Let k be (2/7)/(-5 - (-108)/21). Let r be (20/15)/(2/3). Find w such that -3*w**k + w**2 + w + w**r = 0.
0, 1
Let k(h) = -h**3 - 11*h**2 + 3*h - 299. Let t be k(-13). Solve 0*m - 1/2*m**2 + t - m**3 - 5/8*m**4 - 1/8*m**5 = 0 for m.
-2, -1, 0
Let m(g) = -2*g**2 - g + 3. Let p(w) = w**3 + 18*w**2 + 4*w - 12. Let o(y) = 4*m(y) + p(y). Find r such that o(r) = 0.
-10, 0
Let c(t) be the third derivative of -t**6/60 - 26*t**5/75 - 13*t**4/12 - 6*t**3/5 - 77*t**2. Solve c(g) = 0.
-9, -1, -2/5
Let s(h) = 41*h + 167. Let d be s(-4). Factor -6/5 - 2*m + 2/5*m**d - 2/5*m**2.
2*(m - 3)*(m + 1)**2/5
Let x(k) be the second derivative of 0 - 1/9*k**3 + 1/72*k**4 + k + 1/3*k**2. Factor x(m).
(m - 2)**2/6
Factor 10 + 35/3*u - 30*u**2 + 25/3*u**3.
5*(u - 3)*(u - 1)*(5*u + 2)/3
Factor 35*x - 4*x**3 + 4*x**3 + x**3 - 3*x**2 - 36*x + 3.
(x - 3)*(x - 1)*(x + 1)
Let z(j) be the third derivative of -9*j**7/70 - 3*j**6/40 + 29*j**5/5 + 37*j**4/2 + 24*j**3 - 127*j**2. Find h such that z(h) = 0.
-3, -2/3, 4
Let f be 8/(1008/(-2286)) - -19. Determine o, given that -6/7 + 6/7*o**3 - f*o + 6/7*o**2 = 0.
-1, 1
Factor -4/5*l + 316/5*l**2 + 0 - 6241/5*l**3.
-l*(79*l - 2)**2/5
Suppose 96*f + 30 = 95*f. Let k be f/(-18) + (-2)/12. Let -9*x - 27/2 - k*x**2 = 0. Calculate x.
-3
Factor 0*n**2 - 2/13*n**3 - 32/13 + 24/13*n.
-2*(n - 2)**2*(n + 4)/13
Let w(h) be the second derivative of -h**6/135 + 2*h**5/45 - 5*h**4/54 + 2*h**3/27 + 82*h + 1. Determine a, given that w(a) = 0.
0, 1, 2
Suppose 0 = b - 5*b + 24. Suppose -u = u - b. Factor u*x - 3*x - 260*x**3 + 265*x**3.
5*x**3
Suppose -52*b**2 + 32/3*b + 0 + 3*b**4 + 52/3*b**3 = 0. What is b?
-8, 0, 2/9, 2
Let p(h) = -h**2 + 56*h - 31. Let w(z) = 3*z**2 - 167*z + 96. Let d(v) = 17*p(v) + 6*w(v). Suppose d(i) = 0. What is i?
1, 49
Let g(i) be the third derivative of -i**7/42 - 15*i**6/8 - 161*i**5/4 + 2645*i**4/24 + 2*i**2 - 4*i. Factor g(x).
-5*x*(x - 1)*(x + 23)**2
Factor -129/4*w**2 - 1449/4*w - 3/4*w**3 - 1323/4.
-3*(w + 1)*(w + 21)**2/4
Let h be 2/(-6)*(-28 + 262/10). Factor 18/5*x + 3*x**2 + 0 - h*x**3.
-3*x*(x - 6)*(x + 1)/5
Let k = -15 + 17. Suppose 0 = -k*a - 5*r + 22, -5*r + 27 = -2*a + 9. Factor a - 1 - 3*x**2 - 18*x**5 + 16*x**3 + 11*x**2 - 6*x**4.
-2*x**2*(x - 1)*(3*x + 2)**2
Suppose 76/21*y + 2/21*y**2 + 722/21 = 0. Calculate y.
-19
Let j = 1993 - 1990. Determine q, given that -16/5*q**j + 16/5*q - 4/5 + 4/5*q**2 = 0.
-1, 1/4, 1
Let x(b) = 1. Let z(k) = 27*k**2 - 20 + 9*k - 22*k**3 + 3*k**4 - 3*k**3 + 4. Let m(u) = -6*x(u) - 3*z(u). Let m(j) = 0. What is j?
-2/3, 1, 7
Let h(m) be the third derivative of m**9/15120 - m**7/1260 + 11*m**5/60 + 8*m**2. Let y(k) be the third derivative of h(k). Factor y(v).
4*v*(v - 1)*(v + 1)
Factor -2/9*h**2 - 14/3*h + 16.
