 0, -5*k = 0. Let g(o) be the third derivative of -1/300*o**5 + 0*o - 1/15*o**3 + 1/40*o**4 - o**b + 0. Factor g(x).
-(x - 2)*(x - 1)/5
Let x be ((-4212)/(-91))/12 - (-1)/7. Let w(a) be the second derivative of 9*a - 2*a**3 + 0 - 1/20*a**5 + 1/2*a**x + 4*a**2. Let w(u) = 0. Calculate u.
2
What is m in 943/3*m**2 + 73947 + 1/3*m**3 + 74261*m = 0?
-471, -1
Let y(n) be the third derivative of -n**6/600 + 31*n**5/100 - 179*n**4/120 - 91*n**3/10 + n**2 + 268*n + 1. Factor y(z).
-(z - 91)*(z - 3)*(z + 1)/5
Let x(u) be the first derivative of -2*u**3/3 + 86*u**2 + 642. Let x(b) = 0. What is b?
0, 86
Factor 585 - r**2 + 606 + 184*r - 1413 + 792 - r**2.
-2*(r - 95)*(r + 3)
Let g(k) be the second derivative of -1/6*k**4 - 1 + 0*k**2 - 41*k + 0*k**3 - 1/120*k**5. Find h, given that g(h) = 0.
-12, 0
Let v(t) be the third derivative of 1/20*t**6 + 14/3*t**3 + 0*t + 11/4*t**4 - 57*t**2 + 23/30*t**5 + 0 - 1/105*t**7. Determine l so that v(l) = 0.
-2, -1, 7
Let s be ((-1389)/12)/(21/24). Let d = 134 + s. Factor -24/7*j - 15/7*j**2 - 3/7*j**3 - d.
-3*(j + 1)*(j + 2)**2/7
Find b such that 1900/9 + 946/9*b - 2/9*b**2 = 0.
-2, 475
Suppose 4*k - v = 31, -2*k - 36 = -5*k + 5*v. Let i be ((-72)/54)/(k/(14/(-12))). Determine g so that -i - 2/9*g**2 + 4/9*g = 0.
1
Solve -224*m - 226*m - 2*m**3 - 66967*m**2 + 66899*m**2 = 0.
-25, -9, 0
Suppose 15*y + 44 = 104. Suppose -3*z = 3*k - 3, -y*z = 3 - 7. Solve 2/5 + k*h - 2/5*h**2 = 0.
-1, 1
Let o(x) be the first derivative of 2/9*x**3 + 8 + 38/3*x - 20/3*x**2. Suppose o(f) = 0. Calculate f.
1, 19
Let t(x) = 1180*x + x**2 - 1180*x + 2. Let i(w) = 2608*w**2 - 102*w + 15. Let p(o) = -4*i(o) + 28*t(o). Factor p(d).
-4*(51*d - 1)**2
Factor -45 + 1125 + 112185163*k**2 + 278*k - 112185161*k**2.
2*(k + 4)*(k + 135)
Let w = 18635/83979 - -3/9331. Factor 2/9 + 1/9*k**3 - 1/9*k - w*k**2.
(k - 2)*(k - 1)*(k + 1)/9
Let v(r) = 12*r**2 - 191*r + 102. Let j(s) = -25*s**2 + 375*s - 205. Let o(a) = -2*j(a) - 5*v(a). Solve o(c) = 0 for c.
1/2, 20
Let s(y) = -11*y**4 + 206*y**3 + 400*y**2 + 219*y - 9. Let h(g) = 5*g**4 - 103*g**3 - 201*g**2 - 109*g + 4. Let i(v) = 9*h(v) + 4*s(v). Factor i(r).
r*(r - 105)*(r + 1)**2
Suppose 6*z + 10*z - 96 = 0. Determine d so that -12*d**3 + z*d**2 + 41*d**2 - 35*d**2 + 3*d**4 = 0.
0, 2
Let m be (-1395)/(-1085) + 10/14. Let c(y) = 9*y - 2. Let p be c(3). Factor m*d**3 + 0 - p*d**2 + 4 + 84*d - 40.
(d - 6)**2*(2*d - 1)
Let u be (-3)/2 - ((-26)/4 + 2). Suppose 2*f - u*x = f, -f - 4*x + 35 = 0. Find v, given that f*v + v**3 - 11*v + 6*v**2 + v**3 = 0.
-2, -1, 0
Let c be (3/(-12))/((-24)/2880). Suppose -2*l - c*w = -27*w, -2*w = 5*l - 11. What is t in 1/5*t**5 - 5*t**2 + 0 - 11/5*t**4 + 7*t**l + 0*t = 0?
0, 1, 5
Let i = 579748/33 + -193220/11. Factor 1/6*d**4 - 1/3*d**3 - i + 16/3*d - 5/2*d**2.
