ate n.
-1, 0, 1
Suppose 0 = 2*c + 3*a + 2*a + 12, 28 = 4*c - 3*a. Let b(p) be the first derivative of -1/14*p**c + 2/21*p**3 + 0*p + 1 + 0*p**2. Determine r so that b(r) = 0.
0, 1
Let s = -505 - -509. Suppose -1/3*h**3 + 17/3*h**2 - 13/3*h**s - 4/3 + 5/3*h**5 - 4/3*h = 0. What is h?
-1, -2/5, 1, 2
Suppose 0 = 3*g + 5*a + 9, -5*g + 2*a + 8 = -8. Factor -3*v**2 + v**2 + 0*v**g.
-2*v**2
Let k(q) be the second derivative of q**3/2 - q**2/2 + q. Let a be k(3). Suppose 2 - l - 4 - 5*l + a*l**2 = 0. What is l?
-1/4, 1
Suppose 0*y = y + 4*s - 7, 3*y - 8 = s. Factor 2*m**3 - y*m**5 + m**5 - 3*m + 3*m.
-2*m**3*(m - 1)*(m + 1)
Let b(d) be the second derivative of d**8/10080 - d**6/1080 + d**4/4 - 3*d. Let v(i) be the third derivative of b(i). Factor v(z).
2*z*(z - 1)*(z + 1)/3
Let i = 451/36 - 43/4. Factor -8/9 - i*c + 10/9*c**3 + 14/9*c**2.
2*(c - 1)*(c + 2)*(5*c + 2)/9
Let v(b) = b**3 - 5*b**2 - 4*b - 7. Let k be v(6). Determine u so that -6*u**2 - 9*u**3 - 2*u**k + 6*u**5 - u**5 = 0.
-1, 0, 2
Let w(x) = -x**3 + 2*x**2 - x. Let n be w(1). Factor 4*t - 4 - t**2 + n*t + 0*t.
-(t - 2)**2
Let g(o) = 8*o**2 - 23*o + 6. Let h(n) = -n**2. Let s(r) = -g(r) - h(r). Solve s(y) = 0 for y.
2/7, 3
Let r be 1/4 - 1/(-4). Suppose -r - 1/2*k - 1/2*k**5 - 1/2*k**4 + k**2 + k**3 = 0. Calculate k.
-1, 1
Let x(j) = -18*j**3 + 69*j**2 - 81*j + 24. Let s(l) = -35*l**3 + 137*l**2 - 163*l + 47. Let f(c) = 6*s(c) - 11*x(c). Factor f(p).
-3*(p - 3)*(p - 2)*(4*p - 1)
Let q(l) be the first derivative of 0*l**2 + 2 + 1/180*l**6 - 1/30*l**5 + 0*l - 2/3*l**3 + 1/12*l**4. Let f(w) be the third derivative of q(w). Solve f(d) = 0.
1
Let z(q) = -7*q**2 - 9*q - 5. Let u(h) = -15*h**2 - 17*h - 9. Let t(l) = -3*u(l) + 7*z(l). Factor t(n).
-4*(n + 1)*(n + 2)
Suppose 5*l - 42 = 38. Suppose 2*u + 2*u = l. Solve a**5 + 3*a**u + 4*a**3 + a**2 + 0*a**5 - a**3 = 0.
-1, 0
Let i = 5/7 + -11/35. Factor -i*v**2 + 0 + 4/5*v - 2/5*v**3.
-2*v*(v - 1)*(v + 2)/5
Let a(g) = 5*g**4 + 9*g**3 + 11*g**2 + 3*g. Let i(c) = 6*c**4 + 9*c**3 + 12*c**2 + 3*c. Let h(u) = -3*a(u) + 2*i(u). Factor h(j).
-3*j*(j + 1)**3
Let a(z) be the third derivative of -z**6/280 - z**5/70 + z**4/56 + z**3/7 - 37*z**2. Factor a(s).
-3*(s - 1)*(s + 1)*(s + 2)/7
Let j be ((-3 - -2) + 3)*-4. Let d be j/50*(1 - 6). Factor 0 + 0*w + w**4 + d*w**5 + 0*w**2 + 1/5*w**3.
w**3*(w + 1)*(4*w + 1)/5
Suppose 2*m + 0*m = -8. Let w be (6 + -3 + m)*-3. Find x, given that -2/3*x**4 + 0*x**w + 0*x + 0*x**2 + 0 = 0.
0
Let d(x) = -3*x - 5. Let g be d(-5). Let u(i) = -i**2 + 8*i + 20. Let f be u(g). Factor f + 2/3*z**3 + 0*z**2 + 0*z.
2*z**3/3
Suppose -25 = -y + 2*r - 5, -20 = 4*r. Let w be (4/y)/(1/10). Factor -2/5*q + 0*q**2 - 1/5 + 1/5*q**w + 2/5*q**3.
