- 5 = -z. Factor k**3 + z*k - 3*k**3 - 3*k**2 + k**2.
-2*k*(k - 1)*(k + 2)
Let p(j) be the second derivative of 0*j**2 - 1/72*j**3 + 0 + 1/144*j**4 - 7*j. Find b, given that p(b) = 0.
0, 1
Let b(o) be the second derivative of o**6/45 - 3*o**5/10 + 2*o**4/3 + 3*o**3/2 - 7*o. Let u(g) be the second derivative of b(g). Let u(m) = 0. Calculate m.
1/2, 4
Let g = -1170 + 3514/3. Factor 2/3*x**4 - g*x**2 - 2/3*x**3 + 0*x + 0.
2*x**2*(x - 2)*(x + 1)/3
Factor -1/4*b**2 + 1/2*b + 0.
-b*(b - 2)/4
Suppose -7*j + 5*j + 6 = 0. Let y be (-4 - j - -3) + (-42)/(-10). Let 0*w**2 - 1/5*w**3 + y*w + 0 = 0. Calculate w.
-1, 0, 1
Let d be -2 - 126/(-18) - (-14)/(-3). Let l be -2 + 34/6 + -2. Factor l*c**2 + 7/3*c + 1 + d*c**3.
(c + 1)**2*(c + 3)/3
Let f(s) be the third derivative of -s**9/7560 - s**8/1680 + s**7/1260 + s**6/180 + s**4/3 - 6*s**2. Let b(c) be the second derivative of f(c). Factor b(z).
-2*z*(z - 1)*(z + 1)*(z + 2)
Let i = 499 + -997/2. Let c(z) be the second derivative of 3/10*z**5 + 0*z**4 + 0*z**6 - 1/14*z**7 - 5*z - i*z**3 + 0 + 0*z**2. Suppose c(u) = 0. What is u?
-1, 0, 1
Let q(c) = -67*c + 1610. Let t be q(24). Suppose -4/11*a - 2/11*a**t + 0 = 0. What is a?
-2, 0
Let o = -19 + 23. Factor 4*r**5 - r - 8*r**3 - 3*r**4 + 5*r - 4*r**o + 8*r**2 + 3*r**4 - 4.
4*(r - 1)**3*(r + 1)**2
Let r(n) be the first derivative of n**3/5 + 27*n**2/10 + 42*n/5 + 101. Factor r(f).
3*(f + 2)*(f + 7)/5
Let b(g) be the first derivative of -2/33*g**3 + 2/55*g**5 + 0*g + 1/11*g**2 - 1/22*g**4 + 11. Find d, given that b(d) = 0.
-1, 0, 1
Let h(m) be the first derivative of -m**5/10 + 3*m**4/8 - m**2 + 95. Find r, given that h(r) = 0.
-1, 0, 2
Let y(z) = -22*z**3 + 1785*z**2 - 53971*z + 52208. Let i(a) = 7*a**3 - 595*a**2 + 17991*a - 17403. Let h(r) = 7*i(r) + 2*y(r). Factor h(x).
5*(x - 59)**2*(x - 1)
Suppose 2*p - 4*j - 1 + 13 = 0, 2*p - 2*j + 2 = 0. Let -3*k**2 - 12 - 9*k - p*k - k + 2*k = 0. Calculate k.
-2
Let t(m) be the second derivative of 7*m**7/9 + 406*m**6/45 + 337*m**5/30 - 116*m**4 + 144*m**3 - 25*m + 2. Determine l, given that t(l) = 0.
-36/7, 0, 1
Let w(s) be the first derivative of -1/2*s**6 - 73*s**3 - 129/4*s**4 - 33/5*s**5 - 84*s**2 + 13 - 48*s. Factor w(n).
-3*(n + 1)**3*(n + 4)**2
Suppose -1248*q = -1236*q - 48. Determine p so that 3/4*p**3 + 5/4*p**2 - p**q - 3/4*p - 1/4 = 0.
-1, -1/4, 1
Let j = -1205 + 1213. Let z(m) be the first derivative of -4/3*m**3 - 16*m + 2 - j*m**2. Determine q, given that z(q) = 0.
-2
Let n(d) = 5*d**4 - 10*d**3 + 4*d**2 + 4. Let t(y) = 5*y**4 - 10*y**3 + 5*y**2 + 5. Let h(z) = -5*n(z) + 4*t(z). Find o such that h(o) = 0.
0, 2
Let c be (-1)/(-2) + (-3)/6. Suppose 3*j - 4 = q, c = -q - 2 + 4. Factor -2/7*x**j - 2/7*x + 4/7.
