) = 0.
0, 1
Let o(i) be the third derivative of 1/30*i**6 + 0*i + 1/15*i**5 - 1/105*i**7 - 1/12*i**4 - 1/168*i**8 + i**2 - 1/3*i**3 + 0. Factor o(z).
-2*(z - 1)**2*(z + 1)**3
Factor 117*v + v**3 + 125 + 36*v + 15*v**2 - 78*v.
(v + 5)**3
Let h(q) be the second derivative of -q**7/2160 - q**6/864 + q**5/360 - 7*q**4/12 - 5*q. Let n(c) be the third derivative of h(c). Solve n(v) = 0 for v.
-1, 2/7
Let r(w) = 36*w**2 + 21*w. Let g = -2 - 0. Let v(q) = -5*q**2 - 3*q. Let k(y) = g*r(y) - 15*v(y). Factor k(u).
3*u*(u + 1)
Let z = -32/3 + 34/3. Factor 1/3 - q + z*q**2.
(q - 1)*(2*q - 1)/3
Let x = 40 + -199/5. Let l be 0/2*(-3 - -2). Factor x*i**2 + 1/5*i + l.
i*(i + 1)/5
Let q(r) be the third derivative of -r**8/560 + r**7/350 + r**6/200 - r**5/100 - 5*r**2. Determine p, given that q(p) = 0.
-1, 0, 1
Let n(o) be the first derivative of 1/13*o**4 - 3 + 1/39*o**6 - 3/13*o**2 + 6/65*o**5 - 4/39*o**3 - 2/13*o. Factor n(q).
2*(q - 1)*(q + 1)**4/13
Let b(g) = -25*g**2 + 19*g + 8. Let n(i) = 66*i**2 + 13*i - 128*i + 21*i + 58*i**2 - 41. Let h(o) = -11*b(o) - 2*n(o). Factor h(q).
3*(q - 1)*(9*q + 2)
Let s = -551 - -1669/3. Suppose 2/3*b**4 + 0 + 10/3*b**3 + 8/3*b + s*b**2 = 0. What is b?
-2, -1, 0
Factor -45*l**2 + 2 + 49*l**2 + 6 - 12*l.
4*(l - 2)*(l - 1)
Let j(f) = -52*f**5 - 222*f**4 - 292*f**3 - 144*f**2 - 10*f - 6. Let g(u) = u**4 - u + 1. Let h(i) = -6*g(i) - j(i). Determine l, given that h(l) = 0.
-2, -1, -2/13, 0
Let i = 157 - 155. Let o(x) be the third derivative of 1/2*x**3 + x**i + 0 + 0*x + 3/4*x**4 + 9/20*x**5 + 1/10*x**6. Factor o(g).
3*(g + 1)**2*(4*g + 1)
Let a = 0 + 3. Let d(c) be the second derivative of 5/12*c**4 + 1/3*c**a + 0*c**2 + 2*c + 0. Factor d(l).
l*(5*l + 2)
Let s be 6*(-6)/(-1440) - 6/(-16). Factor 0 - 4/5*w**4 + 2/5*w**2 + 0*w + s*w**3.
-2*w**2*(w - 1)*(2*w + 1)/5
Let h(j) be the second derivative of 1/30*j**4 + 0*j**3 - 1/75*j**6 + 0 - 1/50*j**5 + 0*j**2 + 1/105*j**7 + 3*j. Factor h(z).
2*z**2*(z - 1)**2*(z + 1)/5
Let b(u) be the third derivative of -2/735*u**7 + 0*u**6 + 0*u + 0 + 1/105*u**5 - 2*u**2 - 1/84*u**4 + 1/1176*u**8 + 0*u**3. Factor b(n).
2*n*(n - 1)**3*(n + 1)/7
Let g be 4/22 - (-30)/(-165). Find u such that g + 0*u + 4/9*u**2 + 2/3*u**3 + 2/9*u**4 = 0.
-2, -1, 0
Let k(c) = 2*c**2 + 4*c - 5. Let v be k(-5). Let i be v/6 + (-3)/18. Factor 2/3*l**i + 0*l**3 + 0*l**2 + 0*l + 0.
2*l**4/3
Let u(j) = j**2 - 2*j - 1. Let y be u(3). Determine q, given that 2*q**3 - 4*q**3 - 4*q**y + 0*q**3 + 0*q**3 = 0.
-2, 0
Let -2*r**3 - 5 - 4*r**2 + 17 + 24*r - 32*r + 18*r = 0. Calculate r.
-3, -1, 2
Suppose -4*x - p + 28 = 0, 3*p - 12 = -5*x + 30. Let h(v) be the second derivative of 0 - 1/9*v**3 - 1/90*v**x + 1/30*v**5 + 0*v**4 - v + 1/6*v**2. Factor h(u).
