et 101*r - 247*r - 3*r**2 + 0*r**2 + 98*r = 0. What is r?
-16, 0
Let q be 4/7*(-35)/(-10). What is d in 72*d + 30 - 17*d + 35*d**3 + 10*d - 130*d**q = 0?
-2/7, 1, 3
Suppose 11 = -4*f + 5*c, -2*f - 4 = -0*f - 2*c. Let m be 1/((-24)/(-20) - f). Factor -18*d**m + 34*d**5 + 3*d**2 - 19*d**5 - 3*d**4 + 3*d**3.
-3*d**2*(d - 1)*(d + 1)**2
Find y such that -1 + 43/4*y**4 - 19*y**3 + 33/2*y**5 - 21/4*y**2 + 7*y = 0.
-1, 2/11, 1/2, 2/3
Let r(h) be the first derivative of -h**4/12 - 37*h**3/3 - 1369*h**2/2 - 50653*h/3 - 269. Determine c, given that r(c) = 0.
-37
Let v = -4 - -16. Suppose -4*a - v = -10*a. Factor 39*d**2 + d**3 + 0*d**3 - 38*d**a.
d**2*(d + 1)
Solve -64 + 32*a - 111*a**2 + 54*a**2 + 53*a**2 = 0.
4
Let c be (605/1452)/(10/16). Solve 0 + 1/3*n**2 + c*n = 0 for n.
-2, 0
Let q(g) be the second derivative of -1/10*g**5 - 3/4*g**2 + 3/8*g**4 - 29*g + 0 + 5/6*g**3. What is d in q(d) = 0?
-1, 1/4, 3
Factor -5929 - 77*x - 1/4*x**2.
-(x + 154)**2/4
Let t(a) = a**5 - a**4 - a - 1. Let k(c) = 20 - 5*c**2 + 39*c - 9*c - 2*c**4 - 15*c**3 + 27*c**4 - 15*c**5. Let v(i) = k(i) + 20*t(i). What is x in v(x) = 0?
-2, -1, 0, 1
Let c(k) = 2*k**2 + 1. Let y(z) = -9*z**2 + 9*z + 9. Let b(d) = -3*c(d) - y(d). Solve b(o) = 0 for o.
-1, 4
Suppose 2*w + 5*g - 9 = 5*w, -w - 10 = -4*g. Factor -m**2 - 2*m**2 - 3*m**w - 9*m + 3*m**3.
3*m*(m - 3)*(m + 1)
Suppose -7*l + 2*i = -3*l - 4, 5*i = 2*l + 6. Let b(f) = -f**2 - 19*f - 14. Let h be b(-18). Factor n + 5/4*n**3 + 0 - 2*n**l - 1/4*n**h.
-n*(n - 2)**2*(n - 1)/4
Suppose l + l - 10 = -p, 10 = 2*l - 4*p. Suppose l*c - 4*c - 4*c = 0. Factor 0*s**2 + 1/3*s**3 + c - 1/3*s.
s*(s - 1)*(s + 1)/3
Let j(c) be the second derivative of c**5/20 + c**4/4 + c**3/3 - 179*c. What is z in j(z) = 0?
-2, -1, 0
Determine u so that -4/17*u**2 - 10/17*u + 24/17 = 0.
-4, 3/2
Let m = -68 - -206/3. Let n be (0 - 2 - -8) + (12 - 16). Solve -8/3*k - m*k**2 - n = 0.
-3, -1
Let 0 - 51/2*r**3 + 58*r**2 + 7/2*r**5 - 14*r - 22*r**4 = 0. What is r?
-2, 0, 2/7, 1, 7
What is g in 2*g**2 - 9*g**4 - 6*g + 3*g**3 - 6*g**5 + 7*g**2 + 9*g**5 = 0?
-1, 0, 1, 2
Let o(u) = 2*u**3 + u**2. Let i(p) = 12*p**3 + 25*p**2 - 2*p - 20. Let s(q) = -i(q) + 5*o(q). Factor s(h).
-2*(h - 1)*(h + 1)*(h + 10)
Let 784/5 + 448/5*i + 1/10*i**3 + 29/5*i**2 = 0. What is i?
-28, -2
Let x = 4 - 2. Factor x*k**2 + k + 0*k**3 + 0*k**2 - k**3 + 0*k**3 - 2.
-(k - 2)*(k - 1)*(k + 1)
Let y = -2737 + 2741. Suppose 3/5*p**3 - 6/5 - 33/5*p - 36/5*p**2 + 12/5*p**y = 0. Calculate p.
-1, -1/4, 2
Let r(y) = 5*y**2 + 71*y - 242. Let j(m) = 25*m**2 + 358*m - 1211. Let o(z) = -2*j(z) + 11*r(z). Let o(u) = 0. What is u?
-16, 3
Let u be -7 + (-500)/(-30) + -7*1. Solve -2*o**2 - u - 1/3*o**3 - 4*o = 0.
