y - 1)/4
Let g(r) be the first derivative of 2*r**5/45 - 4*r**4/9 - 34*r**3/27 + 68*r**2/3 - 40*r + 11726. Factor g(u).
2*(u - 6)**2*(u - 1)*(u + 5)/9
Let h be (-2009)/119 + (5 - 30/(-5)) + 6. Factor h*b**3 - 2/17*b + 8/17*b**2 - 8/17.
2*(b - 1)*(b + 1)*(b + 4)/17
Suppose 8 + 4*m**3 + 134*m - 74 + 11 + 11 - 94*m**2 = 0. What is m?
1/2, 1, 22
Let c(v) be the first derivative of v**5/30 + 23*v**4/3 + 2116*v**3/3 - 11*v**2/2 + v - 143. Let g(h) be the second derivative of c(h). Factor g(a).
2*(a + 46)**2
Find a, given that 261*a**3 - 88*a**3 - 89*a**2 - 87*a**3 + 5918 - 1840*a + 430 - 87*a**3 = 0.
-46, 3
Let y(j) = -19*j**2 + 268*j + 263. Let t(z) = -104*z**2 + 1342*z + 1314. Let o(n) = 2*t(n) - 11*y(n). What is u in o(u) = 0?
-1, 265
Let i(z) be the first derivative of -z**5/10 - 219*z**4/2 - 47961*z**3 - 10503459*z**2 - 2300257521*z/2 - 2173. Find v, given that i(v) = 0.
-219
Let h = 2259 + -866. Let y = -1391 + h. Let -12 - 1/3*m**4 - 20*m + 10/3*m**3 - 13/3*m**y = 0. What is m?
-1, 6
Let x(z) be the first derivative of 16/9*z - 17/9*z**2 + 88 + 4/27*z**3. Suppose x(j) = 0. What is j?
1/2, 8
Let x be ((-68)/(-10) - 0)*3220/56. Factor -214 + 191*k - 115*k**2 - 19*k**3 - x + 14*k**3 - 906*k.
-5*(k + 1)*(k + 11)**2
Let n(z) be the first derivative of -z**5/55 - 41*z**4/44 - 62*z**3/11 - 108*z**2/11 + 2507. Find o such that n(o) = 0.
-36, -3, -2, 0
Suppose -4/5*n - 6/5*n**3 + 18/5*n**2 + 0 - 8/5*n**4 = 0. Calculate n.
-2, 0, 1/4, 1
Let d(o) be the first derivative of -o**6/33 + 124*o**5/55 - 448*o**4/11 - 4096*o**3/33 - 1573. Determine y, given that d(y) = 0.
-2, 0, 32
Let x(m) be the second derivative of -8/21*m**3 - 1/105*m**6 + 72*m + 0*m**2 - 1/147*m**7 + 0 + 2/21*m**4 + 3/35*m**5. Let x(p) = 0. Calculate p.
-2, 0, 1, 2
Let i(w) be the first derivative of 5/4*w**2 - w**3 + 11/4*w - 5/8*w**4 + 1/20*w**5 - 63. Solve i(a) = 0.
-1, 1, 11
What is d in 8*d**2 + 44 + 29*d - 22*d**3 - 9*d**3 - 3*d - 50*d**2 + 5*d**3 - 2*d**4 = 0?
-11, -2, -1, 1
Let b(r) = r**2 + 12*r - 84. Let h be b(9). Determine s so that 4 + 2*s**4 + 3*s**3 + 7*s**3 + 119*s + 18*s**2 - h*s = 0.
-2, -1
Let g be (-630)/(-60) + 1/2. Factor -g*w**3 - 10*w**2 + w**4 + 0*w**4 + 7*w**3 + 13*w**2.
w**2*(w - 3)*(w - 1)
Let v(s) be the second derivative of 29*s - 5/12*s**4 - 3/2*s**2 - 7/6*s**3 + 0 - 1/20*s**5. Factor v(p).
-(p + 1)**2*(p + 3)
Let y(n) be the first derivative of 0*n - 2/15*n**5 + 1/3*n**4 + 10/3*n**2 - 1 + 26/9*n**3. Factor y(w).
-2*w*(w - 5)*(w + 1)*(w + 2)/3
Factor -1/6*o + 2/3*o**2 - 5/6.
(o + 1)*(4*o - 5)/6
Let -m - 44489*m**2 + 22248*m**2 + 22245*m**2 + 133*m = 0. What is m?
-33, 0
Let l(u) = 8*u - 204 + 482 - 265 + 4*u**2. Let y be (6/4)/(2/(-4)). Let n(v) = -5*v**2 - 8*v - 12. Let q(r) = y*n(r) - 4*l(r). Solve q(m) = 0.