-(u - 1)**3*(u + 1)/3
Suppose r + 9 = 4*r. Let x(g) be the third derivative of -1/108*g**4 - g**2 + 0 + 0*g**r + 1/540*g**6 + 0*g + 0*g**5. Factor x(o).
2*o*(o - 1)*(o + 1)/9
Let p be 90/27 - (-4)/6. Suppose -c + 0*c + 4 = -5*d, p*d - 3*c + 12 = 0. Factor -1/2*k**4 + 0*k + d + 0*k**2 + 1/2*k**3.
-k**3*(k - 1)/2
Let b(n) be the second derivative of -n**6/240 + 3*n**5/80 - 5*n**4/96 + 16*n. Factor b(f).
-f**2*(f - 5)*(f - 1)/8
Let t be 43/12 - (-4)/(-16). Let b be (-3 + 6 + -3)/(-2). Determine m so that 0*m - 4/3*m**2 + b + t*m**5 + 6*m**3 - 8*m**4 = 0.
0, 2/5, 1
Suppose 6*h - 5*h = 3. Suppose 2*z + 2*r = r - 1, -z - 13 = h*r. Solve 0 + 2*d**z - 4/3*d = 0 for d.
0, 2/3
Let s(l) be the first derivative of 2 - 3/20*l**4 - 2/5*l - 9/10*l**2 - 2/3*l**3. Factor s(f).
-(f + 1)*(f + 2)*(3*f + 1)/5
Factor -7*t**3 + 6*t**3 + 5*t**4 - 7*t**4 + t**2.
-t**2*(t + 1)*(2*t - 1)
Let f = -1 - -1. What is k in 0*k + 0*k**3 - 1/3*k**5 - 1/3*k**4 + f*k**2 + 0 = 0?
-1, 0
Let a(j) be the first derivative of j**6/360 + j**5/30 + j**4/6 - j**3/3 + 3. Let g(n) be the third derivative of a(n). Solve g(b) = 0 for b.
-2
Suppose -4*t = 4*c - 3*c - 23, -3*t = 3*c - 15. Let y be 1/(1 - t/9). Find m such that y*m**4 - 2*m**4 + 2*m**3 + m**2 + 0*m**3 = 0.
-1, 0
Let 2/3*h**2 + 0 - 2/3*h = 0. Calculate h.
0, 1
Let u = 2 - 2. Let k(c) be the first derivative of -1/20*c**4 + 1 + 1/10*c**2 - 4/25*c**5 + u*c + 4/15*c**3. Factor k(m).
-m*(m - 1)*(m + 1)*(4*m + 1)/5
Factor 40/7*b - 16/7*b**2 - 32/7 + 2/7*b**3.
2*(b - 4)*(b - 2)**2/7
Let u(q) = -q + 1. Let z(a) be the second derivative of a**6/30 + a**5/10 + 3*a**3/2 - 6*a**2 - 2*a. Let k(j) = 22*u(j) + 2*z(j). Factor k(n).
2*(n - 1)*(n + 1)**3
Let k(z) be the first derivative of -z**6/12 + 3*z**4/8 + z**3/3 + 5. Determine d, given that k(d) = 0.
-1, 0, 2
Let 8/3*j - 2/3 + 15/2*j**4 + 25/6*j**2 - 41/3*j**3 = 0. Calculate j.
-2/5, 2/9, 1
Let i be ((-2)/(-4))/(2/16). Let u(d) = -d**3 + 6*d**2 - 3*d - 6. Let t be u(5). Factor 0*j**2 - 4*j**i + 2*j**5 + j + t*j**2 - 3*j + 0*j**2.
2*j*(j - 1)**3*(j + 1)
Let v(d) = 4*d**4 - 5*d**3 - 7*d**2 + 8*d - 3. Let a(t) = -t**3 + t**2 + 1. Let k(p) = 3*a(p) + v(p). Factor k(c).
4*c*(c - 2)*(c - 1)*(c + 1)
Let d(y) be the first derivative of 0*y + 4/3*y**3 - 1 + y**2 + 1/2*y**4. Factor d(p).
2*p*(p + 1)**2
Factor 12*q**3 - 6 - 3*q**5 - 6*q + 6*q**2 - 3*q + 0*q.
-3*(q - 2)*(q - 1)*(q + 1)**3
Let s(i) be the second derivative of 3*i + 1/15*i**5 + 0*i**4 + 0*i**2 + 1/63*i**7 + 0 + 0*i**3 - 1/15*i**6. Factor s(x).
2*x**3*(x - 2)*(x - 1)/3
Let x(l) = 2*l**3 + 3*l**2 - 6*l + 3. Let o be x(1). Determine g, given that 2/5*g**o + 8/5 - 8/5*g = 0.
2
Let -2/5*g - 2/5*g**2 + 2/5 + 2/5*g**3 = 0. What is g?
