 - 1/18*a**4 - 1/45*a**6 + 0*a + 0*a**3 + 5*a**2 + 1/315*a**7. Factor g(i).
2*i*(i - 2)*(i - 1)**2/3
Let b be (-20)/(-185) + 4 + -4. Let w = b - -62/111. Let -w*c - 1/6 - 2/3*c**3 - 1/6*c**4 - c**2 = 0. What is c?
-1
Let a(t) = 1904*t**2 - 1906*t + 2. Let g be a(1). Let x = 4 - 2. Factor -6/7*v**x + g - 2/7*v**3 + 0*v.
-2*v**2*(v + 3)/7
Let k(m) be the third derivative of m**5/150 - 2*m**4/5 + 21*m**3/5 - 232*m**2. Factor k(t).
2*(t - 21)*(t - 3)/5
Let o(w) be the second derivative of 2*w**6/75 + 14*w**5/25 + 4*w**4 + 20*w**3/3 - 50*w**2 - 179*w - 3. Factor o(i).
4*(i - 1)*(i + 5)**3/5
Suppose 0 = -3*r - 2*u - 363, -4*u - 461 = 4*r - 9*u. Let c be 2/(-7) + (-272)/r. Factor 0*p**2 + p - 7 + p**c + 1 + 4.
(p - 1)*(p + 2)
Suppose 0 = -2*p - n + 9 + 15, -p - n = -12. Solve 19*t - p*t**2 - 16 - 5*t**3 - 43*t + 3*t**3 = 0 for t.
-2
Let o(l) be the second derivative of -l**4/6 - 2*l**3/3 + 8*l**2 + l + 19. Let o(w) = 0. What is w?
-4, 2
Let i(t) = 2*t**2 - 4*t + 7. Let a be i(3). Suppose 14*b - 10 = a*b. Suppose v**2 - 4*v**4 - b*v + 11*v**2 + 2*v = 0. Calculate v.
-2, 0, 1
Suppose -44*w + 47*w = -2*n - 6, 2*n = -2*w - 2. Let c(i) be the first derivative of -1/2*i**4 + 3/4*i**2 - i + 1/12*i**6 + 0*i**5 - 7 + 1/3*i**n. Factor c(r).
(r - 1)**3*(r + 1)*(r + 2)/2
Factor 24*o**2 + 20*o + 207*o**3 - 401*o**3 + 203*o**3 + o**4.
o*(o + 2)**2*(o + 5)
Factor 0*q + 3/2*q**3 - 27/8*q**5 + 0*q**2 + 6*q**4 + 0.
-3*q**3*(q - 2)*(9*q + 2)/8
Factor -6*m**2 + 8*m**2 + 18*m + 10*m - 4*m**2 - 48.
-2*(m - 12)*(m - 2)
Let s(i) be the first derivative of -i**3 + 24*i**2 - 84*i + 191. Factor s(h).
-3*(h - 14)*(h - 2)
Let y(d) be the third derivative of d**7/70 + d**6/20 - 3*d**5/5 + 7*d**4/4 - 5*d**3/2 + 109*d**2. Factor y(h).
3*(h - 1)**3*(h + 5)
Factor 8 - 2 - 4*p**2 + 3*p**2 + 3*p - 18*p**3 - 5*p**2 + 15*p**3.
-3*(p - 1)*(p + 1)*(p + 2)
Let m(k) = 3*k**2 - 9*k + 6. Suppose -n - p + 13 = 3*n, -5*n = p - 15. Let y(h) = -h**2 + h. Let t(a) = n*m(a) + 10*y(a). Let t(b) = 0. What is b?
-3, 1
Let d(h) be the third derivative of -1/15*h**5 - 14*h**2 + 10/3*h**3 + 0 - 2/3*h**4 + 0*h. What is x in d(x) = 0?
-5, 1
Let g(o) be the third derivative of -o**7/945 + o**6/540 + o**5/90 - 11*o**4/12 + 3*o**2. Let i(u) be the second derivative of g(u). Solve i(x) = 0 for x.
-1/2, 1
Determine z so that -8/3 + 1/3*z**2 + 2/3*z = 0.
-4, 2
Let i(d) be the first derivative of -d**6/195 + 3*d**5/65 - d**4/6 + 4*d**3/13 - 4*d**2/13 + 3*d - 19. Let h(s) be the first derivative of i(s). Factor h(w).
-2*(w - 2)**2*(w - 1)**2/13
Let a(l) = l**3 + 265*l**2 - 3813*l - 13887. Let m(h) = 2*h**3 + 266*h**2 - 3814*h - 13890. Let q(x) = -6*a(x) + 5*m(x). Let q(z) = 0. Calculate z.
