 = -7*a. Let o(t) = t**3 - t**2 + t + 1. Let k(d) = 5*d**3 - 6*d**2 + 7*d + 6. Let s(z) = a*k(z) - 6*o(z). Factor s(y).
-y*(y - 1)*(y + 1)
Determine c, given that -1734*c - 29478 - 2/9*c**3 - 34*c**2 = 0.
-51
Let 1/8*r - 1/4 + 1/8*r**2 = 0. What is r?
-2, 1
Let y(t) = -8*t**2 + 66. Let l(j) = 11*j**2 + j - 69. Let b(z) = 2*l(z) + 3*y(z). Factor b(f).
-2*(f - 6)*(f + 5)
Let q(j) = 2*j**2 + 26*j + 18. Let x(w) = w + 2. Let r(v) = q(v) + 6*x(v). Factor r(c).
2*(c + 1)*(c + 15)
Let k(y) = 7*y**5 - 9*y**4 + 3*y**2 + 3. Let c(n) = -6*n**5 + 10*n**4 - 2*n**2 - 2. Let l(i) = -3*c(i) - 2*k(i). Solve l(r) = 0 for r.
0, 3
Suppose -4*r = -5*t + 7, 5*r + t = -t + 16. Factor 0 - 18*l**2 + 13*l**r - 11*l - 2.
-(l + 2)*(5*l + 1)
Suppose -9 + 5 = -i + 2*h, -16 = -4*i - 5*h. Let o(x) be the first derivative of 1/2*x**i - 2/3*x**3 - 1 + 0*x - 2*x**2. Suppose o(n) = 0. What is n?
-1, 0, 2
Let a(f) be the second derivative of -1/16*f**3 - 3/160*f**5 + 0*f**2 - 14*f + 0 + 1/16*f**4. Factor a(p).
-3*p*(p - 1)**2/8
Let s(b) = 1. Let o(n) = n + 10. Let r(x) = 2*o(x) - 14*s(x). Let m be r(-3). Factor -3/4*g + m - 3/4*g**2.
-3*g*(g + 1)/4
Let q be (-2)/((1/6)/(3/6)). Let j(i) = -i**2 + 6*i + 1. Let y(o) = -o. Let k(h) = q*y(h) - j(h). Factor k(d).
(d - 1)*(d + 1)
Let m be 6 - ((-16)/18)/((-14)/63). Let b = 17 - 33/2. What is y in 1/8*y**4 - 1/2 - b*y + 1/2*y**3 + 3/8*y**m = 0?
-2, -1, 1
Let x(v) be the second derivative of -v**5/4 - 85*v**4/12 + 185*v**3/6 - 95*v**2/2 + 113*v + 2. Let x(q) = 0. Calculate q.
-19, 1
Let w(x) = -45*x**3 - 45*x**2 + 35*x. Let n(t) = 5*t**3 + 5*t**2 - 4*t. Let o(q) = -55*n(q) - 6*w(q). Suppose o(a) = 0. Calculate a.
-2, 0, 1
Let t(b) = -b - 11. Let j be t(-12). Let i(d) = 2*d**4 - 9*d**3 + 5*d**2 + 4*d - 2. Let k(x) = -x**3 + x**2. Let w(z) = j*i(z) - 5*k(z). Factor w(q).
2*(q - 1)**3*(q + 1)
Let f(d) be the second derivative of d**6/15 - 3*d**4/2 + 4*d**3/3 + 12*d**2 + 110*d. Factor f(l).
2*(l - 2)**2*(l + 1)*(l + 3)
Let x(g) be the first derivative of -g**3/3 - 25*g**2/2 - 66*g - 102. Factor x(i).
-(i + 3)*(i + 22)
Let g(o) be the third derivative of o**7/168 - o**6/24 + o**5/12 - 3*o**3/2 + 27*o**2. Let w(r) be the first derivative of g(r). Factor w(q).
5*q*(q - 2)*(q - 1)
Let h(n) be the first derivative of -n**8/1344 + n**7/224 - n**6/96 + n**5/96 - 5*n**3/3 + 12. Let s(q) be the third derivative of h(q). Factor s(b).
-5*b*(b - 1)**3/4
Let u(t) be the third derivative of -t**6/120 + t**5/20 - t**4/8 + t**3/6 - 55*t**2. Factor u(y).
-(y - 1)**3
Let z(m) = -m**3 + 7*m**2 + 7*m + 13. Let d be z(8). Factor 32*n**d + 24*n**5 - 54*n**5.
2*n**5
Let h be (3/2 - -1)*116/145. Factor -14 - 5*l**h - 12 + 6 - 20*l.
-5*(l + 2)**2
Let x(d) be the second derivative of -d**4/12 + d**3/2 + 75*d. Factor x(i).