(q - 1)*(q + 1)**3/5
Factor 0*g - 14/3*g**4 + 0 - 8/3*g**3 - 4/3*g**5 + 8/3*g**2.
-2*g**2*(g + 2)**2*(2*g - 1)/3
Suppose -x + 10*p + 14 - 54 = 0, -3*p = 5*x - 12. Factor 1/2*m**2 + 1/2*m**3 + x - 1/2*m**4 - 1/2*m.
-m*(m - 1)**2*(m + 1)/2
Let k = 3 - 4. Let d be 0/2*k/2. Factor 3*h - 16*h**4 - 6*h**5 - 12*h**3 + d*h**4 - h.
-2*h*(h + 1)**3*(3*h - 1)
Factor -8 + 40*b + 198*b**2 + 24 + 6*b**3 - 170*b**2.
2*(b + 2)**2*(3*b + 2)
Let k be 20/(-15) + (-4)/6. Let t be 0*k*(-1)/4. Let t - 2/3*u**2 - 2/3*u = 0. What is u?
-1, 0
Let d be (-6)/(-8) - 19537/(-1092). Let q = -55/3 + d. Factor -8/13*f**2 + q + 14/13*f.
-2*(f - 2)*(4*f + 1)/13
Let b = -3 + 12. Let z be b/5 + 1/5. Determine t so that 0*t + 0 + 3/4*t**4 + 1/2*t**z - 5/4*t**3 = 0.
0, 2/3, 1
Let g(k) be the third derivative of k**8/3024 + k**7/1890 - k**6/1080 - k**5/540 + 5*k**2. Factor g(r).
r**2*(r - 1)*(r + 1)**2/9
Suppose -3/8*y - 3/8 + 3/8*y**3 + 3/8*y**2 = 0. What is y?
-1, 1
Let l(h) be the first derivative of h**5/20 - h**3/2 - 5*h**2/2 + 2. Let z(k) be the second derivative of l(k). Factor z(n).
3*(n - 1)*(n + 1)
Let h(y) be the second derivative of 2*y**7/7 + 14*y**6/15 + 3*y**5/5 - y**4 - 4*y**3/3 + 10*y. Solve h(p) = 0 for p.
-1, 0, 2/3
Let k(p) = p**2 - p + 1. Let l(z) = 3*z**2 - 5*z + 4. Let h(v) = 4*k(v) - l(v). Factor h(m).
m*(m + 1)
Factor 0 - 2/7*n**3 + 0*n**2 + 0*n.
-2*n**3/7
Solve 3*l + 1/2*l**2 + 0 = 0 for l.
-6, 0
Factor 4*s**4 - 353 + 3*s**3 - s**2 + 353.
s**2*(s + 1)*(4*s - 1)
Solve -3*l**2 - 36*l - 588 - 10*l - 38*l = 0 for l.
-14
Let u(v) be the third derivative of v**7/210 + v**6/120 - v**5/60 - v**4/24 - 20*v**2. Factor u(f).
f*(f - 1)*(f + 1)**2
Let r(g) = 8*g**4 + 21*g**3 - 5*g**2 - 21*g - 13. Let w(j) = -4*j**4 - 10*j**3 + 2*j**2 + 10*j + 6. Let n(d) = -2*r(d) - 5*w(d). Factor n(t).
4*(t - 1)*(t + 1)**3
Let f(m) be the second derivative of m**7/105 - m**5/30 + m**2 + m. Let d(p) be the first derivative of f(p). Solve d(z) = 0.
-1, 0, 1
Suppose k + o + 0*o - 4 = 0, -2*o + 8 = -3*k. Let 10/7*j**2 - 10/7*j**4 - 4/7*j + k + 4/7*j**3 = 0. Calculate j.
-1, 0, 2/5, 1
Suppose 0 = 2*w - 2*u + 4*u + 2, -1 = u. Let p(d) be the second derivative of 1/60*d**5 + w*d**3 + d + 0 + 0*d**2 + 1/36*d**4. Determine o so that p(o) = 0.
-1, 0
Let k be -34*2*1/(-4). Let f = k + -11. Factor -4*m**3 + 1 + f*m**2 - 4*m + 2*m**4 + 3*m**4 - 4*m**4.
(m - 1)**4
Let d(j) be the first derivative of -2/13*j**4 + 8/13*j + 4/13*j**2 + 1 - 2/13*j**3 - 2/65*j**5. Solve d(y) = 0.
-2, -1, 1
Solve 9/4 + 6*m + 9/2*m**2 - 3/4*m**4 + 0*m**3 = 0 for m.
-1, 3
Find x, given that -20*x**5 + 21*x**5 - 11*x**3 + x**4 - x**2 + 10*x**3 = 0.
-1, 0, 1
Let r(p) be the first derivative of -p**4/26 + 2*p**3/13 - 2*p**2/13 + 2. Determine m, given that r(m) = 0.