-3, 34
Let b(h) be the second derivative of -h**8/1120 - 13*h**7/1680 - 11*h**6/480 - h**5/40 + 5*h**4/6 - 12*h. Let u(p) be the third derivative of b(p). Factor u(y).
-3*(y + 1)*(y + 2)*(4*y + 1)/2
Let k(g) = g + 7. Suppose 29 = z + 33. Let x be k(z). Find p, given that 0 - 4/5*p**4 + 4/5*p**2 - 2/5*p + 2/5*p**5 + 0*p**x = 0.
-1, 0, 1
Let u be (-76)/(-18) - 358/1611. Factor 1/7*n**5 + 4/7*n + 0 - 2/7*n**u - 3/7*n**3 + 4/7*n**2.
n*(n - 2)**2*(n + 1)**2/7
Suppose -5*n = -4*c - 21, -20 = -3*n - 0*n - 5*c. Let s be (-2)/n*(3 + -4). Suppose -4/5 - s*q + 2/5*q**2 = 0. What is q?
-1, 2
Let q be 13/((-390)/20)*(1 + -15). Let k(p) be the first derivative of q*p**3 + 10 + 4*p**4 + 0*p - 4*p**2. Determine r so that k(r) = 0.
-2, 0, 1/4
Let g(v) be the first derivative of v**4/16 + 11*v**3/6 + 19*v**2/2 + 18*v - 273. Factor g(q).
(q + 2)**2*(q + 18)/4
Let t(q) = q**2 + 8*q + 3. Let m(i) = i. Suppose 5 + 7 = -3*h. Let o(b) = h*m(b) + t(b). Solve o(a) = 0.
-3, -1
Let t(r) = -r**3 - 17*r**2 - 35*r - 13. Let i(q) = 3*q**3 + 35*q**2 + 69*q + 27. Let f be 4/(-16) + (-11)/4. Let g(v) = f*i(v) - 5*t(v). Factor g(b).
-4*(b + 1)*(b + 2)**2
Let p(u) = 3*u. Let s(k) = -k. Let w(q) = -3*p(q) - 8*s(q). Let n(l) = l**2 + 8*l. Let i(m) = n(m) + 6*w(m). Find f such that i(f) = 0.
-2, 0
Let p(r) = -r**4 + 24*r**3 + 27*r**2 - 40*r. Let o(m) = 2*m**4 - 60*m**3 - 66*m**2 + 100*m. Let y(j) = -5*o(j) - 12*p(j). Let y(c) = 0. Calculate c.
-5, -2, 0, 1
Factor -1/7*l**4 + 8/7*l + 4/7 + 3/7*l**2 - 2/7*l**3.
-(l - 2)*(l + 1)**2*(l + 2)/7
Let p = -46984/5 - -9397. Solve p*t**2 + 6/5 + t = 0.
-3, -2
Let k(c) be the first derivative of -c**4/12 - 3*c**3 - 28*c**2 + 196*c/3 - 108. Factor k(o).
-(o - 1)*(o + 14)**2/3
Let p(y) be the first derivative of y**6/15 - 34*y**5/25 + 8*y**4/5 - 198. Solve p(o) = 0 for o.
0, 1, 16
Let v be (-30)/(-75) + (-4)/10. Let m(h) be the third derivative of -1/150*h**5 - 1/30*h**4 - 5*h**2 + v + 0*h - 1/15*h**3. Factor m(b).
-2*(b + 1)**2/5
Let j be 2 + -3 - (-7 - -2). Find m, given that -8*m**5 + 7*m**5 + 2*m**2 - m**2 - 2*m**2 + m**3 + m**j = 0.
-1, 0, 1
Let o(s) be the first derivative of 0*s**2 - 7 + 2/3*s**3 + s**4 + 0*s. Factor o(n).
2*n**2*(2*n + 1)
Let k = 69/22 + -577/198. Let q(j) be the first derivative of -j**2 - 8 + 4/3*j + k*j**3. Find f, given that q(f) = 0.
1, 2
Suppose 746*i - 3*i**5 + 32*i**3 - 24*i**4 + 24*i**2 - i**5 - 774*i = 0. What is i?
-7, -1, 0, 1
Let r(z) be the third derivative of 1/6*z**6 + 0 - 17*z**2 + 1/2*z**5 + 0*z - 5/6*z**4 - 25/6*z**3 - 1/42*z**7. Suppose r(w) = 0. Calculate w.
-1, 1, 5
Let b(g) = -2*g**4 + 15*g**3 - 25*g + 32. Let l(k) = -k**4 + 7*k**3 - 13*k + 16. Let w(u) = 3*b(u) - 7*l(u). Solve w(a) = 0.
-2, 2
Let x(f) = -f**2 + 4*f - 40. Let s be x(0). Let n = -40 - s. Let 0*p**3 + n*p**2 + 0*p + 1/7*p**4 + 0 = 0. What is p?