-2*(x - 1)*(x + 2)/7
Let g(n) be the third derivative of n**8/10920 - n**7/5460 - n**6/585 + n**5/195 + 23*n**3/6 - 12*n**2. Let k(j) be the first derivative of g(j). Factor k(x).
2*x*(x - 2)*(x - 1)*(x + 2)/13
Let a(o) = 7*o**3 + 4417*o**2 + 1305377*o + 128361873. Let b(m) = 15*m**3 + 8830*m**2 + 2610755*m + 256723745. Let c(r) = -5*a(r) + 2*b(r). Factor c(t).
-5*(t + 295)**3
Let q(j) be the first derivative of 19*j**3/3 + 14*j**2 - 5*j + 4. Let k(v) = -56*v**2 - 84*v + 16. Let s(l) = -3*k(l) - 8*q(l). Factor s(g).
4*(g + 2)*(4*g - 1)
Let f(t) be the first derivative of -1/2*t**4 + 4*t**2 + 8*t - 36 - 2/3*t**3. Factor f(m).
-2*(m - 2)*(m + 1)*(m + 2)
Let p(j) = 17*j**2 + 12*j + 4. Let h(d) = d**2 - 2. Let n(c) = -2*h(c) - 2*p(c). Factor n(i).
-4*(3*i + 1)**2
Let s = 18 - 16. Factor o**3 + 0*o**2 - o**5 + 5*o**4 - s*o**2 - 3*o**4.
-o**2*(o - 2)*(o - 1)*(o + 1)
Suppose -5 + 1 = -2*o. Let x = o - 0. Factor s**x + 6*s + 2*s**2 - 9 + 0 + 0*s.
3*(s - 1)*(s + 3)
Let g(h) be the third derivative of h**8/224 - h**7/70 - h**6/20 + h**5/20 + 3*h**4/16 + 143*h**2. Suppose g(s) = 0. What is s?
-1, 0, 1, 3
Let g(s) be the second derivative of s**5/100 + 2*s**4/15 - 2*s**3/3 + 2*s + 35. Factor g(i).
i*(i - 2)*(i + 10)/5
Let b = 62 - 67. Let g be (b - (-135)/25)/(16/10). Factor -3/2*x + 9/4 + g*x**2.
(x - 3)**2/4
Let h = 646/165 + -116/33. Find z, given that -2/5*z**4 + 4/5 - 6/5*z**3 + 6/5*z - h*z**2 = 0.
-2, -1, 1
Factor l**3 - 8*l**2 + 5*l**3 + 3*l - 8*l**3 - 11*l.
-2*l*(l + 2)**2
Let l(w) be the third derivative of w**8/168 + w**7/15 + 19*w**6/60 + 5*w**5/6 + 4*w**4/3 + 4*w**3/3 - 29*w**2. Factor l(i).
2*(i + 1)**3*(i + 2)**2
Let h(z) = -3*z**3 - 3*z**2 + 3*z + 1. Let b(i) be the first derivative of -1/3*i**3 + 1/2*i**2 + 0*i - 1/4*i**4 + 4. Let m(d) = -6*b(d) + 3*h(d). Factor m(j).
-3*(j - 1)*(j + 1)**2
Suppose 48/5 + 272/5*c - 316/5*c**3 - 36/5*c**5 - 276/5*c**4 + 308/5*c**2 = 0. Calculate c.
-6, -2, -1/3, 1
Let o(m) = 54 - m**2 - 54 + m. Let x(d) = 5*d**2 - 5*d. Let n(v) = 4*o(v) + x(v). Factor n(l).
l*(l - 1)
Let u(j) be the third derivative of j**8/40 + 39*j**7/350 + 31*j**6/200 - j**5/100 - 9*j**4/40 - j**3/5 - 5*j**2. Solve u(x) = 0 for x.
-1, -2/7, 1/2
Let z(b) be the second derivative of b**7/84 - b**5/40 - 49*b + 2. Factor z(h).
h**3*(h - 1)*(h + 1)/2
Let c be (1 - -3)/(-1) - (-7 + 4). Let h be (-2 - 4)/(-2) + c. Suppose 0*f + 9/2*f**3 + 0 - 3*f**h = 0. Calculate f.
0, 2/3
Let f(g) = -g**3 + 11*g - 5. Let a(l) = -6*l + 3. Suppose 12 = -5*c - s, -3*s + 6*s - 9 = 0. Let w(r) = c*f(r) - 5*a(r). Find m such that w(m) = 0.
-1, 0, 1
Let u(c) be the third derivative of -2*c**7/735 - c**6/210 + 2*c**5/21 - 4*c**4/21 + 296*c**2. Factor u(j).
-4*j*(j - 2)*(j - 1)*(j + 4)/7
Let s(n) be the first derivative of n**5/5 - n**4/2 - 4*n**3 + 4*n**2 + 32*n - 576. What is g in s(g) = 0?