-4
Let 262*f**2 - 4*f**4 - 295936 - 11524*f**2 - 11650*f**2 - 242284*f - 576*f**3 + 85612*f = 0. Calculate f.
-68, -4
Factor -1922/7 - 32/7*h**2 - 496/7*h.
-2*(4*h + 31)**2/7
Let q(r) be the first derivative of -2/15*r**6 - 17/5*r**2 + 18/25*r**5 - 12/5*r + 19/10*r**4 - 2/5*r**3 + 146. Determine j so that q(j) = 0.
-1, -1/2, 1, 6
Let p be 4/38 - (-3 - 72/38). Let f(q) = 9*q**2 + 24*q + 33. Let v(m) = 7*m**2 + 24*m + 32. Let o(y) = p*f(y) - 6*v(y). Suppose o(n) = 0. What is n?
-1, 9
Let f(s) be the second derivative of s**5/150 - 11*s**4/45 + 41*s**3/45 - 4*s**2/3 + 77*s + 3. Factor f(o).
2*(o - 20)*(o - 1)**2/15
Factor -145*v**4 - 1728 - 6*v**3 + 909*v**2 - 25*v**5 + 521*v - 13*v**3 - 89*v.
-(v + 3)**3*(5*v - 8)**2
Let q(n) = -n**2 + 37*n + 2630. Let d be q(73). Let i = 5 + -5. Suppose z**3 + 0 + i*z**d + 1/4*z**4 + 0*z = 0. What is z?
-4, 0
Let i(o) be the third derivative of -o**6/160 + 13*o**5/40 - 9*o**4/2 + 21*o**2 - 24. Factor i(s).
-3*s*(s - 18)*(s - 8)/4
Let q be 6/27 - (-104)/18. Suppose 0 = -2*a + 2*s - q, s = 4*a - 2*a + 1. Factor 3*d**a - 2 - 4*d**2 + 37*d - 40*d.
-(d + 1)*(d + 2)
Let g be (-2 - -2)/(54/18). What is d in -d**2 - 24*d + 10*d + g*d**2 = 0?
-14, 0
Let 90/13*q - 2/13*q**4 + 138/13*q**2 + 0 + 4/13*q**5 - 86/13*q**3 = 0. Calculate q.
-5, -1/2, 0, 3
Factor -16212084*h**3 - 7938*h + 5*h**4 - 11664 - 2*h**4 + 16212072*h**3 - 1089*h**2.
3*(h - 24)*(h + 2)*(h + 9)**2
Let l(b) be the third derivative of b**8/2352 + b**7/735 - b**6/168 - b**5/70 + 884*b**2. Factor l(g).
g**2*(g - 2)*(g + 1)*(g + 3)/7
Suppose -11*c = c - 48. Solve -97*q**5 + 985*q**c - 317*q**5 - 11*q**5 - 671*q**3 + 32*q + 83*q**2 - 4 = 0.
-1/5, 2/17, 2/5, 1
Let q be 42*12/30*(-15)/(-12). Solve -3381*h**2 + 10 + 90 + q*h + 3385*h**2 + 19*h = 0 for h.
-5
Let n(x) be the first derivative of -x**5/60 + 13*x**4/24 - 2*x**3 + 3*x**2 + 7*x - 33. Let s(y) be the second derivative of n(y). What is i in s(i) = 0?
1, 12
Let o(f) be the second derivative of f**7/14 + 14*f**6/15 + 21*f**5/10 - 13*f**4/3 - 7*f**3/2 - 511*f. Suppose o(l) = 0. Calculate l.
-7, -3, -1/3, 0, 1
Let a = -85 + 152. Let -24*y**2 - 68*y**3 + 18*y + 3*y**4 - a*y**3 + 21 + 117*y**3 = 0. What is y?
-1, 1, 7
Let d = 5/24 - 1/24. Let o = -9185/3 + 3062. Suppose -1/3 - 2/3*k**3 + 0*k**4 + 1/2*k + o*k**2 + d*k**5 = 0. Calculate k.
-2, -1, 1
Let g(v) = -9*v - 148. Let l be g(-17). Determine u so that -3*u + 0*u**2 - 7*u**4 + 8*u**4 + 7*u**2 - l*u**3 = 0.
0, 1, 3
Let f(t) be the third derivative of t**6/240 + 29*t**5/60 + 315*t**4/16 + 243*t**3 - 1302*t**2 - 1. Suppose f(z) = 0. What is z?
-27, -4
Let y(g) be the first derivative of -g**5/30 + g**3/2 + g**2/3 - 2*g + 1327. Determine b so that y(b) = 0.