0
Suppose -2*f + 0 + 24/11*f**4 + 2/11*f**5 - 24/11*f**2 + 20/11*f**3 = 0. What is f?
-11, -1, 0, 1
Find z, given that 24/5*z**3 - 3/5*z**2 + 0 + 0*z = 0.
0, 1/8
Suppose -4*t + 5 = -0*t - 3*k, 3*t + 4*k = 10. Suppose -3*l + t = -7. Determine n, given that -11*n**2 - 33*n - 6*n**3 + 6 + 59*n**2 - 15*n**l = 0.
2/7, 1
Let n be (96/152)/6 - (-471)/399. Determine c, given that -3/7*c**4 - 12/7 + n*c**2 + 12/7*c - 6/7*c**3 = 0.
-2, 1
Let m(r) be the first derivative of 363*r - 47*r**3 + 48*r**3 - 30*r**2 - 3*r**2 + 40. Factor m(f).
3*(f - 11)**2
Let y = -78/1723 - -4148/15507. Determine o, given that 2/3*o**2 + 2/9 + 2/3*o + y*o**3 = 0.
-1
Let i(t) = 2*t**2 - 50*t + 268. Let k(a) = -2*a**2 + 49*a - 267. Let b(n) = 3*i(n) + 4*k(n). Factor b(c).
-2*(c - 12)*(c - 11)
Let p(x) be the third derivative of -x**8/3360 - x**7/840 + x**5/120 + x**4/48 - 11*x**3/6 - x**2. Let c(i) be the first derivative of p(i). Factor c(r).
-(r - 1)*(r + 1)**3/2
What is d in -29 - 20 + 99*d**2 - 21 - 19 - 102*d + 92 = 0?
1/33, 1
Let a(g) be the first derivative of -4*g**3/3 + 74*g**2 + 152*g + 553. Factor a(c).
-4*(c - 38)*(c + 1)
Let u(q) be the first derivative of -8*q - 1/3*q**6 + 9 - 2/3*q**3 + 2/5*q**5 + 5/2*q**4 - 8*q**2. Factor u(r).
-2*(r - 2)**2*(r + 1)**3
Let q(x) be the first derivative of -5*x**2 + 6 + 25*x + 1/3*x**3. Factor q(p).
(p - 5)**2
Let k(g) = -4*g - g + 9*g**3 - 12*g**3 - 6*g**2. Let l(f) = 3*f**3 + 6*f**2 + 6*f. Let m(h) = 3*k(h) + 2*l(h). Suppose m(d) = 0. What is d?
-1, 0
Let u = -21745 - -21754. Suppose 3/2*c**5 + u*c**4 + 0 + 18*c**3 + 15*c**2 + 9/2*c = 0. Calculate c.
-3, -1, 0
Let o(r) be the first derivative of 1681*r**3/6 + 41*r**2 + 2*r - 25. Solve o(s) = 0 for s.
-2/41
Let b(x) be the second derivative of 0 + 3/16*x**4 + 3/2*x**2 - x**3 + 1/40*x**5 - 8*x. Let d(r) be the first derivative of b(r). Factor d(a).
3*(a - 1)*(a + 4)/2
Let l = 13098 + -13096. Solve 38/9*a**l - 8/9 - 28/9*a**3 + 2/3*a**4 - 8/9*a = 0 for a.
-1/3, 1, 2
Let n = -112 - -112. Let g be (4/(-16))/(n + -1). Factor 3/4*d - g*d**2 - 1/2.
-(d - 2)*(d - 1)/4
Let l(z) be the first derivative of z**4/24 - 19*z**3/18 + 33*z**2/4 - 27*z/2 + 561. Solve l(c) = 0.
1, 9
Let f(a) be the first derivative of 4*a**3/15 - 8*a**2/5 - 48*a/5 + 335. Solve f(t) = 0.
-2, 6
Let w = 77 - 47. Suppose -o + t = -w, 5*t - 4 = 3*t. Solve -10*s - o*s**2 - 20*s**3 + 26*s + 0*s**3 = 0 for s.
-2, 0, 2/5
Let j(a) be the second derivative of 0*a**3 - 1/6*a**4 + 0 + 0*a**2 + 2*a. Let j(q) = 0. What is q?
0
Let i = 218 + -245. Let w be (-12)/(-8)*-1*24/i. Factor -1/3*l**2 - 1 - w*l.
-(l + 1)*(l + 3)/3
Let g(j) be the first derivative of -1/7*j**4 + 4/7*j - 4/21*j**3 + 2/7*j**2 - 22. Factor g(w).
-4*(w - 1)*(w + 1)**2/7
Let f(l) be the second 