 r = -182 - -180. Let t be 0/5*1/r. Suppose -4/7*v**3 + t + 4/7*v**2 + 4/7*v - 4/7*v**4 = 0. Calculate v.
-1, 0, 1
Let q = 33737 - 33733. Let v(i) be the second derivative of 0 - 1/18*i**q + 4/9*i**3 + 13*i + 5/3*i**2. Factor v(k).
-2*(k - 5)*(k + 1)/3
Let q(d) = -d**3 - 27*d**2 + 145*d + 131. Let y(g) = -25*g**2 + 155*g + 130. Let j(h) = -5*q(h) + 4*y(h). Let j(t) = 0. What is t?
-9, -1, 3
Let i(m) = -m**2 - 11*m + 48. Let c be i(-14). Suppose 3*f + c = 2*s, -5*s + 4*f = -10 + 2. Factor 4/3*o - 1/3*o**2 + s.
-o*(o - 4)/3
Let a = -4674 - -4678. Let l(d) be the first derivative of -2/45*d**5 + 2/27*d**3 + 5 + 0*d - 2/9*d**2 + 1/9*d**a. Let l(x) = 0. What is x?
-1, 0, 1, 2
Let g = 1258 - 1248. Let o be (12/(-150))/(g/(-100)). Suppose 12/5*a + 4/5*a**4 - 12/5*a**3 - o*a**2 + 0 = 0. What is a?
-1, 0, 1, 3
Let o(i) = -11*i**3 - i**2 - 1. Let p(w) = -19*w**3 - 95*w**2 + 474*w - 602. Let k(l) = -2*o(l) + p(l). Suppose k(r) = 0. What is r?
2, 4, 25
Let f be (-3)/5 + (-6864)/(-65). Factor 8*g**2 + f*g + 21 - 23*g - 17 + 16.
2*(g + 10)*(4*g + 1)
Factor 22/7*c**3 + 17/7*c**2 - 7*c + 10/7.
(c - 1)*(c + 2)*(22*c - 5)/7
Let y = 6086 + -12171/2. Let l(i) be the second derivative of 0 + 11*i - 3/20*i**5 - 1/2*i**3 + y*i**4 + 0*i**2. Find d, given that l(d) = 0.
0, 1
Factor 5/2*p**2 + 477*p - 191/2.
(p + 191)*(5*p - 1)/2
Let n(q) be the second derivative of -q**7/14 - 7*q**6/10 - 6*q**5/5 + 4*q**4 + 1647*q. Determine r so that n(r) = 0.
-4, 0, 1
Let 25*z**3 - 2*z**3 - 41*z**4 + 36*z + 4*z + 42*z**4 + 62*z**2 = 0. What is z?
-20, -2, -1, 0
Factor -65*t**2 + 106 - 70*t + 63*t**2 - 714.
-2*(t + 16)*(t + 19)
Let m(u) be the second derivative of u**6/90 - u**5/12 + u**4/12 + u**3/2 - 53*u + 2. Determine k, given that m(k) = 0.
-1, 0, 3
Suppose 113/2*v**4 + 7*v**5 - 15*v**3 - 275/2*v**2 + 113*v - 24 = 0. Calculate v.
-8, -2, 3/7, 1/2, 1
Let v(b) be the first derivative of -3*b**4/4 - 13*b**3 - 81*b**2 - 216*b + 823. Suppose v(x) = 0. Calculate x.
-6, -4, -3
Suppose 3*l + 12*w = 10*w + 22, 0 = -l + 2*w - 22. Factor -16/7*j**2 - 16/7*j + l - 4/7*j**3.
-4*j*(j + 2)**2/7
Let d = 5803281/6286930 + 3/483610. Let 14/13*h**2 + d - 46/13*h = 0. Calculate h.
2/7, 3
Determine d so that 1/5*d**2 + 112/5 + 22/5*d = 0.
-14, -8
Let o be ((-8)/(-24))/((-1)/(-42)). Let g(m) be the first derivative of 5*m**4 - 17*m**3 + 7*m**3 - 4*m**2 + 5 + o*m**3. Factor g(j).
4*j*(j + 1)*(5*j - 2)
Let 0*y + 0 + 32/5*y**3 + 1792/5*y**2 - 5*y**4 + 1/5*y**5 = 0. What is y?
-7, 0, 16
Let w be (672/90 - 2)/((-4)/438). Let n = 599 + w. Suppose -n + 2*v**5 - 18/5*v**4 + 4*v**2 - 6/5*v - 4/5*v**3 = 0. What is v?
-1, -1/5, 1
Let -130*j + 1/5*j**2 - 651/5 = 0. Calculate j.
