t**2 - 12*t - 7*t**3 - 25*t**3 + d. Let x(k) = -k**2 - k + 1. Let z(o) = -n(o) + 10*x(o). Factor z(c).
2*c*(4*c + 1)**2
Determine c, given that 2*c - 14*c**2 + 4 - 22*c**2 - 10*c**4 - 26*c**3 + 18*c**2 = 0.
-1, 2/5
Factor -14*s + 1 - s + 5 + 9*s**2 - 6*s.
3*(s - 2)*(3*s - 1)
Let a(h) be the first derivative of 13*h**2 + 3*h**4 + 0*h - 12*h - 6 + 5*h**2 + 15*h**3. Suppose a(y) = 0. Calculate y.
-2, 1/4
Let q(d) be the third derivative of -d**7/70 - 7*d**6/40 - 9*d**5/10 - 5*d**4/2 - 4*d**3 - 6*d**2. Factor q(g).
-3*(g + 1)*(g + 2)**3
Let p(f) be the third derivative of 0*f + 1/21*f**3 + 2*f**2 - 1/42*f**4 + 1/210*f**5 + 0. Solve p(q) = 0.
1
Determine r, given that 0 + 2*r**5 + 4/9*r**2 + 40/9*r**4 + 0*r + 26/9*r**3 = 0.
-1, -2/9, 0
Let u(q) be the third derivative of 1/12*q**3 + q**2 + 0 - 1/240*q**6 - 1/16*q**4 + 1/40*q**5 + 0*q. Factor u(j).
-(j - 1)**3/2
Let l(p) = p - 7. Let q be l(5). Let k be q/((-2)/(3 - 1)). Solve 2*z + k*z**2 + 2*z - 2*z = 0.
-1, 0
Let g(p) = 3*p**5 + 6*p**3 - 9*p. Let q(r) = r**4 - r**3 - r**2 + r. Let i(h) = -g(h) - 6*q(h). Determine b so that i(b) = 0.
-1, 0, 1
Suppose 4*n + h = -n + 17, 4*h - 17 = -3*n. Let t = n + -1. Determine l so that 2*l + 0*l**2 + 2 - 2*l**2 - t*l**2 = 0.
-1/2, 1
Let x(h) = 24*h**3 - 4*h**2 - 3*h + 2. Let f(q) = q**2 + 1. Let t(y) = -2*f(y) + x(y). Factor t(b).
3*b*(2*b - 1)*(4*b + 1)
Let g(z) be the second derivative of -1/2*z**2 + 0 - 2*z + 5/6*z**3 - 1/3*z**4. Factor g(v).
-(v - 1)*(4*v - 1)
Let j(q) = 2*q. Let l be j(1). Factor -2*t**3 + t**4 - l*t**2 + 2*t + 2*t**2 - 1.
(t - 1)**3*(t + 1)
Let j(z) = z**5 + z**4 - z**3 - z. Let n(k) = -k**5 + 3*k**4 + 3*k**3 - 8*k**2 + 3*k. Let o(s) = -3*j(s) - n(s). Let o(f) = 0. What is f?
-2, 0, 1
Let p = -70 - -70. Let n(u) be the first derivative of -3/2*u**2 + p*u**3 + 3/4*u**4 + 0*u - 2. Factor n(r).
3*r*(r - 1)*(r + 1)
Factor -3/2*l - 9/4*l**2 + 3/4*l**4 + 0*l**3 + 0.
3*l*(l - 2)*(l + 1)**2/4
Let i = -1/870 + 1/29. Let s(n) be the second derivative of 3/100*n**5 + 0 - 2*n - 1/20*n**4 + i*n**3 + 0*n**2 - 1/150*n**6. Solve s(b) = 0 for b.
0, 1
Suppose -22 = -m - 18. Factor 2/7*p + 0*p**2 + 2/7*p**5 - 4/7*p**3 + 0 + 0*p**m.
2*p*(p - 1)**2*(p + 1)**2/7
Let y(u) be the second derivative of u**4/4 + 2*u**3 + 9*u**2/2 + 10*u. Let y(z) = 0. Calculate z.
-3, -1
Let g = -14 - -24. Factor -4 - 2*z**3 - 4*z**2 - 2*z**2 - 2*z**2 - g*z.
-2*(z + 1)**2*(z + 2)
Factor 0 + 4/3*j - 4*j**4 + 28/3*j**3 - 20/3*j**2.
-4*j*(j - 1)**2*(3*j - 1)/3
Let o(j) be the first derivative of -j**7/126 + j**6/90 + j**5/60 - j**4/36 - 4*j + 4. Let l(b) be the first derivative of o(b). What is a in l(a) = 0?
-1, 0, 1
What is h in 2/3 + 2*h - 4/3*h**4 - 2*h**3 + 2/3*h**2 = 0?