-1, 1
Let s(u) be the third derivative of u**8/840 - u**7/140 + u**6/60 - u**5/60 + u**3/3 + 2*u**2. Let r(a) be the first derivative of s(a). Factor r(g).
2*g*(g - 1)**3
Let p(n) be the second derivative of n**4/60 + n**3/30 + 7*n. Suppose p(f) = 0. Calculate f.
-1, 0
Let x = 576/5 - 114. Suppose -x*r**3 + 0*r - 2/5*r**4 + 0 - 4/5*r**2 = 0. Calculate r.
-2, -1, 0
Let c(o) be the second derivative of o**4/66 - 8*o**3/33 - 9*o**2/11 - 3*o - 2. Suppose c(r) = 0. Calculate r.
-1, 9
Let n = 28 + -24. Determine c so that 2/3*c + 0*c**3 + 4/3*c**2 - 2/3*c**5 + 0 - 4/3*c**n = 0.
-1, 0, 1
Suppose -5*a + 3*a = -6. Let z(u) be the first derivative of 0*u**2 + 1/10*u**5 + 1 - 5/16*u**4 + 1/6*u**a + 0*u. Factor z(m).
m**2*(m - 2)*(2*m - 1)/4
Suppose -2*o**2 - 1 + 0*o**2 + o + 3 - 4*o**3 + 3*o**3 = 0. Calculate o.
-2, -1, 1
Let o = 6 + -2. Suppose -3*z - 2 = -o*z. Factor 4*g**4 - g**5 + 2 - z - g**2 + g**3 - 3*g**4.
-g**2*(g - 1)**2*(g + 1)
Find u, given that -27*u**2 + 1 - 32*u**2 - 5 + 60*u**2 = 0.
-2, 2
Let f(p) = 4 - 3*p - p - 2 + p**2 + p. Let k be f(3). Factor 4/3*w**k + 0*w + 0 - 2*w**3 - 10/3*w**4.
-2*w**2*(w + 1)*(5*w - 2)/3
Let g be (4/(-16))/(2*(-5)/24). Factor 6/5*f**2 + 0 + g*f**3 + 3/5*f.
3*f*(f + 1)**2/5
Let g(a) be the second derivative of -a**6/25 - 13*a**5/100 + 47*a**4/60 + a**3/3 - 4*a**2/5 + a - 9. Find f, given that g(f) = 0.
-4, -1/2, 1/3, 2
Factor 1/4*g - 1/4*g**3 - 5/4 + 5/4*g**2.
-(g - 5)*(g - 1)*(g + 1)/4
Let x(c) be the third derivative of -c**7/350 + c**6/200 + 9*c**2. Factor x(g).
-3*g**3*(g - 1)/5
Find l such that -2/9*l**2 + 4/9 - 2/9*l = 0.
-2, 1
Let o(j) = 3*j**2 - 5*j - 6. Let b = -4 + 6. Let t(d) = 6*d**2 - 11*d - 12. Let q(p) = b*t(p) - 5*o(p). Let q(k) = 0. Calculate k.
-1, 2
Let o(b) be the second derivative of b**4/42 + 17*b - 2. Determine n so that o(n) = 0.
0
Suppose -45 - 45 = 2*n. Let q = n - -157/3. Factor 14/3*m**3 - 32/3*m**2 + q*m - 4/3.
2*(m - 1)**2*(7*m - 2)/3
Suppose -5*s + 17 = 3*o, 0 = -5*o - 0*o - 5. Let z(h) = -h**2 - h + 2. Let v(t) = -t**2 - t + 2. Let l(j) = s*z(j) - 3*v(j). Factor l(u).
-(u - 1)*(u + 2)
Factor -4/17*c**2 + 2/17*c + 2/17*c**3 + 0.
2*c*(c - 1)**2/17
Suppose 9*g = 5*g + 20. Factor 1 + 3*l + l**3 + g*l**2 + 5*l**2 - 7*l**2.
(l + 1)**3
Let q(h) be the second derivative of h**4/30 - 13*h**3/15 - 14*h**2/5 + 34*h. Factor q(c).
2*(c - 14)*(c + 1)/5
Let l be 4154/18 + 4/18. Let h be 4/(-14) - (-1375)/l. Suppose 16/3*z + 5/3*z**3 + h*z**2 + 4/3 = 0. Calculate z.
-2, -1, -2/5
Let c be (-20)/(-75) + (-3)/12. Let t(m) be the third derivative of c*m**5 + 1/24*m**4 + 2*m**2 + 0 + 0*m + 0*m**3. Determine z so that t(z) = 0.
-1, 0
Suppose 3*g = -2*g - v - 45, -2*v - 18 = g. Let n = -6 - g. Factor 0*q**5 - 3*q**4 + 1 + 0 - 3*q + q**5 + n*q**3 + 2*q**2.
(q - 1)**4*(q + 1)
Suppose 1/2*a - 1/2*a**3 - 5/2*a**2