, 4*o + 18 = 2*v. Suppose y + y - y - y**v = 0. What is y?
-1, 0, 1
Determine h, given that 4/19*h**2 - 10/19*h**4 + 12/19*h**3 + 2/19*h**5 - 14/19*h + 6/19 = 0.
-1, 1, 3
Let y(f) = 30*f**2 + 40*f + 4. Let r(h) = -h. Let s(x) = 6*r(x) + y(x). Factor s(a).
2*(a + 1)*(15*a + 2)
Factor -2/3 + 1/6*g**4 - 2/3*g + 1/2*g**2 + 2/3*g**3.
(g - 1)*(g + 1)*(g + 2)**2/6
Let u(m) be the first derivative of 2*m**5/35 + m**4/14 - 2*m**3/21 - m**2/7 - 4. Solve u(q) = 0.
-1, 0, 1
Let b(y) be the second derivative of -y**7/525 - y**6/300 + y**5/75 + y**2 - 3*y. Let d(n) be the first derivative of b(n). Factor d(z).
-2*z**2*(z - 1)*(z + 2)/5
Suppose -10 = -4*j + 2*j. Let w(c) be the second derivative of 1/120*c**6 + 0 + 0*c**2 - 1/48*c**4 + 1/168*c**7 + 0*c**3 + c - 1/80*c**j. What is g in w(g) = 0?
-1, 0, 1
Suppose -5*q - 39 = -39. Factor q - 1/6*o**2 + 0*o.
-o**2/6
Let y(n) = -165*n. Let m be y(-1). Let z = -1151/7 + m. Determine w so that z*w + 2/7 + 2/7*w**2 = 0.
-1
Let n be (-6)/7 + 1 - (-11)/(-77). Suppose n + 5/2*j**3 + 2*j - 6*j**2 = 0. What is j?
0, 2/5, 2
Find p, given that 8 + 10*p**2 - 4 + 6*p - 8*p**2 = 0.
-2, -1
Let v(x) be the third derivative of -x**8/168 - 4*x**7/105 - x**6/10 - 2*x**5/15 - x**4/12 + 28*x**2. Factor v(j).
-2*j*(j + 1)**4
Let z(n) be the second derivative of n**4/48 + n**3/24 - n**2/4 + 6*n. Factor z(u).
(u - 1)*(u + 2)/4
Find y such that -6/5*y**3 - 9/5*y + 0 - 21/5*y**2 = 0.
-3, -1/2, 0
Let u be (-4 + 20)*38/(-8). Let f = u - -157/2. Solve 0*g**2 + 5/4*g - 3/4*g**5 - 5/2*g**4 - f*g**3 + 1/2 = 0 for g.
-1, 2/3
Suppose -5*j + 3*q - 24 = 4*q, 3*j - 4*q - 4 = 0. Let c be (-27)/(-18)*j