0, 1, 2
Let p(w) be the second derivative of -w**7/10080 - w**6/1440 - w**5/480 - w**4/6 + 2*w. Let y(m) be the third derivative of p(m). Factor y(a).
-(a + 1)**2/4
Let w be 95/70 - (-1)/(-2). Suppose 3/7*a - 3/7*a**3 - 6/7*a**2 + w = 0. What is a?
-2, -1, 1
Let h = 206/9 - 533/9. Let y = -36 - h. Factor -y*f**2 + 1/3*f**3 + 1/3 - 1/3*f.
(f - 1)**2*(f + 1)/3
Suppose 0 = -5*l + 33 + 32. Determine s so that 16*s - 15*s**2 + 12 + 21*s - l*s = 0.
-2/5, 2
Let n be (8/10)/(4/20). Suppose 3*v + 2 = n*v. Factor d**2 - 4*d**2 + v*d**2 - d.
-d*(d + 1)
Factor 6*f**3 + 0 - 22/3*f**2 + 4/3*f.
2*f*(f - 1)*(9*f - 2)/3
Let g(v) be the second derivative of 17*v**4/6 - 2*v**3/3 + 33*v. Factor g(z).
2*z*(17*z - 2)
Let v(a) = a + 1. Let k(p) = -2*p**3 + 2*p**2 + p + 1. Let j(i) = -2*k(i) + 2*v(i). Suppose j(b) = 0. What is b?
0, 1
Let t(z) be the first derivative of 0*z - 1/2*z**2 + 49/30*z**5 - 7/3*z**4 + 2 + 4/3*z**3. Let c(r) be the second derivative of t(r). What is p in c(p) = 0?
2/7
Suppose 0 + 3 = -3*o. Let c(z) = -z + 1. Let v be c(o). Suppose -2/7*m**4 - 2/7*m - 6/7*m**3 + 0 - 6/7*m**v = 0. What is m?
-1, 0
Let c(o) be the first derivative of -o**4/4 - 7*o**3/3 + 9*o**2/2 + 11*o - 2. Let y be c(-8). Let y*u**3 - 4 + 3*u**2 - u**4 + 0 - u**3 - 4*u = 0. What is u?
-1, 2
Let n be (20/6)/((-66)/(-9) + -5). Let y be 1/(-1) - (-75)/35. Find k, given that 16/7*k - y + 2/7*k**3 - n*k**2 = 0.
1, 2
Let w(q) = q**3 - 1. Let j(d) = -4*d**4 + 16*d**3 + 12*d**2 - 16*d - 24. Let p(k) = -j(k) + 8*w(k). Factor p(x).
4*(x - 2)**2*(x + 1)**2
Let m = 40 - 40. Factor -4/7*o**4 - 2/7*o + 6/7*o**3 + 0*o**2 + m.
-2*o*(o - 1)**2*(2*o + 1)/7
Suppose -3*x = 5*g - 21, -3*g - 2*g + 27 = x. Let l = 6 - g. Let l + 1/3*w - 1/3*w**2 = 0. What is w?
0, 1
Let w = 111/235 + 6/47. Let 3*g**2 + w*g**3 + 0 + 6/5*g - 3*g**4 - 9/5*g**5 = 0. Calculate g.
-1, -2/3, 0, 1
Let p(w) be the third derivative of w**5/30 - w**4/3 + w**3 - 56*w**2. Suppose p(b) = 0. What is b?
1, 3
Let k = -7 + 7. Factor 0*q + 12*q**2 - 10*q**2 + k*q.
2*q**2
Let c(i) = -3*i**4 + 12*i**2 + 12*i + 3. Let n(z) = 6*z**4 + z**3 - 23*z**2 - 25*z - 7. Let j(b) = -7*c(b) - 3*n(b). Factor j(u).
3*u*(u - 3)*(u + 1)**2
Let m(z) be the first derivative of 3*z**5/5 - 11*z**4/6 + 4*z**3/3 + 3*z**2 - 7. Let j(r) be the second derivative of m(r). Suppose j(i) = 0. What is i?
2/9, 1
Suppose 5*g = -5*f, -2*f = -f - g - 10. Let r(l) be the first derivative of -10/3*l**3 + 13/6*l**4 + 7/3*l**2 - 8/15*l**f - 1 - 2/3*l. Solve r(c) = 0 for c.
1/4, 1
Let i(l) = -l**3 - 7*l**2 + 8*l. Let a be i(-8). Let w(m) be the third derivative of -1/24*m**4 - 1/20*m**5 + 0 + m**2 + 1/3*m**3 + a*m. Factor w(h).
-(h + 1)*(3*h - 2)
Suppose 3*i - 3 = 2*i. Let h(s) be the first derivative of 1/3*s**i + s - 1 + s**2. Suppose h(n) = 0. Calcula