)*(2*v + 1)
Let s be (-10)/(-3)*21/14. Suppose -s*x - 3 = 17. Let w(h) = -6*h**2 - 9*h + 1. Let c(u) = -5*u**2 - 8*u. Let p(j) = x*w(j) + 5*c(j). Find n such that p(n) = 0.
-2
Let h(v) = -87*v**3 + 26819*v**2 - 9612300*v + 1147067831. Let x(n) = -17*n**3 + 5364*n**2 - 1922460*n + 229413566. Let a(g) = 6*h(g) - 31*x(g). Factor a(i).
5*(i - 358)**3
Factor -104 + 56*m**2 - 44*m + 157*m**3 + 76*m**3 - 237*m**3.
-4*(m - 13)*(m - 2)*(m + 1)
Let a(b) = b**3 + 2*b**2 - b + 2. Suppose 4*g + 4*n = 2*g - 2, g + n = 0. Let t(y) = -5*y**3 + 59*y - 6. Let d(v) = g*t(v) + 3*a(v). Factor d(f).
-2*f*(f - 7)*(f + 4)
Find f, given that -320*f - 18*f**3 + 83 + 122*f + 53*f**2 + f**4 + 50*f**2 + 29 = 0.
1, 2, 7, 8
Let i be 394/10 + (4891 - 4918). Let i*m + 32/5 - 4/5*m**2 = 0. What is m?
-1/2, 16
Factor -1/3*z**4 + 1/3*z**2 + 0 - 34/3*z + 34/3*z**3.
-z*(z - 34)*(z - 1)*(z + 1)/3
Let y(g) = -27*g - 52. Let q be y(-3). Suppose 67 + 99*i - 662*i**2 + 665*i**2 + q = 0. Calculate i.
-32, -1
Let p(n) be the second derivative of -1/80*n**6 + 0 + 29*n - 19/2*n**2 - 1/40*n**5 + 1/4*n**4 + n**3. Let k(d) be the first derivative of p(d). Factor k(r).
-3*(r - 2)*(r + 1)*(r + 2)/2
Let s = -389 + 393. Let i be (20/(-30))/(s/(-21)). Factor -3/2 - 1/2*q**5 - 3*q**3 - q**2 + 5/2*q**4 + i*q.
-(q - 3)*(q - 1)**3*(q + 1)/2
Let i(y) = -y - 1. Let d(s) = -4*s**3 - 456*s**2 + 920*s - 468. Let f(k) = -d(k) + 4*i(k). Factor f(l).
4*(l - 1)**2*(l + 116)
Let s = -2070 + 2075. Let t(c) be the third derivative of 0*c**s + 0*c**4 + 0 + 1/350*c**7 + 1/100*c**6 + 4*c**2 + 0*c + 0*c**3. Factor t(n).
3*n**3*(n + 2)/5
Let v(y) = -14*y**2 + 296*y - 42. Let o be v(21). Let r(t) be the second derivative of 0 + 1/2*t**3 + o*t**2 - 1/8*t**4 - 3/40*t**5 - 18*t. Factor r(w).
-3*w*(w - 1)*(w + 2)/2
Let v(o) be the third derivative of -o**5/15 - 167*o**4/3 - 3177*o**2. Suppose v(s) = 0. What is s?
-334, 0
Let y(s) = -37*s**2 + 1. Let u be y(-1). Let w = 38 + u. Let -3*d**2 + 7*d**3 + 10 - 3*d - 2*d - w*d**3 - 7*d**2 = 0. Calculate d.
-1, 1, 2
Suppose 0 = -13*n - 185*n - 185*n + 1149. Suppose 58/19*m + 2/19*m**n - 32/19*m**2 - 28/19 = 0. Calculate m.
1, 14
Let y(r) be the first derivative of -1 + 1/32*r**4 - r + 7/8*r**3 + 147/16*r**2. Let c(f) be the first derivative of y(f). What is s in c(s) = 0?
-7
Suppose 9839 = 2*f - 3*b + 9855, 0 = 2*f - 2*b + 8. Factor -2/7*t**5 - 24/7*t**f - 144/7 - 114/7*t**3 - 268/7*t**2 - 312/7*t.
-2*(t + 2)**3*(t + 3)**2/7
Let m be (-1)/(-3)*78/(-52)*-244. Suppose m*n = 143*n. Solve y + 1/3*y**2 + n = 0 for y.
-3, 0
Let z(f) = -f**2 + 36*f + 387. Let l(c) = c**2 + 9. Let q(g) = 3*l(g) - z(g). Let q(m) = 0. Calculate m.
-6, 15
Let m(t) be the third derivative of t**7/1995 - t**6/190 - t**5/570 + t**4/38 - 1456*t**2. Factor m(h).
