(q). Find x such that a(x) = 0.
0, 1
Let w(p) be the third derivative of 0 + 8*p**2 + 1/70*p**7 - p**3 + 0*p - 3/8*p**4 + 1/20*p**5 + 3/40*p**6. Factor w(c).
3*(c - 1)*(c + 1)**2*(c + 2)
Let z(h) = h**2 + 7*h - 11. Let r be z(-8). Let v(u) = -2*u**2 + 33*u - 42. Let s(p) = -p**2 + 34*p - 41. Let d(x) = r*s(x) + 4*v(x). Factor d(l).
-5*(l - 3)**2
Solve 4*o**3 - 34*o**3 + 28*o**3 + o**4 + o**2 = 0 for o.
0, 1
Suppose t + z = -47, -5*t = 4*z + 213 + 17. Let d be (-24)/t*(-7)/(-2). Find a such that -21*a**3 - 15*a**2 - 12*a - 3 - 6*a**4 - 12*a**d - 10*a + 7*a = 0.
-1, -1/2
Let a(x) be the third derivative of -2*x**7/75 + 23*x**6/150 - 2*x**5/25 - 14*x**4/15 + 16*x**3/15 - 53*x**2. Suppose a(v) = 0. Calculate v.
-1, 2/7, 2
Let w(j) be the third derivative of -j**5/540 + j**4/216 + j**3/9 + 71*j**2. Suppose w(o) = 0. What is o?
-2, 3
Factor -1/2*u + 1/4 + 1/4*u**2.
(u - 1)**2/4
Let l be 474/(-24) - (-6)/8. Let y = l + 21. Suppose 8*o - o**y - o - 3*o - 3 = 0. What is o?
1, 3
Let m = 74128/135861 + -2/12351. Factor -2/11*i**4 - 4/11*i - m*i**3 + 2/11*i**5 + 10/11*i**2 + 0.
2*i*(i - 1)**3*(i + 2)/11
Factor -1/3 + 1/6*h + 1/2*h**2 - 1/6*h**3 - 1/6*h**4.
-(h - 1)**2*(h + 1)*(h + 2)/6
Factor 181/3*h + 2 - 59/3*h**3 + 116/3*h**2.
-(h - 3)*(h + 1)*(59*h + 2)/3
Let l be 1*(-3)/6*2 + 5. Let p be 4 - (-2 + (0 - -2)). Factor 0*g - 6*g + 2*g**3 + l*g - p*g**2 + 4.
2*(g - 2)*(g - 1)*(g + 1)
Let n(c) be the second derivative of -1/6*c**4 + 0*c**3 + 0 + 9*c + 1/10*c**5 + 0*c**2. Factor n(g).
2*g**2*(g - 1)
Let c(m) = -15*m**2 + 1. Let t(a) be the second derivative of a**4/3 + 18*a. Let x = 4 - 18. Let r(i) = x*t(i) - 4*c(i). Factor r(q).
4*(q - 1)*(q + 1)
Let p(q) = -5*q + 2. Let o be (-32)/(-24)*(-6)/4. Let c be p(o). Find u, given that -8 + 5 - c*u**2 + 0 - 15*u = 0.
-1, -1/4
Solve -1/8*d**2 + 35/8 + 17/4*d = 0.
-1, 35
Let u(p) be the first derivative of p**8/2016 - p**7/1260 - 5*p**2 - 12. Let z(g) be the second derivative of u(g). Find n such that z(n) = 0.
0, 1
Let x be 1/((-7)/2)*-7. Suppose -45 = -3*r - x*r. Factor -7 - 2*k**2 + 0*k**2 + r.
-2*(k - 1)*(k + 1)
Suppose -205*k**3 - 100 - 664*k**2 - 440*k - 596*k**4 + 496*k**4 - 8*k**5 - 211*k**3 = 0. What is k?
-5, -1, -1/2
Let n(f) = -f**2 - 14*f - 42. Let w be n(-9). Let -4/5*x + 0*x**2 + 4/5*x**w + 0 = 0. Calculate x.
-1, 0, 1
Let v(l) be the second derivative of 1/2*l**4 + 0 + 0*l**2 + 3/2*l**3 - 12*l + 1/20*l**5. What is i in v(i) = 0?
-3, 0
Let j be (0 - 2*-1)*1. Let i(y) = 12*y - 750. Let x be i(63). Factor x*w - 8/3*w**j - 4/3.
-2*(w - 2)*(4*w - 1)/3
Let l be (-3333)/(-22)*1*2. Let m = l + -1211/4. Factor -1/4*y**2 + 0 + 0*y - m*y**3.
-y**2*(y + 1)/4
Let n(k) be the third derivative of k**8/2016 - k**7/90 + k**6/60 + 7*k**5/180 - 13*k**4/144 - k**2 + 25*k. Find f such that n(f) = 0.