-i*(i - 3)
Let s(r) be the third derivative of 0 - 1/120*r**6 + 0*r**3 - 1/1050*r**7 - 7/300*r**5 + 0*r + 19*r**2 - 1/40*r**4. Find j such that s(j) = 0.
-3, -1, 0
Let a(r) be the second derivative of r**4/30 - 8*r**3/5 + 129*r. Factor a(o).
2*o*(o - 24)/5
Let t = 1 + 4. Determine f so that -26*f - 23*f + 44*f + t*f**2 = 0.
0, 1
Suppose -22*p = 7*p + 16 - 103. Determine t, given that 78/7*t**2 + 4/7*t**4 - 16/7*t - 34/7*t**p - 32/7 = 0.
-1/2, 1, 4
Let f(u) = 6*u**2 + 59*u + 734. Let s(p) = -p**2 - p - 1. Let j(q) = -f(q) - 5*s(q). Let j(w) = 0. What is w?
-27
Let f be (4/3)/((-4)/24*4). Let y be (f/(-6))/((-90)/(-54)). Factor -y + 1/5*s**2 + 0*s.
(s - 1)*(s + 1)/5
Let k be ((-2)/(-14))/((-7)/(-42)). Suppose h - 198*j = -196*j + 6, -3*h + 8 = -j. Factor 2/7*q**h + k*q + 4/7.
2*(q + 1)*(q + 2)/7
Let h(b) be the first derivative of b**4/4 - b**3/3 - b**2 - 410. Factor h(d).
d*(d - 2)*(d + 1)
Let z(u) = -u**2 + 3*u - 4. Let w(k) = -k**2 + k - 1. Let l(d) = 6*w(d) - 3*z(d). Let m(o) = 3*o**2 + 2*o - 5. Let y(b) = -5*l(b) - 6*m(b). Factor y(t).
-3*t*(t - 1)
Let m(p) = -6*p - 2. Let w be m(-3). Suppose -6 + w = 5*g. Factor -9 - 4*y**3 + 3*y**3 + 9 - y**g.
-y**2*(y + 1)
Let s be -2*(3 + -1) - -9 - 0. Suppose -s*a + 7*a - 8 = 0. Suppose -5/3*p**a + 0 + 1/3*p**5 - 7/3*p**2 + 2/3*p + 3*p**3 = 0. Calculate p.
0, 1, 2
Let m = -12231/2 - -6118. Factor 0 - 5*w - m*w**2.
-5*w*(w + 2)/2
Let a(s) be the second derivative of -2*s**6/35 + 142*s**5/35 - 589*s**4/7 + 184*s**3 + 4232*s**2/7 - 266*s + 2. Solve a(d) = 0 for d.
-2/3, 2, 23
Suppose 0 = -0*w + 2*w - 20. Suppose 4*j = -58 + 114. Suppose j - 56*x - w*x**3 + 22*x**2 + 2 + 22*x**2 = 0. What is x?
2/5, 2
Factor 0 - 2/5*p**4 - 4*p + 8/5*p**3 + 14/5*p**2.
-2*p*(p - 5)*(p - 1)*(p + 2)/5
Let j(o) be the first derivative of 2*o**5/15 + 5*o**4/18 - 2*o**3/27 - 5*o**2/9 - 4*o/9 - 46. Let j(m) = 0. What is m?
-1, -2/3, 1
Let g(x) be the third derivative of x**6/180 + 13*x**5/90 + 35*x**4/36 - 49*x**3/9 + 10*x**2 - 4. What is j in g(j) = 0?
-7, 1
Let o = -12/5789 + 5837/23156. Factor -11/4 - o*j**2 - 3*j.
-(j + 1)*(j + 11)/4
Suppose 320 = 48*l + 176. Let b(d) be the first derivative of -l + 1/3*d**2 - 4/9*d**3 + 0*d + 1/6*d**4. Determine r so that b(r) = 0.
0, 1
Let x(v) be the first derivative of 26/21*v**3 - 14*v + 5*v**2 + 1/14*v**4 - 8. Let x(k) = 0. Calculate k.
-7, 1
Factor 11/4*x**2 + 0 - 1/4*x**3 + 0*x.
-x**2*(x - 11)/4
Let z be 0/((-2 - -2) + -2). Suppose z = -0*x + 3*x - 6. Let -4 - x + t**3 + 3*t + 7 + 3*t**2 = 0. Calculate t.
-1
Let z(h) be the third derivative of h**5/30 - 7*h**4/48 - 11*h**3/12 + 163*h**2 - h. Factor z(o).
(o + 1)*(4*o - 11)/2
Let g(l) be the third derivative of -l**8/672 - 3*l**7/140 - l**6/80 + 73*l**5/120 - 2*l**4 + 3*l**3 - 2*l**2 + 167*l. Factor g(f).