-1, 651
Let c be ((560/175)/(-16))/(33/(-150)). Suppose -3*k + 9 = -0. Find y such that 10/11*y**k + c*y**2 - 8/11 - 2/11*y**5 - 2/11*y**4 - 8/11*y = 0.
-2, -1, 1, 2
Let j(p) be the second derivative of -p**4/12 + p**3 - 5*p**2/2 + 15*p. Let r be j(5). Determine x, given that -4*x**5 + r*x**5 - 3*x**5 + 3*x**5 = 0.
0
Let a(f) be the first derivative of -2*f**6/3 + 208*f**5/5 - 771*f**4 + 3264*f**3 - 3456*f**2 + 978. Suppose a(h) = 0. What is h?
0, 1, 3, 24
Let n(b) be the second derivative of 0*b**2 + 0 + 19/24*b**4 + 56*b + 1/30*b**6 + 1/3*b**3 + 5/16*b**5. Let n(y) = 0. Calculate y.
-4, -2, -1/4, 0
Suppose -1974 + 1722 = t. Let k be (-4)/(-49)*(t/8)/(-9). Determine p so that 0 + 0*p + k*p**2 = 0.
0
Let l(y) = 24945*y + 723405. Let m be l(-29). Suppose -16/9*h**4 + m*h - 2/3*h**5 + 0*h**2 + 2/3*h**3 + 0 = 0. What is h?
-3, 0, 1/3
Factor -44*l**3 + 612*l + 132*l**3 - 237 - 564*l**2 + 268*l - 163 - 4*l**4.
-4*(l - 10)**2*(l - 1)**2
Suppose -6*q**5 + 20*q**4 + 195*q**2 + 19*q**3 - 167*q**2 + 33*q**3 + 2*q**5 = 0. Calculate q.
-1, 0, 7
Let x be (-225)/6*(124/10 - 13). Factor 0 + 21/2*h + x*h**2 + 3/2*h**4 + 27/2*h**3.
3*h*(h + 1)**2*(h + 7)/2
Let w(k) be the second derivative of -1/84*k**4 + 1/14*k**2 + 4 - 2*k + 0*k**3. Let w(r) = 0. What is r?
-1, 1
Factor 735042*r + r**3 - 733426*r - 4 + 2 + 2 - 810*r**2.
r*(r - 808)*(r - 2)
Let w be ((-60)/21)/(-5)*7/2. Factor -2*f**3 - f**3 - 252*f**2 - 13467*f + w*f**3 - 300763 + 51*f**2.
-(f + 67)**3
Let h(b) = 11*b**3 + 17*b + 17. Let i(j) = -227*j**2 + 227*j**2 + 2*j**3 + 6 + 6*j + 2*j**3. Let p(d) = -6*h(d) + 17*i(d). Factor p(m).
2*m**3
Let c(w) = w**3 - 3*w**2 - 14*w - 15. Let p be c(8). Suppose z - 193 = -2*j, -3*j + p = z + j. Factor z*l**4 + 192*l**4 + 2*l**3 - 2*l - 386*l**4 + l**2.
-l*(l - 2)*(l - 1)*(l + 1)
Let s(b) be the first derivative of -b**3/2 - 27*b**2/16 + 39*b/8 + 1356. Factor s(z).
-3*(z - 1)*(4*z + 13)/8
Find t, given that -284*t - 229*t - 7*t - 20 + 695*t**2 - 430*t**2 = 0.
-2/53, 2
Let h(l) be the second derivative of 1/6*l**3 - 3*l - 1/48*l**4 + 3 - 3/8*l**2. Factor h(k).
-(k - 3)*(k - 1)/4
Let n(k) = k**2 + 14*k - 27. Let t be n(-14). Let w = -24 - t. Suppose -5*o**5 + 8*o**5 + 3*o**2 + 0*o**2 - 3*o**w - 3*o**4 = 0. Calculate o.
-1, 0, 1
Let v(y) be the third derivative of y**6/8 + 73*y**5/12 - 125*y**4/12 - 1637*y**2. Factor v(w).
5*w*(w + 25)*(3*w - 2)
Let r(q) = -13*q**3 - 424*q**2 + 3*q - 3. Let h(x) = 8*x**3 + 424*x**2 - 2*x + 2. Let a(o) = -3*h(o) - 2*r(o). Find c such that a(c) = 0.
0, 212
Let k(g) be the first derivative of 0*g - 1/2*g**4 + 4/7*g**2 + 17 - 8/21*g**3 - 1/7*g**6 + 4/7*g**5. Suppose k(j) = 0. Calculate j.
-2/3, 0, 1, 2
Let v be (1 - (3 + -1)) + 5. Factor -8*k**2 - 37 - 4*k + v*k**3 + 78 - 33.