-2*(h - 3)*(h + 24)/9
Let -3/4*c**5 + 45/8*c**4 - 27/2*c + 87/4*c**2 + 3 - 129/8*c**3 = 0. Calculate c.
1/2, 1, 2
Let f(v) = 1 - 5 - v + 4 + 4. Let z be f(0). Factor 11 + 2*t**3 - 3*t**z + 4*t**2 - 10 - 2*t - 2.
-(t - 1)**2*(t + 1)*(3*t + 1)
Find i such that 50*i**4 - 135*i**4 + 41*i**4 + 6*i**3 + 47*i**4 = 0.
-2, 0
Let y(z) be the third derivative of 0*z**3 - 1/60*z**6 + 0 - 18*z**2 + 1/60*z**5 + 1/12*z**4 - 1/210*z**7 + 0*z. Suppose y(j) = 0. What is j?
-2, -1, 0, 1
Let v(z) be the third derivative of z**6/24 + z**5/4 - 5*z**4/6 - 126*z**2. Factor v(f).
5*f*(f - 1)*(f + 4)
Let j(y) = y + 2. Let r be -1*(-1 + 1)*(-4)/(-12). Let m be j(r). Factor u**m - 2/3*u - 1/3.
(u - 1)*(3*u + 1)/3
Let y be (-6 - -2)*(-14)/8. Let -22 - 15*o + y + 5*o - 2*o + 3*o**2 = 0. What is o?
-1, 5
Suppose -2/7*y**2 + 16/7 + 2*y = 0. Calculate y.
-1, 8
Let i = -2041 - -2045. Determine b so that -3/7*b**5 + 6/7*b**3 + 0 - 12/7*b**2 - 8/7*b + b**i = 0.
-1, -2/3, 0, 2
Let j = -52 + 56. Suppose -j*s**2 + 6*s**2 - 2*s**2 + 5*s**2 = 0. What is s?
0
Let r(o) be the second derivative of -o**8/3360 - o**7/420 + o**5/15 + 7*o**4/6 + 42*o. Let y(j) be the third derivative of r(j). Factor y(h).
-2*(h - 1)*(h + 2)**2
Let q(h) be the first derivative of -10 + 1/3*h**2 + 1/18*h**4 + 0*h + 10/27*h**3 - 2/45*h**5. Factor q(x).
-2*x*(x - 3)*(x + 1)**2/9
Let o(j) be the first derivative of 2 + 0*j + 1/6*j**6 - 1/4*j**2 + 3/8*j**4 + 1/2*j**5 - 1/6*j**3. Factor o(p).
p*(p + 1)**3*(2*p - 1)/2
Suppose 2*x - 1 = -3*x + d, 5*x + 4 = -4*d. Factor -4/7*v**3 + 4/7*v + x + 0*v**2.
-4*v*(v - 1)*(v + 1)/7
Find o, given that 187 - 620*o**3 + 129 + 3016*o**2 + 36*o**4 + 196 - 2944*o = 0.
2/9, 1, 8
Let q(d) be the second derivative of d**4/4 + 25*d**3/12 + 21*d**2/4 + 2*d - 9. Factor q(j).
(j + 3)*(6*j + 7)/2
Let r(v) = -5*v**2 + 29*v - 6. Let f(b) = b**2 - b + 2. Let k(i) = -3*f(i) - r(i). Factor k(l).
2*l*(l - 13)
Suppose -3*d + 0 = -6. Factor 3*r**2 - 10 + 2*r**d - 2*r + 14*r - 7*r.
5*(r - 1)*(r + 2)
Let n(k) be the first derivative of k**4/10 - 4*k**3/15 - 43*k**2/5 - 16*k + 636. Factor n(a).
2*(a - 8)*(a + 1)*(a + 5)/5
Let c(v) be the second derivative of v**7/1260 - v**6/270 - v**5/180 + v**4/18 + 17*v**3/6 + 4*v. Let m(a) be the second derivative of c(a). Factor m(p).
2*(p - 2)*(p - 1)*(p + 1)/3
Let x = 16208 - 32411/2. Solve -x*l + 1/2*l**2 + 3 = 0 for l.
2, 3
Let a = 19532 - 19529. Factor 1/4*j**a + 0 + 1/4*j - 1/2*j**2.
j*(j - 1)**2/4
Let m(i) be the first derivative of -3 - 3/2*i**5 + 0*i + 37/16*i**4 + 1/2*i**2 - 5/3*i**3 + 3/8*i**6. Factor m(l).
l*(l - 1)**2*(3*l - 2)**2/4
Let y be (6/(-35))/(3*(-39)/182). Let x(v) be the second derivative of 0*v**2 + y*v**6 - 2/3*v**4 - 2/21*v**7 - 6*v + 0*v**5 + 0 + 2/3*v**3. Factor x(a).
