at is b in q(b) = 0?
-5, -2, 1/3, 1
Let p = 1602 - 1600. Factor -1/5*y**p + 0 + 1/5*y**3 - 2/5*y.
y*(y - 2)*(y + 1)/5
Let d = -86 + 87. Suppose -5*v + d = u - 14, 3*u + 6 = 2*v. Let 0 - 1/2*t**4 + 1/2*t**2 + 0*t**v + 0*t = 0. Calculate t.
-1, 0, 1
Let c(m) = m**2. Let u(z) = -4*z**2 + 9*z - 20. Let p(g) = 6*c(g) + 2*u(g). Factor p(i).
-2*(i - 5)*(i - 4)
Let l be 1 + (0 + 1)/((-3)/(-9)). Suppose 0 = -l*v + 2312 + 432. Factor -784*m**4 - 32/7*m - v*m**5 + 0 - 64*m**2 - 336*m**3.
-2*m*(7*m + 2)**4/7
Let j(n) be the second derivative of -1/3*n**3 - 6*n + 2 + 1/12*n**4 + 0*n**2. Factor j(u).
u*(u - 2)
Let k(c) be the second derivative of c**4/60 - 9*c**3/5 + 729*c**2/10 - 12*c. Factor k(t).
(t - 27)**2/5
Let a be ((-110)/15)/22 - (2 + (-48)/9). Determine p so that 1/2 - 15/4*p + 9*p**a + 19/4*p**2 = 0.
-1, 2/9, 1/4
Suppose -1/7*a**4 + 1/7*a**2 + 30/7*a**3 + 0 - 30/7*a = 0. Calculate a.
-1, 0, 1, 30
Let z = 98 - 96. Suppose -4*q = 3*m + 3 + 5, -3*q - 6 = z*m. Find d, given that -6/5*d**3 + m - 2/5*d**4 + 2*d**2 + 2/5*d**5 - 4/5*d = 0.
-2, 0, 1
Let g be 16/48*(972/(-8))/(-9). Suppose 0*n + g*n**3 - 3*n**2 - 3/2*n**4 + 0 = 0. What is n?
0, 1, 2
Let f(w) be the second derivative of w**7/147 - 4*w**6/105 + 2*w**5/35 - 157*w. Factor f(r).
2*r**3*(r - 2)**2/7
Let d(x) be the third derivative of 0*x**3 + 1/90*x**6 + 1/108*x**4 + 2/135*x**5 + 0 + 0*x - 11*x**2 + 4/945*x**7 + 1/1512*x**8. Factor d(n).
2*n*(n + 1)**4/9
Let h(l) be the second derivative of -l**7/210 + l**5/10 + l**4/3 + l**3/3 + 5*l. Let b(z) be the second derivative of h(z). Suppose b(f) = 0. What is f?
-1, 2
Determine x, given that -30/11*x - 24/11*x**2 - 6/11*x**3 - 12/11 = 0.
-2, -1
Let m = 1994/9 + -701/3. Let i = -35/3 - m. Factor -2/9 - 2/9*y**2 - i*y.
-2*(y + 1)**2/9
Let m(i) be the first derivative of i**4 - 20*i**3/3 + 116. Factor m(w).
4*w**2*(w - 5)
Let x(a) be the first derivative of -4*a**5/15 - 164*a**4/9 - 140*a**3/9 + 328*a**2/9 + 48*a + 475. Find o, given that x(o) = 0.
-54, -1, -2/3, 1
Let t = 128 + -123. Suppose t*k = 11*k - 12. Factor -6/7 - 3/7*u**k + 9/7*u.
-3*(u - 2)*(u - 1)/7
Factor 1/3*t**2 + 20/3*t + 0.
t*(t + 20)/3
Let k(h) be the third derivative of 0 + h**3 - 1/6*h**4 + 1/20*h**5 - 1/180*h**6 + h**2 + 0*h. Let b(s) be the first derivative of k(s). Factor b(m).
-2*(m - 2)*(m - 1)
Find w, given that 2/5*w**2 - 6/5*w - 8/5 = 0.
-1, 4
Let r(z) = -8*z + 4. Let n(u) = 6*u + 0*u - u**2 + 2*u - 3 - u**3. Suppose 8*q = -135 + 111. Let v(i) = q*r(i) - 4*n(i). Suppose v(b) = 0. What is b?
-2, 0, 1
Suppose 36*w**4 - 82*w + 267*w**3 - 155*w - 92*w**3 - 213*w**2 + 278*w**3 - 39 = 0. What is w?
-13, -1/3, -1/4, 1
Let i**4 + 0*i**4 + i**4 - 8*i**2 - 2*i**2 + 391*i**3 - 383*i**3 = 0. Calculate i.