-2
Let -33/5*w**4 + 12/5*w - 36/5*w**3 + 3/5*w**2 + 0 - 6/5*w**5 = 0. What is w?
-4, -1, 0, 1/2
Let p(w) be the second derivative of 0*w**3 + 0*w**2 + w**4 - 3/4*w**5 + 1/10*w**6 + 36*w + 0. Factor p(u).
3*u**2*(u - 4)*(u - 1)
Let x(y) = 14*y + 56. Let p be x(-4). Let n(o) be the third derivative of 0*o + p*o**4 - 1/120*o**6 + 0*o**3 + 0*o**5 + 0 - 5*o**2. Find t such that n(t) = 0.
0
Suppose -291 = -7*k + 2*k + a, -5*k = 3*a - 307. Factor -15 - 5*p**2 - 10*p**2 + k*p - 9*p.
-5*(p - 3)*(3*p - 1)
Let p = 148/225 + 2/225. Let t(d) be the first derivative of 1/12*d**4 - p*d - 1/6*d**2 + 2/9*d**3 + 3. Suppose t(y) = 0. Calculate y.
-2, -1, 1
Let r(u) = -u**3 + 6*u**2 + 70*u - 12. Let c be r(-6). Factor c - 6/13*b**3 + 2/13*b + 4/13*b**2.
-2*b*(b - 1)*(3*b + 1)/13
Let k be 7*-3*(0 + 1/(-3)). Factor -2*b**4 + 6*b**3 - k*b**3 + 3*b**3 - 2*b + 2*b**2.
-2*b*(b - 1)**2*(b + 1)
Let a(h) be the third derivative of -h**6/120 - 2*h**5/15 - 5*h**4/6 - 8*h**3/3 + 171*h**2. Factor a(n).
-(n + 2)**2*(n + 4)
Suppose 0 = 5*f + 5, -4*f - 1 = -t + 3. Let l(m) be the second derivative of -1/5*m**6 + 0*m**2 + 0 + t*m**4 + 0*m**3 - 1/21*m**7 + 4*m - 1/5*m**5. Factor l(q).
-2*q**3*(q + 1)*(q + 2)
Factor -20 - 21*y**2 + 70*y**2 + 25*y - 16*y**2 - 17*y**2 - 21*y**2.
-5*(y - 4)*(y - 1)
Let x(m) be the second derivative of m**5/4 + 35*m**4/12 - 439*m. Suppose x(l) = 0. What is l?
-7, 0
Let n(r) = -112*r + 677. Let j be n(6). Let y(m) be the first derivative of 4 + 4/5*m + 6/5*m**2 + 13/15*m**3 + 3/10*m**4 + 1/25*m**j. Factor y(a).
(a + 1)**2*(a + 2)**2/5
Let a(k) = 3*k - 13. Let j be (2 - 3)*(-1 - 4). Let v be a(j). What is g in -9*g**v + 39 - 24 - 19 + 20*g = 0?
2/9, 2
Suppose -3*w = -v - 22, 0*w + 20 = 2*w - 2*v. Let y(l) = -l**2. Let n(z) = -8*z**2 + 2*z + 4. Let m(r) = w*y(r) - n(r). Determine k, given that m(k) = 0.
-1, 2
Let i(u) be the third derivative of -u**10/37800 + u**8/2520 - u**6/180 + 11*u**5/30 + 3*u**2. Let g(l) be the third derivative of i(l). What is r in g(r) = 0?
-1, 1
Let i be ((-286)/(-55))/1 + -2*1. Factor -4/5 - 7/5*n**2 - i*n.
-(n + 2)*(7*n + 2)/5
Let i be 1/4 - 27/(-4). Factor 3*z**4 + i*z**4 + 5*z**2 - 5*z**4 - 10*z**3.
5*z**2*(z - 1)**2
Let g = 15 + -132. Let z = g + 120. Factor -3/2*w**z - 1/2*w**5 + 0 + 1/2*w**2 + 3/2*w**4 + 0*w.
-w**2*(w - 1)**3/2
Suppose 6 = -3*d, -y + 16 = -4*d + 3. Factor -5*j**2 + 10*j**4 + 398*j**3 - 384*j**3 + 2*j**y + 11*j**2.
2*j**2*(j + 1)**2*(j + 3)
Let u = -31 + 9. Let g = u + 24. Factor g - 5*i - 9*i**4 - 32*i**3 - 21*i**2 - 2*i + 4*i + 7*i**3.
-(i + 1)**3*(9*i - 2)
Let a be (-4)/(32/(-36))*4/9. Let y(n) be the first derivative of -a*n**2 - 8*n - 1/8*n**4 + 7/6*n**3 + 5. Factor y(j).