-1, 0, 1, 13
Let t(w) = -6*w**2 + 33*w - 69. Let m(s) = -11*s**2 + 66*s - 139. Let c(b) = 3*m(b) - 5*t(b). Factor c(g).
-3*(g - 8)*(g - 3)
Let f = -11289/56 + 1335/8. Let k = 35 + f. Factor 2/7*i**3 - 2/7*i**2 + k - 2/7*i.
2*(i - 1)**2*(i + 1)/7
Let f(n) be the first derivative of 2*n**3/27 - 10*n**2/9 + 50*n/9 - 206. Find d such that f(d) = 0.
5
Let p(z) be the first derivative of -z**6/1440 + z**5/120 + 14*z**3/3 - 24. Let v(r) be the third derivative of p(r). Factor v(u).
-u*(u - 4)/4
Let b be (-4 - 26/(-10))/(((-16)/(-4))/(-16)). What is n in 0 + 104/5*n**2 + 32/5*n - b*n**3 = 0?
-2/7, 0, 4
Let v(q) be the first derivative of -5/3*q**3 + 0*q**2 + 2 + 5*q. Factor v(f).
-5*(f - 1)*(f + 1)
Let v(f) = 2*f**3 + 45*f**2 + 297*f + 686. Let s(z) = -8*z**3 - 94*z**2 + 142*z - 110*z**2 - 1329*z + 25*z**2 - 2744. Let r(i) = 6*s(i) + 22*v(i). Factor r(y).
-4*(y + 7)**3
Factor -17 - 26 + 15*a - 2*a**2 - 8 + 1 + 7*a**2.
5*(a - 2)*(a + 5)
Suppose -24 = -s + 24*s - 24. Determine v so that 0 + 0*v**2 - 1/4*v**4 - 1/4*v**3 + s*v = 0.
-1, 0
Let w(d) = d**3 - 12*d**2 - 13*d + 3. Let b be w(13). Let c = b + -1. What is u in 4*u**3 - c*u - 3*u**2 - 2*u**3 + 2*u**4 + u**2 = 0?
-1, 0, 1
Solve c**2 - 5*c**2 + 18*c - 62500 - 72*c + 1054*c = 0 for c.
125
Determine y so that 3/7*y**2 - 129/7 - 18*y = 0.
-1, 43
Suppose -2*c + 15 = 1. Let q(f) be the first derivative of c*f - 3 + f**2 + 7*f - 10*f - 2*f**3. Determine i so that q(i) = 0.
-2/3, 1
Let t(k) be the third derivative of -1/1680*k**8 + 0*k - 1/525*k**7 + 1/120*k**4 + 0*k**3 + 0*k**6 + 1/150*k**5 + 0 + 11*k**2. Factor t(l).
-l*(l - 1)*(l + 1)**3/5
Suppose 149*c - 6 = 147*c. Let m(x) = -4*x**2 + 4*x**3 + 9 + 3*x - 23*x + 11. Let w(r) = -r**3 + r**2 + 4*r - 4. Let y(h) = c*m(h) + 16*w(h). Factor y(z).
-4*(z - 1)**2*(z + 1)
Suppose -7*j + 45 = 5*y - 12*j, 4*j + 8 = -3*y. Let 4/9*q**2 + 0*q + 2*q**3 + 0 + 14/9*q**y = 0. Calculate q.
-1, -2/7, 0
Let w = 959/3 - 319. Let r(v) be the second derivative of 0 - 8*v + 1/120*v**5 + 1/3*v**3 - 1/12*v**4 - w*v**2. Factor r(k).
(k - 2)**3/6
Let a(z) be the first derivative of z**4/10 + 8*z**3/15 - z**2/5 - 8*z/5 - 125. Factor a(u).
2*(u - 1)*(u + 1)*(u + 4)/5
Let d = 7286 + -7284. Let q be ((-6)/(-5))/((-18)/(-20)). Let -q*z - 14/3*z**d - 8/3*z**5 + 0 + 14/3*z**4 + 4*z**3 = 0. What is z?
-1, -1/4, 0, 1, 2
Let w be 7 - 3 - -40*2. Factor 6*f**3 - w*f + 24 - 13*f**4 + 34*f**4 - 18*f**2 + 51*f**3.
3*(f - 1)*(f + 2)**2*(7*f - 2)
Let -1 - 4*w - 5*w**3 + 0*w**2 + 3 + 6*w**3 + 2*w**2 - 10 = 0. What is w?
-2, 2
Let u(j) = 5*j**4 - 20*j**3 - 25*j**2 - 10*j. Let h(t) = t**3 + t. Let l be (1/5)/((-2)/(-10)). Let g(f) = l*u(f) + 25*h(f). Let g(m) = 0. What is m?
