Let k(i) = i**2 + i + 1. Let p be -3*(-1)/(-2)*2. Let f(q) = p*k(q) + v(q). Find c such that f(c) = 0.
-1, 1
Factor -365*n + 0 + 1/2*n**2.
n*(n - 730)/2
Let g(v) = 19*v**2 - 562*v + 2818. Let t(p) = -55*p**2 + 1690*p - 8455. Let m(w) = 20*g(w) + 7*t(w). What is d in m(d) = 0?
5, 113
Let k = 74 - 116. Let p = -37 - k. Determine u, given that -p*u**2 - 21*u + 8*u + 3*u + 0*u = 0.
-2, 0
Let v(h) = h**5 - 3*h**4 + 2*h**3 - 1. Let m(u) = 5*u**5 - 29*u**4 - 22*u**3 - 24*u**2 - 6. Let s(r) = 5*m(r) - 30*v(r). Find k such that s(k) = 0.
-6, -4, -1, 0
Let n(r) = -r**2 - 5*r + 27. Let o be n(-8). Suppose 0*w - 5*w = -10. Factor 62 - 21 - 3*f**o + 6*f**w + 21*f - 29.
-3*(f - 4)*(f + 1)**2
Let l(y) be the first derivative of 0*y + 2/9*y**3 - 68 + 22/3*y**2. Factor l(p).
2*p*(p + 22)/3
Let -3/7*x**2 - 9264/7*x - 7151808/7 = 0. What is x?
-1544
Let s(x) be the third derivative of x**6/300 + x**5/10 + 47*x**4/60 + 11*x**3/5 + x**2 - 782*x. Find d such that s(d) = 0.
-11, -3, -1
Let r(c) be the first derivative of -14/55*c**5 + 3/11*c**2 + 0*c - 1/2*c**4 - 2/33*c**3 - 64. Factor r(s).
-2*s*(s + 1)**2*(7*s - 3)/11
Determine q, given that 128/9 + 1458*q**2 - 288*q = 0.
8/81
Let g(l) be the first derivative of -l**2/2 + 5*l - 13. Let r be g(2). Let 188*d**r + 18*d**4 - 54*d**5 + 21 - 20*d**3 - 64*d + 64*d**2 - 53 = 0. What is d?
-1, -2/3, 2/3, 2
Determine p, given that -3/4*p**4 + 1/4*p**5 + 0 + 66*p**2 - 65/2*p**3 + 0*p = 0.
-11, 0, 2, 12
Let n be (-42)/(-357) - 49/9520. Let t(l) be the second derivative of 3/8*l**4 + 1/80*l**6 - 1/2*l**3 - n*l**5 + 0*l**2 + 0 + 5*l. Factor t(b).
3*b*(b - 2)**3/8
Let h = 216 + -191. Solve -21 + 0*a - 3*a**2 + h*a - a = 0.
1, 7
Suppose 0 = 14*m - 44*m + 150. Suppose -22 = -16*t + m*t. Factor 3/7*r**t + 15/7*r + 0.
3*r*(r + 5)/7
Factor -40/3*j - 12 + 32/3*j**2 + 40/3*j**3 + 4/3*j**4.
4*(j - 1)*(j + 1)**2*(j + 9)/3
Let x(h) = h**2 + 133*h + 4186. Let k be x(-82). Determine z, given that -272/5*z**3 + 168/5*z**2 + 128/5*z + 16/5 + 77/5*z**k = 0.
-2/7, -2/11, 2
What is k in 0 + 4/5*k**2 - 756/5*k = 0?
0, 189
Let w(b) = -18*b + 93. Let v be w(5). Factor 3*y**4 - 61*y**3 - 61*y**3 + 128*y**v.
3*y**3*(y + 2)
Let f(o) be the third derivative of -o**6/24 - 77*o**5/4 - 22425*o**4/8 - 66125*o**3/6 + 167*o**2 + 4. Factor f(n).
-5*(n + 1)*(n + 115)**2
Let d(r) be the first derivative of r**4/60 + 2*r**3/15 - 16*r**2/5 + 267*r - 112. Let h(w) be the first derivative of d(w). What is l in h(l) = 0?
-8, 4
Let u(w) = w**4 + 4*w**3 - 2*w**2 - 7*w + 1. Let o(j) = -3*j**4 + 924*j**3 + 2093*j**2 + 1422*j + 268. Let a(f) = 5*o(f) - 20*u(f). Find p, given that a(p) = 0.
-1, -2/7, 132
Let w(g) = -8*g**4 + 28*g**3 - 7*g**2 - 210*g + 5. Let z(u) = -5*u**4 + 15*u**3 - 4*u**2 - 105*u + 3. Let q(m) = -3*w(m) + 5*z(m). Factor q(l).