-5, 0, 1
Let n(j) = -j**2 + 47*j + 263. Let l be n(52). Suppose 0 - 6/5*b + 4/5*b**2 - 2/15*b**l = 0. What is b?
0, 3
Let w(u) be the first derivative of -1/4*u**3 + 0*u**2 + 1/16*u**4 + 9/80*u**5 + u + 3. Let q(b) be the first derivative of w(b). Factor q(i).
3*i*(i + 1)*(3*i - 2)/4
Let s = -345 - -348. Let f(o) be the second derivative of -1/65*o**5 - 1/39*o**4 - 1/13*o**2 - 1/273*o**7 + 1/65*o**6 - 2*o + 0 + 1/13*o**s. Factor f(t).
-2*(t - 1)**4*(t + 1)/13
Let d(u) be the second derivative of 0 - 3/100*u**5 - 1/75*u**6 + 0*u**4 + 1/30*u**3 + 0*u**2 + 12*u. Factor d(m).
-m*(m + 1)**2*(2*m - 1)/5
Let o(g) = 2*g**2 - 127*g + 1922. Let t(h) = -6*h**2 + 382*h - 5766. Let v(x) = -10*o(x) - 3*t(x). Factor v(u).
-2*(u - 31)**2
Let o be -6 - (-6*(-22)/(-33))/(20/34). Suppose 28/5*s**3 + o*s**5 + 4/5*s**2 + 16/5 - 32/5*s - 4*s**4 = 0. Calculate s.
-1, 1, 2
Let d(k) = -5*k**2 - 96*k. Let z(m) = -5*m**2 - 94*m. Let u(j) = 3*d(j) - 2*z(j). What is g in u(g) = 0?
-20, 0
Let k = -1033 - -1036. Let v(n) be the first derivative of 6*n + 0*n**2 - k - 1/2*n**3. Factor v(y).
-3*(y - 2)*(y + 2)/2
Let c(t) = -t**2 + t - 1. Let k(s) = -17*s + 28*s - 4*s**2 - 12*s - 7. Suppose 8 + 4 = 4*v. Let x(w) = v*c(w) - k(w). Factor x(g).
(g + 2)**2
Let z(r) be the second derivative of 1/36*r**3 + 0*r**2 + 0 - 1/120*r**5 - 2*r + 0*r**4. Factor z(q).
-q*(q - 1)*(q + 1)/6
Let x(v) be the third derivative of -v**6/40 - v**5/5 - 5*v**4/8 - v**3 + 7*v**2. Factor x(n).
-3*(n + 1)**2*(n + 2)
Let a(m) be the second derivative of m**8/3360 - m**7/315 + m**6/90 + 8*m**4/3 - 31*m. Let s(i) be the third derivative of a(i). Factor s(k).
2*k*(k - 2)**2
Suppose -1 = o - p, -5*o + 3*p - 5*p - 26 = 0. Let z(j) = 3*j**2 + 5*j + 2. Let r(x) = -3*x**2 - 4*x - 1. Let w(f) = o*r(f) - 5*z(f). Factor w(d).
-3*(d + 1)*(d + 2)
Let j(w) = w**3 + 14*w**2 - 16*w - 13. Let x be j(-15). Let g = -2 - -6. Find c, given that 3*c**g + 7*c**2 + 0*c**2 + 16*c**3 + x*c**3 + 20*c**2 = 0.
-3, 0
Let u(t) be the third derivative of -1/180*t**5 - 1/36*t**4 - 7*t**2 + 0*t**3 + 0 + 0*t. Solve u(n) = 0 for n.
-2, 0
Let d(i) = 15*i**3 - 5*i**2 - 8*i - 2. Let f(j) = -7*j**3 + 2*j**2 + 4*j + 1. Let u(b) = 6*d(b) + 14*f(b). Factor u(x).
-2*(x - 1)*(x + 1)*(4*x + 1)
Let i(j) = j + 15. Let b be i(-13). Let f(n) = 5*n**2 - 34*n - 39. Let g(y) = -6*y**2 + 33*y + 39. Let z(t) = b*g(t) + 3*f(t). Factor z(w).
3*(w - 13)*(w + 1)
Let n be (-32)/40 - 2/10. Let c be (0/(-5))/(3 - (n + 0)). Suppose -2/5*f**4 + 0*f**3 + c + 0*f + 2/5*f**2 = 0. What is f?
-1, 0, 1
Find n such that -5/8 - 1/2*n + 1/8*n**2 = 0.
-1, 5
Let q be 12 + (-28 - (-15 - 1)). Factor -2*r**5 - 4/3 + 20/3*r**4 + 10/3*r + q*r**2 - 20/3*r**3.
-2*(r - 1)**4*(3*r + 2)/3
Let f(b) be the third derivative of -b**7/1260 + b**5/120 - b**4/72 - 12*b**2 - 12. Factor f(a).