-3, 0, 1
Suppose s = -3*l - 4, -2*s = 7*l + 24 - 14. Determine h, given that 7/2*h**s + 2 - 8*h = 0.
2/7, 2
Let q(g) be the third derivative of -1/300*g**5 + 1/3*g**3 + 0 - 7*g**2 + 0*g**4 - 1/900*g**6 + 0*g. Let a(z) be the first derivative of q(z). Factor a(i).
-2*i*(i + 1)/5
Suppose 6*p - 22 = -10. Suppose 4*l - 62 + 14 = 0. Let -4*n**3 + n**3 + 0*n**3 - l*n**p - 12*n = 0. What is n?
-2, 0
Let i(t) = -t + 16. Let r be i(9). Suppose -3*y - 1 = -r. Factor -u**4 + 4*u**3 + y*u**2 - 5*u**2 - 6*u - 3*u + u**3.
-u*(u - 3)**2*(u + 1)
Suppose 9*z = -51 + 15. Let m be 2 + 14/105 + z/30. Factor -j + 1/2 - 3/2*j**m.
-(j + 1)*(3*j - 1)/2
Let k(c) be the second derivative of c**6/6 - 71*c**5 + 25205*c**4/2 - 3579110*c**3/3 + 127058405*c**2/2 + 4*c. Find o, given that k(o) = 0.
71
Let k(c) be the second derivative of -c**5/4 - 25*c**4/12 + 20*c**3/3 + 120*c**2 + 166*c. Factor k(f).
-5*(f - 3)*(f + 4)**2
Suppose 144/5*w**2 - 2888/5 + 228*w + 4/5*w**3 = 0. Calculate w.
-19, 2
Let p(t) = t**2 + 41*t + 148. Let x be p(-37). Let k(j) be the first derivative of x*j + 1/12*j**3 - 1 + 1/4*j**2. Determine n so that k(n) = 0.
-2, 0
Let v(o) = o**3 - 18*o**2 + 19*o - 34. Let f(t) = t**2 + 8. Let h be f(-3). Let m be v(h). Factor -3/4*i**2 + 0 + m*i + 3/4*i**4 + 0*i**3.
3*i**2*(i - 1)*(i + 1)/4
Let k = -945/38 - -97195/3534. Let t = 1/31 + k. Solve -4*w + t - 8/3*w**2 + 4*w**3 = 0 for w.
-1, 2/3, 1
Let w(i) = 11*i**2 + i + 8. Let v(k) = -k**2 + k - 1. Suppose a + 1 = -5. Let j(c) = a*v(c) - w(c). Factor j(q).
-(q + 1)*(5*q + 2)
Let o be (-798)/(2 + -5) + 1*-4. Let h = o - 242. Suppose -50/3*k**3 - h*k**2 - 5/3 - 5*k**4 - 10*k = 0. What is k?
-1, -1/3
Let s(y) be the third derivative of y**8/168 + 2*y**7/105 - y**6/20 - 37*y**2. Factor s(r).
2*r**3*(r - 1)*(r + 3)
Let i be -1 + 4 + 5/20*0. Let q = 58 + -54. Factor 1/2*r**q + 0 - 1/2*r**2 + 0*r + 0*r**i.
r**2*(r - 1)*(r + 1)/2
Let l(x) be the third derivative of -x**8/144 + x**7/70 + 41*x**6/180 + x**5/45 - 5*x**4/3 + 16*x**3/9 + 217*x**2. Solve l(i) = 0.
-2, 2/7, 1, 4
Let w(l) = l**2 - l - 7. Let n be w(-3). Suppose 0*b = -4*b + n*s + 11, -3*s = -4*b + 13. Solve b*p**2 - 784 - p**3 + 784 - 4*p = 0 for p.
0, 2
Let w(j) = -j**5 + j**4 - j**2 - j. Let m(a) = 6*a**4 + 2*a**3 - 21*a**2 - 25*a. Let x(v) = 4*m(v) - 4*w(v). Find t, given that x(t) = 0.
-3, -2, 0, 2
Let z be 5/3*126/280. Let w = 1 - -1. Factor 1/4*b**3 - z*b + 0*b**w - 1/2.
(b - 2)*(b + 1)**2/4
Let v(w) be the third derivative of w**7/105 - w**5/5 + 2*w**4/3 - w**3 + 66*w**2. Suppose v(r) = 0. What is r?
-3, 1
Let w(m) = 2*m**3 - 21*m**2 + 12*m - 13. Let b be w(10). Factor 3*z + 3*z**2 - 5 - b - z + 7*z.
3*(z - 1)*(z + 4)
Let x(j) be the third derivative of -j**6/480 + j**5/48 + j**4/16 + 51*j**2. Factor x(a).
-a*(a - 6)*