2*h*(h - 6)*(h - 1)*(h + 1)/19
Let v(a) be the first derivative of -35/2*a**2 + 26/3*a + 4/9*a**3 + 226. Suppose v(w) = 0. What is w?
1/4, 26
Let r = -13530 - -13551. Let m(k) be the second derivative of 47/9*k**3 + 0 - 7/18*k**4 + r*k + 14/3*k**2. What is t in m(t) = 0?
-2/7, 7
Let m = 150623/2 + -73389. Let x = m - 1922. Factor -1/8*j**3 + 0 - 1/2*j**2 - x*j.
-j*(j + 2)**2/8
Suppose -9*y = -4*y - 50. Suppose 0*v = -4*x - 5*v + 22, 2*v = -2*x + y. Determine o so that 2*o**x - o**3 - 9*o**3 + 2*o**4 + 6*o**2 + 0*o**2 + 8*o - 8 = 0.
-1, 1, 2
Let -61/7 - 1/7*y**2 - 62/7*y = 0. What is y?
-61, -1
Let j(s) be the first derivative of s**7/420 + 47*s**6/180 + 44*s**5/5 - 48*s**4 + 172*s**3/3 + 175. Let n(r) be the third derivative of j(r). Factor n(k).
2*(k - 1)*(k + 24)**2
Let w = 484 - 479. Suppose -3*r = 4*q - 10, w*r + 18 = 3*q + 2*r. Factor 5/4*h**5 + 0 + 5/2*h**3 + 15/4*h**q + 0*h**2 + 0*h.
5*h**3*(h + 1)*(h + 2)/4
Let y(x) be the first derivative of 4*x**3/9 - 1268*x**2/3 - 1696*x + 10287. Factor y(b).
4*(b - 636)*(b + 2)/3
Let s(w) = 7*w - 3. Let q be s(3). Suppose 2*l + 4 = o - 0*l, o - 4*l = 6. Determine j so that -3*j + q*j**o - 9*j**2 - 12*j**2 = 0.
-1, 0
Suppose 12*j = 7*j - 19*j + 192. Let w(d) be the first derivative of -40 - d**4 + 4*d**3 + 2*d**2 - j*d - 4/5*d**5. Determine m, given that w(m) = 0.
-2, -1, 1
Let o(q) be the third derivative of -q**5/12 + 935*q**4/8 - 1400*q**3/3 + 7*q**2 - 223*q. Factor o(b).
-5*(b - 560)*(b - 1)
Let m(s) = 165*s**2 + 186*s + 45. Let l(n) = -164*n**2 - 186*n - 44. Let r(y) = -12*l(y) - 11*m(y). Factor r(g).
3*(g + 1)*(51*g + 11)
Let c be -3 - (2/(-6)*-9 - 156). Let -328*d - 6*d**2 + 28*d**2 + 6*d**2 + 54 - c = 0. Calculate d.
-2/7, 12
Factor 10*g + 26*g + 4*g + 29 + 4*g**2 - 73.
4*(g - 1)*(g + 11)
Let z(p) = -p**2 + 6*p + 3. Let u be z(6). Suppose 5*b + 3*m + 23 = 36, 4*b - 3*m = 5. Solve 1/4*t**u - 1/4*t + 5/4*t**b - 5/4 = 0.
-5, -1, 1
Let c(x) = -7*x**2 - 1436*x - 3043. Let f be c(-203). Factor -88/3*j**f + 4/3*j + 0.
-4*j*(22*j - 1)/3
Let u(v) = -16 + 4*v - 3 - 8. Let c be u(8). What is k in -75*k**4 - 12*k**c - 38*k**2 - 12 - 34*k**2 - 84*k - 79*k**2 - 174*k**3 - 32*k**2 = 0?
-2, -1, -1/4
Let s(a) = a**2 - a. Suppose 20 = -t - 5. Let m(d) = 20*d**2 - 95*d - 245. Suppose 44*y - 8 - 29 = 7. Let v(l) = t*s(l) + y*m(l). Suppose v(x) = 0. What is x?
-7
Let h(j) = -j**3 + 5*j**2 + 8*j - 1. Let q be h(6). Let w be 3/2 - (-2975)/70. Factor q*x**3 - 60 + 48*x + x**3 + w*x**2 + 76.
4*(x + 1)*(x + 2)*(3*x + 2)
Let m(h) be the third derivative of h**6/1380 - 19*h**5/46 - 143*h**4/138 + 2342*h**2. Determine p, given that m(p) = 0.
