*t**3.
2*t**2*(t + 1)
Let b(s) = s**2 - 4*s + 2. Let m be b(4). Suppose 0*a + 6 = m*a. Factor -2*h + 2*h + 4*h + h**a - 4*h**2.
h*(h - 2)**2
Let s = -1 - -4. Let y be (-8)/(-3) - 2/s. Factor -y*f - 6*f**2 - 4*f**3 + 0*f**2 + 0*f**2.
-2*f*(f + 1)*(2*f + 1)
Let r(j) be the second derivative of j**5/70 - 2*j**4/21 + 5*j**3/21 - 2*j**2/7 + 8*j. Factor r(a).
2*(a - 2)*(a - 1)**2/7
Let y = -8 - -18. Let d be (24/(-30))/((-12)/y). Factor -d*p**5 + 10/3*p**3 + 8/3 - 16/3*p - 2/3*p**4 + 2/3*p**2.
-2*(p - 1)**3*(p + 2)**2/3
Suppose -4/3*d**2 + 0 + d + 1/3*d**3 = 0. What is d?
0, 1, 3
Let a(h) be the first derivative of h**5/5 + 4*h**4 + 32*h**3 + 128*h**2 - 5*h + 3. Let s(r) be the first derivative of a(r). Factor s(l).
4*(l + 4)**3
Let o be 1 - 4 - (-8 - -3). Let d be (1 - o)/(1/(-3)). Factor 2/7*r**d + 0*r**4 + 0*r**2 + 0*r - 2/7*r**5 + 0.
-2*r**3*(r - 1)*(r + 1)/7
Solve -33/2*a - 363/4 - 3/4*a**2 = 0.
-11
Factor 34*t**3 + 444*t**2 + 3195*t - 19*t**3 - 1813 + 463.
3*(t + 15)**2*(5*t - 2)
Suppose y = -2*d + 5, 0 = 3*y - 2 + 11. Suppose -4*r - r + 10 = 0. Determine n, given that -2*n**2 + 2*n - n**d - r*n**3 + 1 + 2*n**2 = 0.
-1, 1
Let v be 31/11 + 42/231 + 0. Suppose 3/2*p**2 + v*p + 3/2 = 0. Calculate p.
-1
Let y(h) = 6*h**2 - 5*h - 11. Let w(i) = 15*i**2 - 12*i - 27. Let v(f) = -5*w(f) + 12*y(f). Factor v(x).
-3*(x - 1)*(x + 1)
Let r(i) = i**3 - 3*i**2 - 4*i - 4. Let j be r(4). Let y = j - -6. Let 2*s + 5/2*s**y + s**3 + 1/2 = 0. Calculate s.
-1, -1/2
Let p = -107/4 + 27. Let x be ((-6)/4 + 2)/1. Factor -1/4 - p*s**4 + 0*s**3 + 0*s + x*s**2.
-(s - 1)**2*(s + 1)**2/4
Let r be 1/(-2)*-2*2. Let 4/3*l**2 - r*l**3 + 2/3*l + 0 = 0. Calculate l.
-1/3, 0, 1
Let y(f) be the first derivative of -f**6/6 + 4*f**5/5 - 5*f**4/4 + 2*f**3/3 + 3. Factor y(r).
-r**2*(r - 2)*(r - 1)**2
Suppose -3*u = u. Suppose -3*o - v = -u*v - 40, 4*v = -4*o + 40. Factor -2*a**2 - 3*a**2 - 3*a + o*a**3 + 2*a**2 - 9*a**4.
-3*a*(a - 1)**2*(3*a + 1)
Factor 8/13 + 2/13*p**2 + 8/13*p.
2*(p + 2)**2/13
Let x(s) = 11*s - 22. Let d be x(2). Factor 0*r + d - 1/4*r**2.
-r**2/4
Let g(z) = 97*z**4 - 55*z**3 - 7*z**2 + z + 3. Let j(q) = -96*q**4 + 55*q**3 + 8*q**2 - 4. Let b(s) = -4*g(s) - 3*j(s). Factor b(f).
-f*(4*f + 1)*(5*f - 2)**2
Let g(f) be the second derivative of -f**5/210 - f**4/18 - 5*f**3/21 - 3*f**2/7 + 21*f. Factor g(r).
-2*(r + 1)*(r + 3)**2/21
Let s(z) = 5*z**4 + 17*z**3 - 11*z**2 - 9*z + 22. Let p(u) = 3*u**4 + 11*u**3 - 7*u**2 - 6*u + 14. Let o(f) = -8*p(f) + 5*s(f). Factor o(l).
(l - 2)*(l - 1)**2*(l + 1)
Let y(c) = -34*c**3 + c**2 + 25*c + 4. Let a(b) = 135*b**3 - 3*b**2 - 99*b - 15. Let o(q) = -2*a(q) - 9*y(q). Factor o(w).
