1)
Suppose -5/2*m**4 - 135/4 - 315/4*m - 255/4*m**2 - 85/4*m**3 = 0. What is m?
-3, -3/2, -1
Let a(w) = w**2 + 6*w + 10. Let s be a(9). Solve -5*d**3 - 53*d**2 - 54*d**2 - 44*d - s*d**3 - 4 - 38*d**2 = 0 for d.
-2/5, -1/6
Let y(j) = -61*j**3 + 710*j**2 - 964*j + 263. Let g(l) = -19*l**3 + 237*l**2 - 321*l + 87. Let s(o) = 13*g(o) - 4*y(o). Factor s(i).
-(i - 79)*(i - 1)*(3*i - 1)
Let a(y) be the first derivative of -2*y**5/15 + y**4/2 + 50*y**3/9 + 7*y**2 + 4963. Factor a(g).
-2*g*(g - 7)*(g + 1)*(g + 3)/3
Let m(o) = 5*o**3 + 2*o**2 - 6. Let j(h) = -6*h**3 - 2*h**2 + 7. Let a = 2238 + -2231. Let r = -1 + 7. Let n(d) = a*m(d) + r*j(d). Factor n(f).
-f**2*(f - 2)
Let p(t) be the second derivative of t**5/25 + t**4 + 112*t**3/15 + 24*t**2 + 127*t. Factor p(j).
4*(j + 2)*(j + 3)*(j + 10)/5
Let m(n) be the second derivative of -n**4/12 - 148*n**3 + 7*n - 161. Solve m(u) = 0 for u.
-888, 0
Let r(o) be the second derivative of o**6/60 + o**5/10 - o**4/3 - 4*o**3 - 209*o**2/2 - 3*o + 3. Let x(z) be the first derivative of r(z). Factor x(l).
2*(l - 2)*(l + 2)*(l + 3)
Determine t, given that -1136/13 + 2/13*t**3 - 44*t + 566/13*t**2 = 0.
-284, -1, 2
Let b(p) = -p**2 - 211*p - 9488. Let h be b(-65). Solve 1/5*x - 2/5*x**h - 7/5*x**3 - 4/5*x**4 + 0 = 0 for x.
-1, 0, 1/4
Suppose 0*h - h = -82. Factor 33*y - 125 + y**5 + h*y**2 + 15*y**4 - 24*y - 14*y**2 + 42*y**2 - 84*y + 74*y**3.
(y - 1)*(y + 1)*(y + 5)**3
Let p(m) be the third derivative of 0 - 2/3*m**4 + 228*m**2 + 1/10*m**6 + 0*m + 0*m**3 - 4/15*m**5. What is i in p(i) = 0?
-2/3, 0, 2
Let m(g) be the second derivative of g**6/2700 + 7*g**5/900 + g**4/15 - 7*g**3/2 - 37*g. Let y(i) be the second derivative of m(i). Factor y(r).
2*(r + 3)*(r + 4)/15
Let s(q) be the third derivative of q**7/210 + q**6/24 - 67*q**5/20 - 639*q**4/8 - 648*q**3 + 3*q**2 + 1176*q. Solve s(l) = 0.
-9, -3, 16
Let i be ((-618)/721)/(24/(-56)). Find v, given that -52/3 + 22/3*v + 2/3*v**i = 0.
-13, 2
Let x = 294 - 163. Suppose -38 + 4*n**2 + 154 + 11*n - x*n = 0. Calculate n.
1, 29
Let c(i) = -21*i - 2. Let q be c(-1). Find t, given that 2*t**2 + 11*t**4 + 17*t**2 - 6*t**2 - 4*t**2 - t**5 - q*t**3 = 0.
0, 1, 9
Let v(u) be the first derivative of -1/14*u**6 + 79/7*u**3 + 67 + 9/5*u**5 - 300/7*u - 51/4*u**4 + 180/7*u**2. Solve v(d) = 0.
-1, 1, 10
Solve 1200*q - 1133*q**2 - q**3 - 1394*q**2 + 1204 - 1082*q**2 + 3906*q**2 = 0.
-2, 301
Let x(c) be the third derivative of c**7/210 + 37*c**6/60 + 114*c**5/5 - 37*c**4/12 - 1369*c**3/6 - 872*c**2 - 2. Determine d so that x(d) = 0.
-37, -1, 1
Let w(q) be the first derivative of 0*q**2 + 6/25*q**5 - 1/30*q**6 + 0*q + 49 + 0*q**3 - 1/4*q**4. What is j in w(j) = 0?
0, 1, 5
Let f(b) be the first derivative of 4*b**3/3 + 1896*b**2 + 3788*b + 952. Determine q, given that f(q) = 0.