-(j - 4)**2*(j + 1)/2
Let o(m) be the first derivative of 5*m**4/4 + 50*m**3/3 + 125*m**2/2 - 183. Find y, given that o(y) = 0.
-5, 0
Let i be 504/594*30/35. Factor i + 2/11*h**2 - 8/11*h.
2*(h - 2)**2/11
Let a be (-4)/5*((-236210)/(-468))/(-79). Factor 4/3*l**5 - 2/9 + 4*l**2 + 4/9*l + 64/9*l**3 + a*l**4.
2*(l + 1)**4*(6*l - 1)/9
Let n = -1/45614 + 182459/136842. Factor -n*v + 0 - 1/3*v**2.
-v*(v + 4)/3
Let q(h) be the second derivative of -h**4/24 - 5*h**3/4 + 4*h**2 - 31*h - 1. Factor q(a).
-(a - 1)*(a + 16)/2
Let a = -619/710 + 9/10. Let c = 65/213 + a. Let 2/3 - c*z**2 + 1/3*z = 0. What is z?
-1, 2
Let s be (-3)/(1 - 12/9). Let j(l) = l**2 - 8*l - 7. Let d be j(s). What is x in -5*x**d + 4*x + 6 + 5*x**2 - 2*x**2 = 0?
-1, 3
Let r(m) be the first derivative of -2/15*m**5 - 1/3*m**3 - 5*m + 8 + 0*m**2 - 7/18*m**4. Let x(i) be the first derivative of r(i). Factor x(t).
-2*t*(t + 1)*(4*t + 3)/3
Let s(i) be the second derivative of 0 + 2/9*i**3 - 1/72*i**4 + 36*i - 7/12*i**2. Factor s(t).
-(t - 7)*(t - 1)/6
Let w = -64 - -36. Let v be 1*4/20 - w/10. Factor 2/7 + 3/7*q**2 - 5/7*q - 1/7*q**4 + 1/7*q**v.
-(q - 1)**3*(q + 2)/7
Let s(d) be the third derivative of d**7/504 + d**6/36 - d**4/2 - 13*d**2. Let r(x) be the second derivative of s(x). Factor r(g).
5*g*(g + 4)
Let m(f) be the third derivative of 81*f**7/490 + 9*f**6/14 + 59*f**5/70 + 5*f**4/14 + f**3/14 + 19*f**2 - 1. Factor m(c).
3*(c + 1)**2*(9*c + 1)**2/7
Factor -a**4 + 1/2*a**5 + 0*a + 0 + 0*a**3 + 0*a**2.
a**4*(a - 2)/2
Let z be -5 + 5 + (-5)/(70/(-368)). Let p = z - 26. Factor 2/7 - 2/7*x**2 + p*x**3 - 2/7*x.
2*(x - 1)**2*(x + 1)/7
Suppose 0 = 2*h - 7 + 3. Suppose -4*p**2 + 0*p + 0*p - h*p - 2*p = 0. Calculate p.
-1, 0
Factor -8/5*a**2 + 6/5*a**3 + 2/5*a + 0.
2*a*(a - 1)*(3*a - 1)/5
Factor -596/7 - 302/7*v - 2/7*v**2.
-2*(v + 2)*(v + 149)/7
Suppose 12 = 4*d - 4*w, w - 31 = -5*d + 2. Let x be 4*(3/d + 0). Factor 4 + 5*h**2 - 3*h + 5*h - 5*h**2 - x*h**2.
-2*(h - 2)*(h + 1)
Let a(t) = -t**4 + t**3 - t**2. Let b(p) = -p**5 - 5*p**4 + 8*p**3 - 3*p**2. Let m(y) = -10*a(y) + 2*b(y). Let m(g) = 0. What is g?
-1, 0, 2
Let k be 8 + -2 + 0 + -1. Suppose k*z - 5 = 5. Let -13*i - i**2 + 13*i + 2*i**z = 0. Calculate i.
0
Let l = -164/13 - -3272/247. Solve 18/19*c**2 + 2/19 - l*c = 0 for c.
1/3
Let v(y) be the third derivative of y**7/1008 - y**6/18 + 4*y**5/3 + y**4/8 - 15*y**2. Let p(k) be the second derivative of v(k). Factor p(h).
5*(h - 8)**2/2
Let v(u) be the third derivative of -u**8/3360 + u**7/1050 + u**6/200 - u**5/30 + 19*u**4/240 - u**3/10 - 45*u**2 - 5*u. Factor v(d).
-(d - 2)*(d - 1)**3*(d + 3)/10
Suppose -76 = -4*x - 4*l, -x - 3*l = -5*l - 13. Suppose 6*g - x - 1 = 0. Find c such that -18/7*c**2 - 2/7*c**g - 54/7*c - 54/7 = 0.
-3
Suppose -6*l = 14*l. Let f(a) be the third derivative of 0*a - 1/20*a**5 + 0*a**4 + a**2 + 0 + 1/40*a**6