-1, -1/2, 1
Let z(v) be the second derivative of -v**8/13440 + v**7/5040 + v**6/1440 - v**5/240 + v**4/4 - 4*v. Let q(i) be the third derivative of z(i). Factor q(l).
-(l - 1)**2*(l + 1)/2
Let i(l) = -10*l**2 - 5*l - 5. Let n(c) = -9*c**2 - 5*c - 4. Let f(h) = -4*i(h) + 5*n(h). Let f(v) = 0. What is v?
-1, 0
Let h = 5 - 3. Let w(d) be the second derivative of 0 + 0*d**2 - h*d - 1/75*d**6 - 1/10*d**4 + 3/50*d**5 + 1/15*d**3. Factor w(s).
-2*s*(s - 1)**3/5
Let a(n) = -n**2 - n. Let i(j) = -7*j**2 - 7*j. Let c(z) = 6*a(z) - i(z). Let d(g) = 3*g**2 + 5*g. Let v(r) = 5*c(r) - d(r). Solve v(q) = 0.
0
Determine n so that -4*n**2 + 2*n + 26 + 3*n**3 - 2*n**2 - 2 - 14*n = 0.
-2, 2
Let u(d) = -3*d**2 - 4*d + 2. Let a(h) be the second derivative of -h**4/6 - 2*h**3/3 + h**2 - 5*h. Let o(c) = -5*a(c) + 4*u(c). Suppose o(p) = 0. What is p?
1
Let x(s) be the second derivative of -2*s**6/15 + 3*s**5/5 - s**4 + 2*s**3/3 - 2*s. Suppose x(w) = 0. What is w?
0, 1
Suppose 3*x + 6*a + 10 = 4*a, 0 = -x + 5*a + 25. Determine t, given that 2/15*t**4 - 2/15*t**3 + 0*t + x*t**2 + 0 + 4/15*t**5 = 0.
-1, 0, 1/2
Let c(j) be the second derivative of -7/8*j**4 - 1/2*j**3 + 0 + 4*j + 0*j**2. Solve c(h) = 0 for h.
-2/7, 0
Factor -8/3 - 6*u + 5/3*u**2.
(u - 4)*(5*u + 2)/3
Factor -2 + b**4 - 3*b**4 - 115*b**2 + 0*b**4 + 119*b**2.
-2*(b - 1)**2*(b + 1)**2
Let b(z) be the second derivative of -z**7/945 + z**6/270 - z**5/270 + 5*z**2/2 - 8*z. Let y(g) be the first derivative of b(g). Factor y(c).
-2*c**2*(c - 1)**2/9
Let j(t) be the second derivative of -t**7/21 + 2*t**6/15 - t**4/3 + t**3/3 - 20*t. Factor j(m).
-2*m*(m - 1)**3*(m + 1)
Factor 3*q**2 + 3 - 5*q**2 + q + q + q**2.
-(q - 3)*(q + 1)
Let q(y) be the first derivative of 2*y**5/35 + y**4/14 - 2*y**3/21 - y**2/7 - 3. Determine h, given that q(h) = 0.
-1, 0, 1
Let s(b) be the third derivative of 0*b**3 + 0 + 1/300*b**6 + 1/150*b**5 + 0*b - 2*b**2 + 0*b**4. Factor s(o).
2*o**2*(o + 1)/5
Let l(i) be the first derivative of -2*i**5/5 - 3*i**4/2 + 4*i**2 - 17. Suppose l(n) = 0. What is n?
-2, 0, 1
Let o(a) = -a - 5. Let r be o(-7). Let f be ((42/(-28))/(18/8))/(-2). Factor 2/3 + f*s - 1/3*s**r.
-(s - 2)*(s + 1)/3
Let p(k) be the third derivative of -k**5/40 - 11*k**4/16 - 5*k**3/2 - 34*k**2. Factor p(m).
-3*(m + 1)*(m + 10)/2
Let v(w) = 3*w + 2*w**3 - 2*w**5 + 1 - 6*w**3 - 4. Let k(q) = 3*q**5 + 7*q**3 - 5*q + 5. Let u(h) = 6*k(h) + 10*v(h). Find g such that u(g) = 0.
-1, 0, 1
Suppose 2*n = 7*n + 4*o + 190, -2*n = 3*o + 69. Let t be ((-6)/n)/((-1)/(-2)). Factor 0*j + 0 + t*j**2.
2*j**2/7
Suppose -15 = 5*w - 10*w. Factor -1/4*j**4 - 3*j + 2 + 1/2*j**2 + 3/4*j**w.
-(j - 2)**2*(j - 1)*(j + 2)/4
Let i = -3/283 - -587/1981. What is j in -i*j**2 + 4/7*j - 2/7 = 0?