-947, -1
Let i(r) be the third derivative of -r**9/5040 + r**8/1120 - r**7/840 - r**4/4 - 3*r**3 + 269*r**2. Let c(v) be the second derivative of i(v). Factor c(m).
-3*m**2*(m - 1)**2
Find l such that -79*l**2 - 1/4*l**4 + 317/4 + 159/2*l - 159/2*l**3 = 0.
-317, -1, 1
Let j(b) be the third derivative of -1/210*b**5 + 82*b + 2*b**2 - 363/7*b**3 - 11/14*b**4 + 0. Factor j(t).
-2*(t + 33)**2/7
Suppose 0 = -12*r - 18*r + 60. Factor c**3 + 8*c - 72*c**r + 19 - 5*c + 53*c**2 - 4*c.
(c - 19)*(c - 1)*(c + 1)
Let k(z) be the first derivative of z**5/15 + z**4 - 20*z**3/3 + 32*z**2/3 + 390. Factor k(x).
x*(x - 2)**2*(x + 16)/3
Determine u, given that -935 + 1871/2*u - 1/2*u**2 = 0.
1, 1870
Suppose 82 - 86 = 4*j. Let a be 28/18*24/(-28)*j. Solve a*h**3 + 16/3*h**2 + 4*h + 0 = 0 for h.
-3, -1, 0
Let o = 113531/13764 - -11/6882. What is t in -o*t**2 - 3 - 18*t = 0?
-2, -2/11
Suppose 0 = 10*w - 859 + 229. Let g = -60 + w. Factor 0*j**2 - g*j**2 - 25*j + 8*j**2 + 0*j**2 - 30.
5*(j - 6)*(j + 1)
Suppose 4*f = -2*o + 6, o + 0*f - 19 = 2*f. Let x be (o/5 + -3)*-5. Factor 4*g**5 + 4*g**4 - 5*g - 4*g**2 - 8*g - x*g**3 + 13*g.
4*g**2*(g - 1)*(g + 1)**2
Solve -2288*y**2 - 1960/3*y + 0 - 14/3*y**3 = 0 for y.
-490, -2/7, 0
Let x be -35 + -2 - (-177859)/4477. Factor 8/11 + x*p - 38/11*p**2.
-2*(p - 1)*(19*p + 4)/11
Suppose 4*f - 2*f + 20 = -2*y, -4*f = 8. Let p be ((-11)/3 - -3)*84/y. Solve -18*q**2 - 7*q**4 - 5 - 3 + 6*q**4 + p*q**3 + 20*q = 0 for q.
1, 2
Let m be (-118)/(((-8420)/295)/(-4) + -7). Let o = m + 872. Solve q**2 - o - 27/4*q = 0.
-1/4, 7
Let x(t) = 2*t**2 - 3578*t + 1692794. Let j(s) = -17*s + 1. Let i(f) = -6*j(f) - x(f). Factor i(u).
-2*(u - 920)**2
Suppose 4*h - i - 9 = 0, 0 = 133*h - 129*h - 4*i - 12. Let c(f) be the first derivative of 0*f**h - 1/15*f**5 - 1/6*f**4 - 1/9*f**3 + 0*f + 2. Factor c(t).
-t**2*(t + 1)**2/3
Let b(r) be the first derivative of 1/6*r**4 + 0*r - r**2 - 4/9*r**3 - 95. Factor b(o).
2*o*(o - 3)*(o + 1)/3
Let q = -858 - -867. Suppose -q*k = -13*k - 6*k. Factor 4/5*l**3 + 0*l + k + 8/5*l**2 - 4/5*l**4.
-4*l**2*(l - 2)*(l + 1)/5
Let p(u) = 3*u**2 + 32*u + 58. Let k be p(-2). Factor -k*c**4 + 22*c**3 - 77*c**2 + 4*c**4 + 57*c**2.
-2*c**2*(c - 10)*(c - 1)
Let y(i) be the first derivative of -7*i**6/12 - 9*i**5/10 + 5*i**4/8 + 3*i**3/2 + i**2/2 - 1598. Find h such that y(h) = 0.
-1, -2/7, 0, 1
Suppose -2*p + 4*z - 20 = 0, 1 - 26 = -4*p - 5*z. Suppose 2*w = -4*t + 16, 2*w - 3*t - 13 = -18. Factor 9/2*i**w + p + i.
i*(9*i + 2)/2
Let h(z) = -z**3. Let x(t) = -8*t**3 - 6*t**2 + 2*t. Let b be 7*-2*(-30)/(-35). Let o(m) = b*h(m) + x(m). Factor o(g).