-l*(l - 3)*(l + 5)*(l + 7)
Let q(k) be the third derivative of -k**5/15 + 13*k**4/12 - 5*k**3/3 + 6*k**2. Let a be q(6). Factor -4*j + a - 5 - 1 + 2*j + 6*j**2.
2*(j - 1)*(3*j + 2)
Let t = -721176 + 721203. Factor -1/2*c**3 - t*c + 0 - 55/2*c**2.
-c*(c + 1)*(c + 54)/2
Let m be -8 + 15 - (1 + 3). Let q(f) = -f**2 + 8*f + 22. Let a be q(-2). Factor 32/5*n + 28/5*n**m - 16/5 + 76/5*n**a.
4*(n + 1)*(n + 2)*(7*n - 2)/5
Let q = 16313 + -16311. Let d(t) be the first derivative of 7 + 24/7*t + 6/7*t**q - 15/28*t**4 - 6/7*t**3 - 3/35*t**5. Find c such that d(c) = 0.
-2, 1
Let x(l) be the second derivative of 2*l + 0 + 3/8*l**5 + 1/4*l**4 + 1/20*l**6 - 2*l**3 + 0*l**2. Factor x(q).
3*q*(q - 1)*(q + 2)*(q + 4)/2
Suppose 19*t + 20 = 24*t. Suppose 0*y = t*y - 12. Let -17 + 17 - 4*z + 4*z**y = 0. What is z?
-1, 0, 1
Let c be (-2)/(4 - 196/42). Let v = 2/9537 + 1401931/38148. Factor 343/4 - v*z - 1/4*z**c + 21/4*z**2.
-(z - 7)**3/4
Let l(m) = 33*m - 658. Let a be l(20). Let 1/2*d**3 - 23*d**a + 529/2*d + 0 = 0. Calculate d.
0, 23
Let z(i) be the second derivative of i**5/70 + 17*i**4/3 + 1856*i**3/21 + 3680*i**2/7 - 13122*i. Factor z(l).
2*(l + 4)**2*(l + 230)/7
Suppose -7 = 3*v - 5*d, 3*d + 1 = -2. Let i be (47 - 7)/v*8/(-30). Factor -4/9*k**5 + i*k**4 + 64/9*k**2 - 56/9*k**3 - 4*k + 8/9.
-4*(k - 2)*(k - 1)**4/9
Suppose -2/3*r**2 - 1004/3*r - 126002/3 = 0. Calculate r.
-251
Suppose 13 = 2*f + 5. Let g be (-6 - -10)*(-24)/(-224). Factor 0*a - g*a**3 + 0 + 0*a**2 + 3/7*a**f.
3*a**3*(a - 1)/7
Let q(m) be the third derivative of m**7/630 + 73*m**6/72 + 11041*m**5/60 - 3721*m**4/8 + 911*m**2. Determine r, given that q(r) = 0.
-183, 0, 1
Let y(a) = -7*a**2 - 757*a - 108. Let f be y(-108). Factor 0 - 4/3*m**3 + 0*m + f*m**2.
-4*m**3/3
Let l(n) = n**4 - n**3 + 2*n**2 - n + 10. Let g(u) = -12*u**4 - 15*u**3 - 15*u**2 + 135*u - 258. Let k(q) = g(q) + 15*l(q). Let k(z) = 0. What is z?
-2, 1, 2, 9
Suppose 2*s = -2*x + 10, 2*s + x - 12 = -3*x. Suppose -2*c - s*a = -16, a + 1 = -c + 2*a. Solve 1731*f**2 - 4*f - 4 + 4 - 1717*f**c = 0 for f.
0, 2/7
Let d = 48 - 45. Let r(u) = 280*u**3 - 72*u**2 - 196*u + 16. Let c(h) = -31*h**3 + 8*h**2 + 22*h - 2. Let i(b) = d*r(b) + 28*c(b). Factor i(s).
-4*(s - 1)*(s + 1)*(7*s - 2)
Let p(r) be the first derivative of 6*r**2 - 1/9*r**3 - 5/72*r**4 - 1/45*r**5 + 17 + 0*r - 1/360*r**6. Let i(j) be the second derivative of p(j). Factor i(v).
-(v + 1)**2*(v + 2)/3
Suppose -3*o - 2*x + 118 = -7*x, -182 = -5*o + x. Let d be -2 - (-3 + -1 - -2)*(23 - 21). Factor 48*u + 24 + 12*u**3 + 3/2*u**4 + o*u**d.
3*(u + 2)**4/2
Let y(x) = -3*x**2 + 55*x + 12. Let f be y(18). Let w = 33 - f. Find s, given that -2/7*s**2 - 2/7*s**5 + 2/7*s**4 + 0 + 0*s + 2/7*s**w = 0.