3*(w - 1)*(3*w + 2)*(4*w + 1)
Let y(g) be the second derivative of g**7/315 + 4*g**6/225 + g**5/30 + g**4/45 + 6*g. Factor y(h).
2*h**2*(h + 1)**2*(h + 2)/15
Suppose 3*c - 21 = -21. Let o(u) be the third derivative of 0*u - 1/15*u**3 + c + 1/300*u**5 - 2*u**2 - 1/120*u**4. Factor o(q).
(q - 2)*(q + 1)/5
Let a be (-4 + 3)*1/(-4). Let d(g) be the first derivative of -7/20*g**5 - a*g**2 + 0*g - g**4 - 11/12*g**3 + 1. Factor d(z).
-z*(z + 1)**2*(7*z + 2)/4
Let c be (-8)/20 + 24/10. Factor k + 3*k**4 - c*k + 0*k**4 - 9*k**2 - 5*k.
3*k*(k - 2)*(k + 1)**2
Let b(k) be the first derivative of 3*k**5/20 - 10. Suppose b(x) = 0. Calculate x.
0
Let 0 - 6/5*k**3 + 0*k + 2/5*k**4 + 0*k**2 = 0. What is k?
0, 3
Let j(n) be the second derivative of n**6/50 - 3*n**4/20 + n**3/5 - 15*n. What is l in j(l) = 0?
-2, 0, 1
Factor -448*o + 196*o**4 - 374*o**2 - 9 - 55 - 394*o**2 + 112*o**3.
4*(o - 2)*(o + 2)*(7*o + 2)**2
Suppose 3*j = 5*j - 2. Suppose 5*m + 5 + m**3 + j + 4*m**2 - 4 = 0. What is m?
-2, -1
Factor 2*f**4 + 0 + 2/3*f**2 + 0*f - 8/3*f**3.
2*f**2*(f - 1)*(3*f - 1)/3
Let q(f) be the first derivative of -f**4/2 - 22*f**3/3 - 35*f**2 - 50*f - 3. Suppose q(j) = 0. Calculate j.
-5, -1
Let h(w) be the third derivative of -w**5/160 - 9*w**4/64 + 5*w**3/8 - 54*w**2. Let h(a) = 0. What is a?
-10, 1
Let t(f) be the second derivative of f**5/50 + f**4/30 - f**3/15 - f**2/5 - 4*f. Find w such that t(w) = 0.
-1, 1
Suppose -5*x = s + 2*s - 24, -5*x = -s - 12. Let q(u) be the second derivative of -1/110*u**5 + 4*u + 1/66*u**4 + 2/33*u**s + 0*u**2 + 0. Factor q(m).
-2*m*(m - 2)*(m + 1)/11
Factor 13*o**2 + 3*o - 12*o**2 - 4*o + 2*o.
o*(o + 1)
Let 0*f**2 + 0 - 1/3*f**5 + 0*f + 2/3*f**4 - 1/3*f**3 = 0. What is f?
0, 1
Let i(o) = -o**3 - 6*o**2 + 8*o + 10. Let z be i(-7). Let s be z*4*3/144. Factor -k - s*k**3 + k**2 + 0.
-k*(k - 2)**2/4
Let i(l) be the second derivative of l**7/315 + l**6/90 + l**5/90 + l**2/2 + 6*l. Let d(h) be the first derivative of i(h). Solve d(w) = 0.
-1, 0
Suppose -6*v - 5*k - 2 = -2*v, v = k + 4. Solve -v - 1 + 6*y - 2*y**2 - 1 = 0.
1, 2
Let o be (2/(-6))/(6/(-36)). Let 36/5*x - 12/5 - 21/5*x**3 + 27/5*x**o = 0. Calculate x.
-1, 2/7, 2
Factor 6*m**2 - 9/2*m + 1 - 5/2*m**3.
-(m - 1)**2*(5*m - 2)/2
Let i(b) be the second derivative of 0 - 1/10*b**5 - 1/2*b**4 - 2/3*b**3 + 3*b + 0*b**2. Factor i(u).
-2*u*(u + 1)*(u + 2)
Suppose -2*m = 5*x + 11, -4*m + 4*x + 23 = -x. Suppose 14*v**3 - 3*v**2 + 0*v - 11*v**3 - 5*v + m*v + 3 = 0. Calculate v.
-1, 1
Let x(m) be the second derivative of 0 + 1/15*m**6 + 3/20*m**5 + 1/6*m**4 + 1/84*m**7 + 0*m**2 + 1/12*m**3 - 4*m. Find a, given that x(a) = 0.
-1, 0
Let s be (4 + -2)/(-2) + (-27)/(-18). Factor 1/4*a**4 - 1/4 + 1/2*a**3 + 0*a**2 - s*a.
(a - 1)*(a + 1)**3/4
Let a be -3 - ((-6)/(-15) - (-117)/(-30)). Suppose 4*g = -g. Factor 1/2*z**3 + g*z**2 + 0*z + 0 + a*z**4.
z**3*(z + 1)/2
Factor -3/4 + 15/2*g**2 - 3*g**5 + 45/4*g**4 - 15*g**3 + 0*g.