-(f - 1)**3*(f + 6)**2/2
Let o(l) = -20*l**2 - 232*l. Let x(b) = -b**2 + b. Let s(v) = o(v) - 24*x(v). Solve s(w) = 0.
0, 64
Let z(u) be the third derivative of -u**7/504 + u**6/120 - u**5/120 - u**4/2 - 10*u**2. Let g(h) be the second derivative of z(h). Let g(m) = 0. What is m?
1/5, 1
Suppose -5 = 13*o - 15 + 10. Solve o - 2/7*i - 1/7*i**3 + 3/7*i**2 = 0.
0, 1, 2
Let j(b) be the second derivative of -b**8/840 - b**7/280 + b**5/120 - 3*b**3/2 + 3*b. Let h(o) be the second derivative of j(o). Factor h(i).
-i*(i + 1)**2*(2*i - 1)
Suppose -k = 40*w - 42*w - 3, -5*k + 15 = -2*w. Factor -56/5*h**k + 4/5 - 12/5*h**5 + 4/5*h - 24/5*h**2 - 44/5*h**4.
-4*(h + 1)**4*(3*h - 1)/5
Let t be (0 - 30/70)/(6/(-4)). Solve 6/7*n**3 - t*n**2 + 2/7*n**5 - 6/7*n**4 + 0 + 0*n = 0.
0, 1
Let b = -11 - -9. Let o be b/4*4 - -9. Solve 7*f + 3*f**2 + o*f - 5*f = 0 for f.
-3, 0
Suppose -2*l = -2*u - 6, 2*u - l = 44 - 47. Let -8/19*r + 2/19*r**2 + u = 0. What is r?
0, 4
Suppose -2500/7*r + 0 - 1/7*r**5 - 325/7*r**3 - 1500/7*r**2 - 30/7*r**4 = 0. What is r?
-10, -5, 0
Factor 4/11*w + 18/11*w**2 + 14/11*w**3 + 0.
2*w*(w + 1)*(7*w + 2)/11
Let l(f) be the first derivative of -f**7/840 + f**5/120 + 4*f**3/3 + 16. Let x(y) be the third derivative of l(y). Factor x(p).
-p*(p - 1)*(p + 1)
Factor 203/4*a**2 + 51/4*a + 0 + 50*a**3 - a**4.
-a*(a - 51)*(2*a + 1)**2/4
Let d(y) be the third derivative of -y**5/120 + 7*y**4/12 - 10*y**2 + 6*y. Factor d(f).
-f*(f - 28)/2
Let a = -149515/11 - -13601. Find h such that -144/11*h + 54/11 + a*h**2 = 0.
3/4
Let b(p) = -75*p**4 + 475*p**3 - 1180*p**2 + 1140*p - 360. Let x(h) = 19*h**4 - 119*h**3 + 295*h**2 - 285*h + 90. Let a(n) = -4*b(n) - 15*x(n). Factor a(j).
5*(j - 3)**2*(j - 1)*(3*j - 2)
Let x(z) be the first derivative of -2/5*z**2 + 9 - 8*z - 1/5*z**3 - 1/30*z**4. Let k(o) be the first derivative of x(o). Let k(a) = 0. Calculate a.
-2, -1
Suppose 0 = -9*p + 7*p - 1580. Let a = 3181/4 + p. Determine m so that 3/4 - 39/4*m**3 - a*m + 3*m**4 + 45/4*m**2 = 0.
1/4, 1
Suppose -5*i - 3*o + 8*o = -55, -3*i - o + 53 = 0. Suppose 5*n = n + i. What is x in -5*x + 4*x + x**n - x**4 + 2*x**3 - x**5 = 0?
-1, 0, 1
Suppose 119*m - 72*m + 4861 + 1766 + 235*m + 3*m**2 = 0. Calculate m.
-47
Let 1/4*f**3 - 45/2*f**2 + 675*f - 6750 = 0. What is f?
30
Suppose 0 - 3/5*p - 3/5*p**2 = 0. What is p?
-1, 0
Let v(x) be the first derivative of x**5/25 - x**4/10 - x**3/5 + 4*x**2/5 - 4*x/5 - 52. Factor v(w).
(w - 2)*(w - 1)**2*(w + 2)/5
Let w(p) be the second derivative of -p**5/13 + 49*p**4/78 + 5*p**3/3 + 6*p**2/13 + 6*p. Determine b, given that w(b) = 0.
-1, -1/10, 6
Factor 14*q**3 - 3*q**4 + 4*q**3 - 30*q - 3*q**3 - 9*q**2 + 3*q**3.
-3*q*(q - 5)*(q - 2)*(q +