-1, 0, 1
Determine y so that -305*y - 13*y**3 + 25*y**3 - 110 + 97*y**2 - 123*y**2 - 239*y**2 - 82*y**3 = 0.
-2, -1, -11/14
Let r be (-13 + 16)/(23 + (-6 - 3) + -10). Factor -r*f**2 + 309/2*f - 31827/4.
-3*(f - 103)**2/4
Let i = -114003 - -570258/5. What is q in -i + 51/5*q**2 + 3/5*q**3 + 189/5*q = 0?
-9, 1
Let r = -9594607/350 + 54823/2. Let p = -38/25 - r. Let 9/7*a + p*a**3 - 4/7 - 6/7*a**2 = 0. Calculate a.
1, 4
Let i = 29251 + -29249. Let 96/7 + 72/7*b**i - 6/7*b**4 - 24*b + 6/7*b**3 = 0. Calculate b.
-4, 1, 2
Let -7/8 - 9/8*s**2 - 3*s = 0. What is s?
-7/3, -1/3
Let b(q) be the first derivative of -245*q**6/6 - 420*q**5 - 2855*q**4/4 - 380*q**3 - 70*q**2 - 4459. Solve b(u) = 0 for u.
-7, -1, -2/7, 0
Let u(p) be the third derivative of -p**6/96 + p**5/3 + 385*p**4/96 + 25*p**3/2 - 761*p**2. Find l, given that u(l) = 0.
-3, -1, 20
Let b = -28505/2 + 14256. Let q(c) be the first derivative of 68/9*c**2 + b*c**4 - 16/9*c - 316/27*c**3 - 7. What is x in q(x) = 0?
2/9, 2/7, 2
Suppose 56*d + 210 = 21*d. Let f(l) = l**2 + 84*l - 4. Let g(t) = -2*t**2 - 84*t + 6. Let r(a) = d*f(a) - 4*g(a). Find v such that r(v) = 0.
0, 84
Let h(z) be the second derivative of 0 + 3/5*z**3 - 2/5*z**2 - 5*z - 2/5*z**4 + 1/10*z**5. Factor h(d).
2*(d - 1)**2*(5*d - 2)/5
Let k(h) be the second derivative of 0 + 1/6*h**2 - 1/36*h**4 + 0*h**3 - 7*h. Solve k(g) = 0.
-1, 1
Let p(d) = d**3 + 211*d**2 + 3*d + 3. Let g(y) = -2*y**2 + y + 1. Let f(h) = 3*g(h) - p(h). Find r, given that f(r) = 0.
-217, 0
Let w be (-23458)/(-131238) - ((-2)/46 - 0). Factor -4/9*s**4 - 4/3*s**3 + w*s**5 + 4/3 + 26/9*s + 8/9*s**2.
2*(s - 3)*(s - 2)*(s + 1)**3/9
Let s(k) = k**3 + 7*k**2 + 5. Suppose -3*z - 3*c - 9 = 0, z + 2*z = 5*c - 41. Let b be s(z). Factor o - o - 10*o**b + 6*o**5 - 4*o**4.
-4*o**4*(o + 1)
Suppose 1821287*c - 1821325*c = 0. Factor c - n**2 + 1/2*n**3 + 1/2*n.
n*(n - 1)**2/2
Let d(b) be the second derivative of -b**5/140 + 5*b**4/12 + 76*b**3/21 + 78*b**2/7 + 340*b. Factor d(v).
-(v - 39)*(v + 2)**2/7
Let o(h) be the second derivative of -h**4/10 - 107*h**3/15 - 14*h**2 + 1191*h. Factor o(k).
-2*(k + 35)*(3*k + 2)/5
Let h(z) be the third derivative of -z**5/60 - 65*z**4/8 - 371*z**2. Factor h(r).
-r*(r + 195)
Factor -54*a**2 - 55*a**2 - 21*a**2 + 13512*a + 162614 + 11248270 + 134*a**2.
4*(a + 1689)**2
Let u(c) = c**2 - 2*c - 5. Let w be u(4). Suppose -w = -3*o + 3*h, -4*o - o - 2*h = 2. Factor 4*z**3 - 12*z - 3*z**2 + o*z**3 + 14*z - 3*z**3.
z*(z - 2)*(z - 1)
Let v be -6*(-3)/4 - 0. Let h = -2347/172 - -748/43. Factor -3/4*u**2 + v - h*u.
-3*(u - 1)*(u + 6)/4
Let w(t) be the second derivative of t**5/140 + 236*t**4/21 - 45*t**3/2 + 8*t - 84. Determine i, given that w(i) = 0.
-945, 0, 1
Let d = -3329 - -332903/