4*(k - 2)*(k - 1)*(k + 1)
Let x(y) = -85*y**3 + 410*y**2 + 6330*y + 33210. Let v(q) = -3*q**3 + 2*q**2 + 3*q + 3. Let i(h) = -30*v(h) + x(h). Factor i(w).
5*(w + 12)**2*(w + 46)
Let o(y) be the second derivative of 30*y**3 - 9*y - 2025*y**2 + 9 - 1/6*y**4. Factor o(m).
-2*(m - 45)**2
Let g(h) = -h**2 + 236*h + 1208. Let b be g(-5). Determine i, given that -9 - 1/4*i**4 - 13/4*i**2 + 15*i - 5/2*i**b = 0.
-6, 1
Factor 70*h**2 - 16*h**3 + 35*h - 18*h**3 - 21*h**3 + 40*h**3 - 50.
-5*(h - 5)*(h + 1)*(3*h - 2)
Let u be (-5)/(-42)*(-20)/(-25)*(-1610)/(-69). Find b, given that 4/3 - 26/9*b**2 - u*b**3 + 34/9*b = 0.
-2, -3/10, 1
Let b(j) be the first derivative of 28/3*j**3 + j**4 + 48*j + 32*j**2 + 70. Factor b(u).
4*(u + 2)**2*(u + 3)
Factor 1/3*g**3 + 0 + 370/3*g**2 - 371/3*g.
g*(g - 1)*(g + 371)/3
Suppose 9*r**3 - 60 + 0*r**3 - 210*r - 101*r + 39*r - 56*r - 259*r**2 = 0. What is r?
-1, -2/9, 30
Let p(f) be the second derivative of 3*f**5/100 - 1469*f**4/20 + 270112*f**3/5 - 808134*f**2/5 + 2*f + 26. Factor p(d).
3*(d - 734)**2*(d - 1)/5
Let r(x) = 24*x**3 - 167*x**2 + 597*x - 447. Let p(w) = -11*w**3 + 83*w**2 - 298*w + 223. Let y(i) = 7*p(i) + 3*r(i). Factor y(n).
-5*(n - 11)*(n - 4)*(n - 1)
Let n = 679 - 670. Let x be (12/n)/((-112)/36 - -4). Factor -x*u**2 - 363/2 - 33*u.
-3*(u + 11)**2/2
Let 2/9*p**5 - 15304/9*p**2 + 172/9*p**4 - 900 + 3340/9*p**3 + 2210*p = 0. What is p?
-45, 1, 2
Let m(j) be the first derivative of 2*j - 24 + 1/2*j**2 - 1/3*j**3. Solve m(l) = 0 for l.
-1, 2
Determine z so that 0*z**2 + 0*z + 1252/7*z**3 + 2/7*z**5 + 0 - 90*z**4 = 0.
0, 2, 313
Let b(s) be the second derivative of -19*s**5/10 + 1196*s**4/3 - 25053*s**3 - 7938*s**2 + 1213*s - 1. Factor b(d).
-2*(d - 63)**2*(19*d + 2)
Let v(j) be the second derivative of -7/120*j**6 + 1 - 1/6*j**3 - 13/40*j**5 + 42*j + 1/2*j**2 - 9/16*j**4. Suppose v(m) = 0. Calculate m.
-2, -1, 2/7
Let v(r) be the first derivative of -3*r**4/16 - 13*r**3 - 135*r**2/2 + 432*r - 1974. Factor v(p).
-3*(p - 2)*(p + 6)*(p + 48)/4
Let t be (1/1)/(4/(-2292)). Let o = -543 - t. Factor o*i**2 + 21*i**3 + 24/7 - 156/7*i.
3*(i + 2)*(7*i - 2)**2/7
Let y(n) be the third derivative of -n**5/20 + 63*n**4/8 + 32*n**3 - 19*n**2 + 5. Factor y(o).
-3*(o - 64)*(o + 1)
Let l be (70/(-10) - -16)*-3. Let y be (15/(-45))/(45/l). Factor 0 + y*c**2 + 7/5*c.
c*(c + 7)/5
Let a(b) = -2*b**2 - b + 8. Let f be a(-2). Factor 26*u + 24 + 88*u - 34*u - 12*u**f + 4.
-4*(u - 7)*(3*u + 1)
Let c(b) be the third derivative of 49 - b**2 + 0*b + 3/7*b**3 + 1/14*b**4 + 1/210*b**5. Solve c(q) = 0.
-3
Let n be (2050/(-1435))/(25/(-35) - 0). Determine s, given that -64/15*s**n + 2/3*s**4 + 2/15*s**5 + 64/15*s + 0 - 4/5*s**3 = 0.
-4, 0, 1, 2
Let k = -138 + 691/5. Let m(l) be the first derivative of -11 - 8/15*l**3 + 0*l - k*l**2. Factor m(a).
-2*a*(4*a + 1)