(d - 4)*(d - 1)**2*(d + 4)/6
Let o(w) be the third derivative of -11/144*w**4 + 0 - 1/720*w**6 + w**2 + 1/60*w**5 - 6*w + 1/6*w**3. Factor o(q).
-(q - 3)*(q - 2)*(q - 1)/6
Let z be (5 - (-32)/8)/((12 - 9) + -2). Determine q so that 3/4*q**2 - 21/4*q + z = 0.
3, 4
Let z = -238 - -242. Suppose 4*l**2 + 705*l**4 - 356*l**4 - 353*l**z + 28*l**3 - 28*l = 0. What is l?
-1, 0, 1, 7
Let p be 138/5 + (-302 - -275). Determine o, given that 6/5*o + 0 - p*o**3 + 3/5*o**2 = 0.
-1, 0, 2
Solve 0 - 34/3*v**3 - 10*v**4 + 8/3*v + 56/3*v**2 = 0.
-2, -2/15, 0, 1
Let y = -680 + 685. Determine x, given that -9*x**2 + 60*x - 5*x**2 + 51*x - 27 + 7*x**2 - y*x**2 = 0.
1/4, 9
Let a be ((-18 + 15)*-2 + -6)/(-3 + 6). Factor a*c + 4*c**4 + 0 + 17/2*c**3 + 1/2*c**5 + 5*c**2.
c**2*(c + 1)*(c + 2)*(c + 5)/2
Let m(k) = -7*k**3 + k**2 + 2. Let i(d) = -235*d**3 + 270*d**2 - 500*d - 180. Let l(q) = i(q) - 30*m(q). Factor l(z).
-5*(z - 6)*(z - 4)*(5*z + 2)
Let m = -258231 - -258234. Find u, given that 132/5*u**m + 16*u**2 + 4*u**5 + 88/5*u**4 + 16/5*u + 0 = 0.
-2, -1, -2/5, 0
Let c(j) = -2*j**2 - 12*j + 157. Let o be c(6). Let a be 0/(o/(78/30)). Let -2/3 + 1/6*g**3 + a*g + 1/2*g**2 = 0. What is g?
-2, 1
What is r in -3190 - 27226*r**2 + 26876*r**2 + 3910*r + 5*r**3 - 375*r = 0?
1, 11, 58
Let c(a) = a**3 - a**2 + 2*a + 2. Let h(f) = -6*f**3 - 183*f**2 - 261*f - 62. Let z(x) = -22*c(x) - 2*h(x). Find w, given that z(w) = 0.
-1, -1/5, 40
Let -k**5 + 0*k**4 - 878*k**2 - 4*k**4 - k**4 + 17*k**3 + 927*k**2 - 160*k + 100 = 0. Calculate k.
-5, 1, 2
Let b(d) = -d**4 + 7*d**3 + d**2 - 2*d. Let l(t) = -5*t**5 - 50*t**4 - 156*t**3 - 38*t**2 + 28*t. Let j(i) = -9*b(i) - l(i). Suppose j(x) = 0. Calculate x.
-10, -1, 0, 1/5
Let c(g) be the third derivative of g**6/480 - 5*g**5/48 + 67*g**4/48 + 20*g**3/3 + 4497*g**2. Solve c(i) = 0.
-1, 10, 16
Let q(o) be the first derivative of 0*o**2 - 1/90*o**5 + 1/36*o**4 + 3 + 0*o + 1/540*o**6 + 4/3*o**3. Let i(h) be the third derivative of q(h). Factor i(r).
2*(r - 1)**2/3
Let j be (-1)/14 - (4/(-70))/(336/12180). Suppose 338/5 + 2/5*o**j + 52/5*o = 0. What is o?
-13
Factor 49*t + 1/3*t**2 - 148/3.
(t - 1)*(t + 148)/3
Suppose 28 = -2*a + 4*d, -790*d + 797*d - 60 = -2*a. Let -9/5*s**3 + 0*s - 3/5*s**4 + 0 + 0*s**a = 0. Calculate s.
-3, 0
Solve -27556/7 - 332/7*q - 1/7*q**2 = 0 for q.
-166
Let h be ((-20)/338)/(3095/(-201175)). Determine j so that h*j - 2/13*j**2 - 48/13 = 0.
1, 24
Let o(d) be the second derivative of -d**4/42 - 8*d**3/7 + 25*d**2/7 + 1046*d. Let o(z) = 0. What is z?
-25, 1
Let j be (-87)/(-6)*(8 - 7) + (-28)/2. Solve -12*k - j*k**2 - 22 = 0.
-22, -2
Let f(a) be the first derivative of -a**5/35 + 6*a**4/7 - 47*a**3/7 + 107*a**2/7 - 96*a/7 - 741. Factor f(y).