1
Suppose 8 = -2*w, -3*w = 2*f + 16 - 4. Let c(q) be the first derivative of 2/3*q**3 - q**2 - 1 + f*q. Find a such that c(a) = 0.
0, 1
Let o be 18/40 + 10/(-50). Factor 0*h + 0*h**3 - o*h**2 + 0 + 1/4*h**4.
h**2*(h - 1)*(h + 1)/4
Suppose 52*h - v = 49*h + 14, -2 = h + 3*v. Solve 1/3*l**3 + h*l - 2*l**2 - 8/3 = 0.
2
Let z be (-4)/((-8)/10)*1. Suppose -8 = -5*y - 0*y - 4*a, -2*y - z*a = -10. Suppose q**2 - 2*q**2 - 2 + y*q**2 + 3*q = 0. What is q?
1, 2
Let 4/5*q**3 - 1/5*q**4 + 4/5*q - 6/5*q**2 - 1/5 = 0. What is q?
1
Let t(f) be the first derivative of f**7/2520 - f**6/1080 + f**3 + 1. Let y(s) be the third derivative of t(s). Factor y(z).
z**2*(z - 1)/3
Let a(z) = 19*z**4 - 4*z**3 - 42*z**2 - 11*z + 3. Let c(b) = 20*b**4 - 4*b**3 - 42*b**2 - 10*b + 2. Let d(f) = 6*a(f) - 5*c(f). Solve d(l) = 0 for l.
-1, 2/7, 2
Let c(n) be the second derivative of n**6/6 + 5*n**5/4 + 5*n**4/4 - 15*n**3/2 + 3*n. Solve c(a) = 0.
-3, 0, 1
Let n(t) be the third derivative of 0*t + 8*t**2 + 1/390*t**5 + 0 + 1/39*t**3 + 1/78*t**4. Factor n(h).
2*(h + 1)**2/13
Let i(m) be the first derivative of 1/300*m**5 + 1/2*m**2 + 2 + 0*m**3 + 0*m + 1/120*m**4. Let b(o) be the second derivative of i(o). Factor b(c).
c*(c + 1)/5
Let p(q) = 49*q**4 - 6*q**3 - 184*q**2 + 44*q. Let i(m) = 685*m**4 - 85*m**3 - 2575*m**2 + 615*m. Let t(f) = -4*i(f) + 55*p(f). What is a in t(a) = 0?
-2, 0, 2/9, 2
Let u(j) be the second derivative of 4*j**3 - 3/4*j**5 + 0 - 4*j - 6*j**2 + 7/4*j**4. Solve u(q) = 0.
-1, 2/5, 2
Let x(a) be the second derivative of -3*a**5/40 + a**4/8 + a**3 - 3*a**2 + 21*a. Factor x(r).
-3*(r - 2)*(r - 1)*(r + 2)/2
Factor 0 - 1/3*u**2 - 1/3*u**3 + 0*u.
-u**2*(u + 1)/3
Let k = 25 + -22. Suppose 2/5*s**k + 0 + 0*s**2 + 4/5*s**4 + 0*s + 2/5*s**5 = 0. Calculate s.
-1, 0
Let b(x) be the second derivative of -x**3/6 - x**2/2 - 2*x. Let g be b(-3). Factor 8*d - 8*d - d**3 + 4*d**g + 3*d**3.
2*d**2*(d + 2)
Let v(t) be the third derivative of t**5/510 + 5*t**4/102 + 25*t**3/51 - 37*t**2. Factor v(p).
2*(p + 5)**2/17
Let g be (-1*(-1)/(-3))/((-2)/18). What is a in 1/4*a + 0 + 0*a**2 - 1/4*a**g = 0?
-1, 0, 1
Let v(p) = -p + 9. Let a be v(6). Find z, given that a + 1 + z**3 + 6*z**3 + 23*z**2 + 10*z + 10*z = 0.
-2, -1, -2/7
Let k(n) = -6*n**2 - 1. Let g be k(1). Let l = g + 7. Find f such that 0*f**3 + 0*f - 1/2*f**5 + 0*f**2 + l + 1/2*f**4 = 0.
0, 1
Let v(a) be the third derivative of 1/30*a**5 + 0 + 2*a**2 + 0*a**6 + 0*a + 0*a**4 + 0*a**3 - 1/105*a**7. Factor v(n).
-2*n**2*(n - 1)*(n + 1)
Suppose -6*y + 29 = 11. Determine u so that 35*u**5 + 0*u**2 + u**4 - u**2 + 2*u**3 - 36*u**5 - u**y = 0.
-1, 0, 1
Factor -16/21*o - 32/21 - 2/21*o**2.
-2*(o + 4)**2/21
Let y(l) be the first derivative of -l**6/4 - 3*l**5/10 + 3*l**4/8 + l**3/2 + 14. Factor y(a).
-3*a**2*(a - 1)*(a + 1)**2/2
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