-a*(a - 1)**2*(a + 2)/6
Let b be 7 - 372/60 - (1 + -1). Factor 16/5*x**2 + b*x**3 + 0 + 16/5*x.
4*x*(x + 2)**2/5
Let s(f) be the first derivative of -26*f**5/45 + 38*f**4/9 - 70*f**3/9 - 2*f**2 - 441. Solve s(o) = 0 for o.
-2/13, 0, 3
Let q = -220 - -231. Suppose -10*h - 16 = -q*h. Factor 4/5 - 34/5*n + h*n**2 - 32/5*n**3.
-2*(n - 2)*(4*n - 1)**2/5
Factor 12*x**3 - 3*x**3 + 6*x**2 + 12*x**4 + x**5 - 18*x + 2*x**5 - 18*x**2 + 6*x.
3*x*(x - 1)*(x + 1)*(x + 2)**2
Let f(a) be the first derivative of -a**3/3 - 45*a**2/2 - 44*a + 23. Factor f(m).
-(m + 1)*(m + 44)
Suppose 14*z = 71*z - 34*z - 46. Factor 8/5*s**3 + 2/5*s**4 + 4/5*s + 0 + 2*s**z.
2*s*(s + 1)**2*(s + 2)/5
Let j(f) be the second derivative of f**9/1008 + f**8/112 + 3*f**7/280 - 3*f**6/40 + f**3/6 + 2*f. Let t(x) be the second derivative of j(x). Factor t(i).
3*i**2*(i - 1)*(i + 3)**2
Let x be ((-270)/(-2457)*13)/(6/14). Let o be (-4)/(-18)*(-12)/(-2). Factor o - x*d - 14/3*d**2.
-2*(d + 1)*(7*d - 2)/3
Let a(u) be the third derivative of u**6/144 + u**5/180 + 23*u**2. Suppose a(z) = 0. What is z?
-2/5, 0
Let p = 6 - 4. Suppose p*r - 14 = -3*y, 5*r = 2*y + 15 + 1. Determine g, given that -1/2*g**y + 2*g - 2 = 0.
2
Factor 0 - 21/4*d**2 + 9/4*d + 15/4*d**3 - 3/4*d**4.
-3*d*(d - 3)*(d - 1)**2/4
Let k(d) = -8*d**3 + 67*d**2 - 157*d - 640. Let o(z) = -17*z**3 + 133*z**2 - 313*z - 1280. Let c(m) = 7*k(m) - 3*o(m). Factor c(g).
-5*(g - 8)**2*(g + 2)
Let m(g) be the first derivative of -2*g**5 - 13*g**4/2 + 4*g**3 + 20*g**2 - 16*g + 463. Find f, given that m(f) = 0.
-2, 2/5, 1
Let g = -767 + 50623/66. Let q(a) be the second derivative of 3/11*a**2 + 4*a - 2/33*a**3 - g*a**4 + 0. Solve q(f) = 0 for f.
-3, 1
Let y(g) be the second derivative of g**7/84 + g**6/24 - g**5/12 - 7*g**3/3 + g. Let q(d) be the second derivative of y(d). Find p, given that q(p) = 0.
-2, 0, 1/2
Let t = 34193/21355 + -5/4271. Determine l so that t*l**2 - 36/5 - 6/5*l + 2/5*l**3 = 0.
-3, 2
Let u(l) = 35*l**2 + 25*l + 5. Let v = -69 - -65. Let p(w) = 9*w**2 + 6*w + 1. Let q(g) = v*u(g) + 15*p(g). Factor q(f).
-5*(f + 1)**2
Let t(a) = 6*a**3 + 35*a**2 - 20*a + 1. Let m(f) = f**3 + f**2 - f + 1. Let z(l) = 4*m(l) - t(l). Let k be z(-16). Factor 2/5*h**k + 2/5 + 6/5*h**2 + 6/5*h.
2*(h + 1)**3/5
Let k(m) be the first derivative of m**3/2 + 24*m**2 + 384*m + 79. Solve k(d) = 0.
-16
Let j(d) = -d**3 + 2*d + 3. Let g(t) = 28*t**3 - 12*t**2 - 120*t - 72. Let a(q) = g(q) + 24*j(q). Solve a(b) = 0.
-3, 0, 6
Solve -24*k**3 + 58*k**3 + 6*k**3 + 13*k**2 - 2*k**4 + 8*k**4 - 3*k**4 = 0.
-13, -1/3, 0
Suppose 5*d = -5, 7*g - 147 = 5*g - 5*d. Determine b so that 56*b**4 + 92*b**5 - g*b**2 + 48 - 104*b - 179*b**5 + 66*b**3 + 97*b**5 = 0.
-3, -2, 2/5, 1