-4*a*(a - 1)**3*(a + 1)
Let o(y) be the first derivative of y**2 - 4 - 4/15*y**3 - 4/5*y. Factor o(w).
-2*(w - 2)*(2*w - 1)/5
Let d(s) be the second derivative of s**6/720 + 11*s**5/120 + 121*s**4/48 - s**3/3 + 3*s. Let f(k) be the second derivative of d(k). Let f(p) = 0. What is p?
-11
Let j(b) = b**2 - 6*b + 5. Let l be j(6). Let d(c) be the first derivative of 8/3*c**3 + 2 + 4*c + 1/2*c**4 + l*c**2. Factor d(h).
2*(h + 1)**2*(h + 2)
Let m be (-54)/378*(-14)/6*0. Factor 0*j**2 + 2/3*j**4 + 2/3*j**3 + m + 0*j.
2*j**3*(j + 1)/3
Let y(w) be the third derivative of 1/15*w**3 - 1/150*w**5 + 1/900*w**6 + 0*w + 0 - 1/180*w**4 + 49*w**2. Solve y(t) = 0.
-1, 1, 3
Let a(v) be the second derivative of v**6/1440 - v**5/288 - v**4/144 + 2*v**3/3 - 20*v. Let f(k) be the second derivative of a(k). Suppose f(o) = 0. What is o?
-1/3, 2
Let i be -62*1/(-22) + 4/22. Suppose -t + 5*t = i*t. Factor t - 5/4*n**3 - 3/4*n**2 + 1/2*n.
-n*(n + 1)*(5*n - 2)/4
Let b(u) = 5*u**2 - 13*u + 32. Let n(k) = -9*k**2 + 27*k - 64. Let m = 6 - 12. Let j(c) = m*n(c) - 10*b(c). Factor j(t).
4*(t - 4)**2
Let k be 3/(-6) - 1/(4/(-1122)). Factor -c**2 + 277 + 6*c - 2*c - k.
-(c - 3)*(c - 1)
Let s = -3093 - -52589/17. Factor s*i + 0 + 2/17*i**3 - 8/17*i**2.
2*i*(i - 2)**2/17
Let c(a) be the third derivative of a**6/60 - 37*a**5/30 + 35*a**4/6 + 224*a**2. Factor c(o).
2*o*(o - 35)*(o - 2)
Let l be ((-3)/5)/(4 - ((-72)/(-60) + 3)). Factor -2/3*c**2 + 2/3*c - 2/9 + 2/9*c**l.
2*(c - 1)**3/9
Suppose 22*y**2 + 20/3*y + 80/3*y**3 + 32/3*y**4 + 2/3 = 0. Calculate y.
-1, -1/4
Let w(q) be the first derivative of 26*q**3/27 - 31*q**2/9 + 4*q - 110. Factor w(i).
2*(i - 1)*(13*i - 18)/9
Suppose 9*s = 24*s - 2550. Let z = s + -168. Let 0*q**3 - q**z - 4/3*q - 1/2 + 1/6*q**4 = 0. Calculate q.
-1, 3
Suppose -3*u + 5*v - 1 - 21 = 0, -3*u - 2*v - 8 = 0. Let x(h) = h**3 + 3*h**2 - 5*h - 1. Let k be x(u). Find g such that -k*g**2 + 2*g**2 + 3*g**2 = 0.
0
Let s(q) be the third derivative of -q**5/210 - q**4/28 - 2*q**3/21 + 39*q**2 - 1. Factor s(a).
-2*(a + 1)*(a + 2)/7
Let l(y) = -14*y**4 + 8*y**3 + 11*y**2 - 32*y. Let k(t) = 44*t**4 - 24*t**3 - 32*t**2 + 96*t. Let s(v) = -5*k(v) - 16*l(v). What is f in s(f) = 0?
-2, 0, 2
Let q be 172/(-516) + 7/3 + (5 - 3). Solve -42/5*s**2 + 14/5*s**q - 8/5 + 4/5*s**3 - 8*s = 0 for s.
-1, -2/7, 2
Let o(v) = 2*v + 8. Let p be o(-3). Suppose -j = -0 - p. Factor 2*u**4 + 0*u**2 - 6*u**3 + 9*u**2 - 11*u**4 + 9*u - 3*u**5 - 3*u**j + 3.
-3*(u - 1)*(u + 1)**4
Let z(i) = i**2 + 4*i + 1. Let y be z(-5). Suppose b = 0, 0*u - 3*u - b = -y. Factor -2/11*f**u - 2/11*f + 0 + 4/11*f**3.
2*f*(f - 1)*(2*f + 1)/11
Let z be ((-826)/472 + 1/4)*42/(-27). Suppose -z*g**2 + 1/3*g**3 + 5*g - 3 = 0. Calculate g.
1, 3
Let t(l) be the third deriv