-3*(g - 1)**4*(4*g + 1)/4
Solve 8/13 - 22/13*p**3 + 42/13*p**2 + 4/13*p**4 - 32/13*p = 0.
1/2, 1, 2
Let m be (-12)/8*4/(-3). Let o(u) be the third derivative of 1/336*u**8 + 0*u**5 - 2*u**m - 1/210*u**7 + 0*u**3 + 0 + 0*u**4 + 0*u + 0*u**6. Factor o(z).
z**4*(z - 1)
Let z = -6 + 15. Suppose 0 = -5*r + 15, -3*r = -q - q - z. Solve -2/3*g**2 + 0 + 0*g**3 + 2/3*g**4 + q*g = 0.
-1, 0, 1
Suppose -16 = -3*f + 4*a - 3, -4*f + 11 = a. Let h be f - 0/(0 - 2). Factor -2*b + b**h + b**2 + b - 1 + 0.
(b - 1)*(b + 1)**2
Let n = 30 + -21. Let q be (-3)/12 + n/4. Factor -2/7*w**q + 6/7*w - 4/7.
-2*(w - 2)*(w - 1)/7
Let j(n) be the first derivative of 10/3*n**3 - 2*n**5 + 0*n + 3/2*n**4 + 1 + n**2 - 4/3*n**6. Let j(v) = 0. Calculate v.
-1, -1/4, 0, 1
Let j(t) be the first derivative of 4*t + 0*t**2 - 4/3*t**3 + 1. Suppose j(d) = 0. What is d?
-1, 1
Suppose 2*n + 5*u = -21, n + 8 = -0*n - 2*u. Suppose -5*z + 3 = 4*w - 0*w, -5*w - 9 = n*z. Factor 19/3*g**z - 2/3 + 5*g**2 + 7/3*g**4 + 1/3*g.
(g + 1)**3*(7*g - 2)/3
Let n = -42 - -42. Factor 0 + n*p + 1/2*p**2 - 1/2*p**4 - 1/2*p**3 + 1/2*p**5.
p**2*(p - 1)**2*(p + 1)/2
Suppose -19 = -3*d - 2*y, y - 5 + 0 = 0. Factor 14/9*q**2 + 2*q**d + 4/9*q + 0 + 10/9*q**4 + 2/9*q**5.
2*q*(q + 1)**3*(q + 2)/9
Let q = -5/14 + 29/42. Solve 4/3*p - 4/3 - q*p**2 = 0.
2
Let c = -52 - -36. Let d = -16 - c. Solve -1/3*b**2 + 1/3*b + d = 0 for b.
0, 1
Factor 1/7*c**2 + 3/7 - 4/7*c.
(c - 3)*(c - 1)/7
Let q(k) be the third derivative of k**7/8820 - k**6/1260 + 5*k**4/24 + 5*k**2. Let i(s) be the second derivative of q(s). Factor i(l).
2*l*(l - 2)/7
Suppose -5*z - 20 = 5*x, 7*z = 2*z + 4*x - 2. Let j be z/4*-1*12. Let u**3 - j*u**2 + 2*u**3 + u - 7*u**3 + 3*u**5 + 2 + 4*u**4 = 0. Calculate u.
-1, 2/3, 1
Let i(s) be the first derivative of s**9/12096 + s**8/6720 + 5*s**3/3 + 1. Let w(j) be the third derivative of i(j). Find q, given that w(q) = 0.
-1, 0
Suppose -4*u = -5 - 3. Solve -6*c**3 + 0*c**4 - 2*c**4 + 2*c**5 - 2*c**2 + 9*c**u - 4*c + 3*c**2 = 0.
-2, 0, 1
Let r(l) = l**2 + l. Let k(y) = -8*y**2 + 4*y - 4. Let z(a) = k(a) + 4*r(a). Factor z(o).
-4*(o - 1)**2
Let r(d) = d - 1. Let q(y) = -3*y**2 + 5 + 4*y**2 + 2*y - 8*y. Let w be 2/3*9/(-6). Let a(v) = w*q(v) - 3*r(v). Factor a(t).
-(t - 2)*(t - 1)
Let b(q) be the second derivative of -21*q**5/50 + q**4/15 + 43*q. Factor b(a).
-2*a**2*(21*a - 2)/5
Let g(s) be the third derivative of 0*s**7 + 0*s**3 + 0*s**5 + 0*s**4 + 0 - 1/448*s**8 + 1/160*s**6 - 3*s**2 + 0*s. Suppose g(j) = 0. What is j?
-1, 0, 1
Suppose 10*j - 8 = 9*j. What is r in 44*r**3 + j*r**2 + 4*r**5 + 18*r**4 - 32 - 83*r + 35*r + 6*r**4 = 0?
-2, -1, 1
Let q(m) be the seco