-2, 2, 4
Let q(n) be the third derivative of -n**6/40 - n**5/5 + 2*n**4 + 32*n**3 + 98*n**2 - 1. Determine h so that q(h) = 0.
-4, 4
Determine t so that -36512*t**2 + 1800 + 577*t + 3*t**3 + 36590*t**2 + 83*t = 0.
-10, -6
Let d(x) be the second derivative of -x**6/15 + 2*x**5/5 - x**4/2 - 4*x**3/3 + 4*x**2 + 11*x. Factor d(a).
-2*(a - 2)**2*(a - 1)*(a + 1)
What is b in -b**4 + 5*b**3 + 36*b**2 + 35 - 3*b**3 + 0*b**3 + 0 + 88*b + 29 = 0?
-2, 8
Let k = 222 - 220. Let t(s) be the first derivative of -1/6*s**4 - k - 4/9*s**3 + 0*s - 1/3*s**2. Factor t(y).
-2*y*(y + 1)**2/3
Let h(g) be the first derivative of 5*g**4/12 + 26*g**3/3 + 18*g**2 - 56*g/3 + 525. Factor h(q).
(q + 2)*(q + 14)*(5*q - 2)/3
Let w = -929/2 + 465. Let i(b) be the second derivative of 1/10*b**6 + 3/20*b**5 + 0*b**2 - 1/4*b**4 - 9*b + 0 - w*b**3. Solve i(f) = 0 for f.
-1, 0, 1
Let j(l) = -3*l**2 - 3*l - 2. Let x be j(-1). Let n be ((-3)/33)/((-1)/x*-1). Suppose -n*u**2 - 2/11*u**3 + 2/11 + 2/11*u = 0. What is u?
-1, 1
Suppose 9 = -5*c - 11. Let b(u) = 9*u + 10 - 9 + 2. Let q(r) = -r**2 + 10*r + 4. Let h(i) = c*b(i) + 3*q(i). Factor h(k).
-3*k*(k + 2)
Let q(o) be the second derivative of -o**4/30 + 31*o**3/15 + 32*o**2/5 - 14*o - 2. Factor q(g).
-2*(g - 32)*(g + 1)/5
Let b(r) be the second derivative of -2*r**6/15 + 3*r**5/20 + 25*r**4/12 + r**3 + 33*r - 3. Factor b(s).
-s*(s - 3)*(s + 2)*(4*s + 1)
Let f = -8788 - -8790. Let -16/7*w**f - 8/7 - 4/7*w**3 - 20/7*w = 0. What is w?
-2, -1
Let g(s) be the first derivative of 9*s**4/2 - 13*s**3 + 12*s**2 - 3*s + 75. Let g(y) = 0. Calculate y.
1/6, 1
Let j(w) be the third derivative of -w**5/130 - w**4/156 + 2*w**3/39 + 20*w**2 - 2. Factor j(x).
-2*(x + 1)*(3*x - 2)/13
Let c(i) be the first derivative of i**4/10 - 8*i**3/15 - i**2/5 + 8*i/5 - 187. Factor c(b).
2*(b - 4)*(b - 1)*(b + 1)/5
Let h(z) be the first derivative of -z**5/5 - 3*z**4/4 - z**3 - z**2/2 + 136. Factor h(d).
-d*(d + 1)**3
Let a(q) be the third derivative of -q**5/100 + 3*q**4/20 + 4*q**2 + 3*q. Factor a(z).
-3*z*(z - 6)/5
Let i(k) be the first derivative of -4*k**5/5 + 3*k**4 + 100*k**3/3 + 42*k**2 + 43. Factor i(o).
-4*o*(o - 7)*(o + 1)*(o + 3)
Let d(q) = q**2 - 34*q + 149. Let r be d(5). Factor 5/4*t**r + 1/2*t - 5/4*t**2 + 0 - 1/2*t**3.
t*(t - 1)*(t + 1)*(5*t - 2)/4
Let u(t) = t**2 - 18*t + 13. Let w be u(17). Let p be w/18 + (-8914)/(-18). Determine j so that 3*j**3 - 3*j**5 - p + 495 = 0.
-1, 0, 1
Let r be -5*((-8)/4)/2. Suppose m - 16 = r*m, -16 = -5*n - m. Suppose n*s - 3*s**5 - 4*s = 0. What is s?
0
Determine s so that 5*s**3 - 24*s - 488*s**2 + 484*s**2 - s**3 = 0.
-2, 0, 3
Let p(i) be the first derivative of 18 - 6*i + 0*i**3 + 1/4*i**4 - 7/2*i**2. Sol