-1, 0, 286
Let s(h) be the third derivative of -3*h**3 + 2*h**2 + 19*h - 1/20*h**5 - 25/16*h**4 + 0. Find g, given that s(g) = 0.
-12, -1/2
Let a be (-30)/(-525) + (10223/1785 - (-18 + (-5236)/(-289))). Let -1/6*j**3 + a + 7/3*j**2 + 49/6*j = 0. What is j?
-2, -1, 17
Let j = -1137/124 + 292/31. Let c(a) be the second derivative of 11*a + 294*a**2 - 14*a**3 + j*a**4 + 2. Find f, given that c(f) = 0.
14
Solve 256*m**2 + 539*m**2 + 48*m**2 + 5*m**3 - 1430 + 511*m**2 - 644*m**2 - 725*m = 0 for m.
-143, -1, 2
Let a(n) = -n**2 + 45*n - 1. Let l(z) = 35300*z**2 - 1740*z + 25. Let d(p) = 20*a(p) + l(p). Factor d(m).
5*(84*m - 1)**2
Let d be 168/18 - (-8 - -16). Let p(h) be the third derivative of 15*h**2 - d*h**3 - 4/15*h**5 + 0 - 1/30*h**6 - 5/6*h**4 + 0*h. Factor p(x).
-4*(x + 1)**2*(x + 2)
Let h be 162/(-270) + (-117)/(-45). Suppose 1/8*u + 1/8*u**4 - 1/4*u**h + 1/8 - 1/4*u**3 + 1/8*u**5 = 0. What is u?
-1, 1
Let w(v) = -10*v - 33. Let u be w(12). Let j be 34/72 + ((-748)/u)/(-22). Find d such that -5/4*d - j*d**3 + d**2 + 1/2 = 0.
1, 2
Let q(t) be the first derivative of 169*t**4/14 - 520*t**3/7 + 900*t**2/7 + 1548. Factor q(s).
2*s*(13*s - 30)**2/7
Let y(l) = -10*l**3 - 123*l**2 - 357*l - 12. Let c(p) = -3*p**3 + p - 4. Let n(u) = -3*c(u) + y(u). Factor n(h).
-h*(h + 3)*(h + 120)
Let i(t) be the first derivative of -t**6/90 + t**5/10 + 3*t**4 - 114*t**3 + 51. Let v(u) be the third derivative of i(u). Let v(x) = 0. Calculate x.
-3, 6
Let m be ((24/(-5))/(-3))/((-56826)/(-15785)). Find f, given that 2/9*f**2 - 2/9*f**3 + m*f + 0 = 0.
-1, 0, 2
Let h(g) = -g**2 - 20*g - 35. Let b(x) = x + 11. Let u be b(-26). Let m be h(u). Solve 5*c**2 + 200 - 5*c**2 + 4*c**2 - 2*c**2 + m*c = 0 for c.
-10
Let k(x) be the third derivative of -32/3*x**4 - 88/45*x**5 + 0*x + 0*x**3 - 7/72*x**6 + 0 + 259*x**2 - 1/630*x**7. Factor k(a).
-a*(a + 3)*(a + 16)**2/3
Let z(w) be the second derivative of -w**5/100 - 7*w**4/60 - 11*w**3/30 - w**2/2 - w + 303. Factor z(d).
-(d + 1)**2*(d + 5)/5
Let m(x) = x**3 - x**2 + x + 2. Let g be 9/27 - 1/3. Let u be m(g). Find p, given that 6*p + 251 - 44 + 58*p + 4*p**u + 49 = 0.
-8
Let r(s) = 7*s**2 - 896*s + 192709. Let a(p) = 20*p**2 - 2685*p + 578129. Let y(u) = 6*a(u) - 17*r(u). Find f such that y(f) = 0.
439
Let c = 173 + -168. Determine f, given that 5*f**2 - 15*f - 15*f - 5*f - 45*f**2 - c*f**3 = 0.
-7, -1, 0
Let v(p) = 423*p + 10998. Let r be v(-26). Let -32/7*w**3 + r*w + 12/7*w**4 + 8/7*w**5 + 12/7*w**2 + 0 = 0. Calculate w.
-3, 0, 1/2, 1
Suppose -22/19*b**3 + 0*b + 8/19*b**4 + 10/19*b**5 + 4/19*b**2 + 0 = 0. What is b?
-2, 0, 1/5, 1
Let l(p) be the third derivative of p**7/630 - 7*p**6/180 - 8*p**5/45 + 11*p**2 - 28*p. Determine b so that l(b) = 0.
-2, 0, 16
Suppose 2*d = j - 6081, 0 = -2*j + 3*d - 2996 + 15155. What is c in 379*c - 540*c**2 + j + 543*c**2 - 109*c = 0?
-45