-2, 1, 3
Let q = -36721 + 36726. Let g(p) be the first derivative of 0*p + 0*p**2 - 1/11*p**3 - 24 + 1/55*p**q - 1/22*p**4. Factor g(o).
o**2*(o - 3)*(o + 1)/11
Let r be (-38)/722*95*6/(-40). What is d in 27/8*d - 15/8 + r*d**2 = 0?
-5, 1/2
Let b(o) be the second derivative of -13*o**6/210 + 67*o**5/140 - 31*o**4/42 + 4*o**3/21 + o - 13. Determine l so that b(l) = 0.
0, 2/13, 1, 4
Let l(o) = -o**2 - 16*o + 44. Let a be l(-18). Let s be 18/a + (-36)/(-48) + 0. Factor 0*m**2 + 4/9*m + 0 - 1/9*m**s.
-m*(m - 2)*(m + 2)/9
Suppose -5*s = -0*k + 3*k - 21, -5*k - 5 = -5*s. Suppose 0 = -2*d - k + 6. Find n such that -3*n**d + 35*n + 10 + 0*n**2 - 17*n**2 = 0.
-1/4, 2
Let d(f) be the second derivative of -7*f**5/4 - 10*f**4/3 + 55*f**3/2 - 45*f**2 - 322*f - 1. Factor d(v).
-5*(v - 1)*(v + 3)*(7*v - 6)
Let t(m) be the first derivative of -m**6/21 + 114*m**5/35 + 29*m**4/7 - 3429. Determine s, given that t(s) = 0.
-1, 0, 58
Let y be 1125/39 - (-16)/104. Solve y*c - 19*c**2 - 45*c**2 + 3*c**3 + 28*c**2 + 4*c = 0 for c.
0, 1, 11
Let t = -3/107893 + 16831323/539465. Solve t*y + 3/5*y**3 - 144/5 - 48/5*y**2 = 0.
2, 12
Let x(s) = 2*s**2 - 17*s - 33 + 5*s**2 - 13*s**2 - 37*s. Let n(b) = 19*b**2 + 164*b + 100. Let v(f) = 3*n(f) + 8*x(f). Suppose v(q) = 0. What is q?
-6, -2/3
Let y(v) be the third derivative of v**7/180 - 419*v**6/360 - 2*v**5/3 - 15*v**2 - 43. Factor y(w).
w**2*(w - 120)*(7*w + 2)/6
Let g(t) = -t - 7. Let a be g(-10). Factor -5*d**a - 16*d**2 + 4*d**2 - 2*d**2 + 8*d**4 - d**5.
-d**2*(d - 7)*(d - 2)*(d + 1)
Let m(b) be the third derivative of 4*b**3 + 7/15*b**5 + 0*b + 0 + 13/6*b**4 - 1/30*b**6 - 2/105*b**7 - 10*b**2. Let m(z) = 0. Calculate z.
-2, -1, 3
Suppose -8/3*m**2 - 4*m**3 + 8/3*m**4 + 0 + 2/3*m**5 + 10/3*m = 0. Calculate m.
-5, -1, 0, 1
Let c = 116520 + -349558/3. What is m in 2*m - c*m**3 + 4/3*m**2 + 0 = 0?
-1, 0, 3
Let t(a) = -a**4 - a**3 - a. Let q(c) = -11*c**4 - 17*c**3 - 10*c**2 - 13*c. Let k = -54 + 36. Let m(b) = k*t(b) + 2*q(b). Find z such that m(z) = 0.
-2, -1, 0
Let s be (-26)/78*36/3. Let r be 20/(-12)*s/20. Factor 1/3*a**2 - 1/3 - 1/3*a**3 + r*a.
-(a - 1)**2*(a + 1)/3
Let h(i) = 28*i + 171. Let s be h(-6). Let v be (s/45)/(1/18). Determine p, given that 0*p - v*p**3 - 24/5*p**4 - 14/5*p**5 + 0 + 4/5*p**2 = 0.
-1, 0, 2/7
Let y(a) = -5*a**3 + a**2 + 5*a + 5. Let d be y(-2). Let s = d + -33. Factor -5 - 17*l**3 + s*l**3 + 7*l**2 + 6*l**3 + 5*l - 2*l**2.
-5*(l - 1)**2*(l + 1)
Let y(l) = -2*l**3 + 107*l**2 + 56*l - 80. Let i be y(54). Let a be (-14)/(-21) - i/(-21). Determine h, given that 5/4*h + 3/2 - 1/4*h**a = 0.
-1, 6
Suppose 591 = -26*t - 1645. Let g = -82 - t. What is q in 4/9*q**4 - 8/3*q - g + 32/9*q**2 + 8/3*q**3 = 0?
-3, -1, 1
Suppose 7*y - 21*y - 72*y = -344. Let z(g) be the second deri