-(y - 16)*(y - 6)*(y - 1)**2/7
Suppose -152 = -5*s - 4*p, 4*s + 18 - 142 = -4*p. Let b = 37 - s. Suppose 68*m**3 - b*m**4 - 32*m**3 - 30*m**3 = 0. What is m?
0, 2/3
Let h(t) be the third derivative of -t**7/630 - 14*t**2 - 86*t - 1. Factor h(v).
-v**4/3
Let p(k) be the third derivative of -k**6/75 - 7*k**5/150 + 8*k**2 - 121*k. Determine f so that p(f) = 0.
-7/4, 0
Let d(x) be the third derivative of -x**8/336 + 13*x**7/2520 + 7*x**6/96 - 13*x**5/80 + 3*x**4/32 + 6624*x**2. Find z, given that d(z) = 0.
-3, 0, 1/3, 3/4, 3
Let o(d) = d**2 - 4314*d + 64487. Let n be o(15). Factor -4/3*p**5 - 20/3*p**n + 0 - 4*p**4 + 12*p**3 + 0*p.
-4*p**2*(p - 1)**2*(p + 5)/3
Let q = -66787/8 - -333999/40. Factor q*v**2 - 74/5*v - 12.
2*(v - 10)*(4*v + 3)/5
Suppose -17 = -12*t + 175. Suppose -7*x - t = -15*x. Solve -4/3*z**x + 0 + 2/3*z**3 + 2/3*z = 0.
0, 1
Suppose -67 - 258 = -65*q. Suppose -39 = -2*f - 7*y, f + q*y - 27 = -0*y. Factor 17/4*g - 1/2 + 4*g**3 - 10*g**f.
(g - 2)*(4*g - 1)**2/4
Let v(x) = -x**3 + 7*x**2 + 2*x - 33. Let q be v(6). Suppose -9*c + 14*c - q = 0. Factor 2/7*g**c - 2/7*g - 4/7*g**2 + 4/7.
2*(g - 2)*(g - 1)*(g + 1)/7
Let j(n) be the third derivative of -5*n**8/448 - 191*n**7/168 - 299*n**6/96 + 679*n**5/48 - 155*n**4/16 - 120*n**2 + 4*n. Find f, given that j(f) = 0.
-62, -3, 0, 1/3, 1
Factor -2*h**3 - 98304 - 22786*h + 506*h**2 + 45012*h - 53458*h.
-2*(h - 128)**2*(h + 3)
Factor 2736*c + 23*c**4 + 31930 + 476*c**3 - 31930 + 2304*c**2 - 19*c**4.
4*c*(c + 2)*(c + 3)*(c + 114)
Let b(g) be the first derivative of -g**4/18 - 40*g**3/27 + 28*g**2 + 1152*g - 2290. Factor b(t).
-2*(t - 16)*(t + 18)**2/9
Factor -1/4*d**2 - 265/2 - 267/4*d.
-(d + 2)*(d + 265)/4
Solve -29/2*k - 1/2*k**3 + 10 + 5*k**2 = 0 for k.
1, 4, 5
Let d(i) be the first derivative of i**4/66 + 5*i**3/33 - 58*i + 91. Let t(l) be the first derivative of d(l). What is c in t(c) = 0?
-5, 0
Let f(i) be the first derivative of 4*i**3 + 41*i**2/2 + 48*i + 4. Let z(j) = 8*j**2 + 27*j + 32. Let u(x) = -5*f(x) + 7*z(x). Factor u(s).
-4*(s + 2)**2
Let v(z) = -6*z - 3. Let b be v(-12). Solve b*f**3 + 64*f**3 - 130*f**3 - 45*f**2 = 0 for f.
0, 15
Let l(g) be the first derivative of -g**5 + 45*g**4 - 1615/3*g**3 + 19 - 90*g**2 + 1620*g. Factor l(y).
-5*(y - 18)**2*(y - 1)*(y + 1)
Let d be (-2)/4 - (-1)/(10/55). Suppose -4*b + 54*l = 50*l - 16, 20 = b - d*l. Factor -36/5*r**4 - 54/5*r**3 + 0 + b*r - 27/5*r**2 - 8/5*r**5.
-r**2*(2*r + 3)**3/5
Suppose -28*b + 1497 = 265. Factor 5*q**4 - 260*q - 142 + b - 102 - 90*q**2 + 5*q**3.
5*(q - 5)*(q + 2)**3
Let f(l) be the first derivative of 64*l - 85 - 20*l**3 - 8*l**4 + 16*l**2 - 4/5*l**5. Suppose f(g) = 0. What is g?
-4, -1, 1
Let m = 367249/3 + -122416. Let 2*f - 4/3*f