2*g*(g - 1)*(2*g - 1)
Let u = 5 + -5. Suppose -3*q + 2 = -7*d + 8*d, 5*d - 3*q - 10 = 0. Factor u - 4/9*j + 10/9*j**d - 8/9*j**3 + 2/9*j**4.
2*j*(j - 2)*(j - 1)**2/9
Let u(i) = -2*i**3 + 8*i**2 + 12*i - 6. Let y be u(5). Let j(p) be the first derivative of y*p**2 + 2/5*p**5 + 3 + 0*p + 16/3*p**3 + 5/2*p**4. Factor j(k).
2*k*(k + 1)*(k + 2)**2
Suppose -a - 9*l + 10*l + 2 = 0, 3*a + 4*l - 6 = 0. Let y be 0/((-4 - a) + 4). Factor 1/8*b**3 + 0*b**2 + 1/4*b**4 + 0*b + y + 1/8*b**5.
b**3*(b + 1)**2/8
Let i(h) = -4*h**2 + 28*h - 9. Let n(w) = 4*w**2 - 28*w + 14. Let j(r) = -2*i(r) - 3*n(r). Let j(l) = 0. Calculate l.
1, 6
Suppose 273 + 377 = -65*n. Let t(c) = -21*c - 200. Let d be t(n). Solve -10*o - d*o**3 + 0 + 5/3*o**4 + 55/3*o**2 = 0.
0, 1, 2, 3
Let p(o) be the third derivative of -1/24*o**4 + 0 + 19*o**2 + 0*o**3 - 2*o + 13/120*o**5. Find g such that p(g) = 0.
0, 2/13
Factor 17/2*p**2 + 1/4*p**3 + 95*p + 350.
(p + 10)**2*(p + 14)/4
Let l(k) be the first derivative of 8*k**2 - 1/4*k**4 + 0*k - 4/15*k**5 - 13/180*k**6 - 14 + 2/9*k**3. Let s(t) be the second derivative of l(t). Factor s(j).
-2*(j + 1)**2*(13*j - 2)/3
Let w(n) be the first derivative of -1/22*n**4 + 4/33*n**3 + n**2 + 118 - 24/11*n. Determine d so that w(d) = 0.
-3, 1, 4
Let 46/3*x**3 + 205/3*x**2 + 0*x + 1/3*x**4 + 0 = 0. What is x?
-41, -5, 0
Let p be (-77)/((-132)/(-12)) + 11. Let u(m) be the third derivative of m**2 + 1/12*m**p + 0*m + 1/60*m**5 + 0 - 1/2*m**3. Factor u(q).
(q - 1)*(q + 3)
Let v(z) be the third derivative of z**6/120 - 619*z**5/60 + 103*z**4/4 - 6*z**2 - 198. Let v(u) = 0. Calculate u.
0, 1, 618
Let d be -2*(-3)/45 + (426/(-1491))/((-120)/154). Factor -5/4*t**3 - d*t**2 + 1/4*t**4 + 0 + 6*t.
t*(t - 4)*(t - 3)*(t + 2)/4
Factor -1367 - 747*u**3 + 327 + 3*u**4 - 6921*u**2 + 12068*u**2 - 9156*u - 9701*u**2 - 5080.
3*(u - 255)*(u + 2)**3
Let r(i) be the third derivative of 25*i**8/336 - i**7/3 - 53*i**6/24 - 5*i**5/6 + 11*i**2 - 15*i. Suppose r(o) = 0. Calculate o.
-2, -1/5, 0, 5
Let m be (-88)/(-11) - (5 + 7)/3. Let a(f) be the first derivative of 0*f - m + 6/5*f**3 - 3/20*f**4 - 27/10*f**2. Factor a(t).
-3*t*(t - 3)**2/5
Let f = 505 - 489. Suppose f*j - 7*j - 7*j = 0. Determine h, given that 1/8*h**2 + 0*h + j = 0.
0
Let s(r) be the first derivative of 140 + 23*r**4 + 0*r**3 - 4/5*r**5 + 0*r**2 + 0*r. Factor s(l).
-4*l**3*(l - 23)
Suppose 0 = -3*q + 15, -2*c - 90 = -7*c + 3*q. Factor 12 + 38*r**2 - 14*r**2 - c*r**2 - 15*r.
3*(r - 4)*(r - 1)
Let c(w) be the second derivative of -w**5/40 - 323*w**4/24 + 326*w**3/3 - 327*w**2 + 13260*w. Solve c(p) = 0.
-327, 2
Let t(i) = -4*i**2 - 8*i + 220. Let z(r) = -4*r + 2. Let n(y) = -t(y) + 22*z(y). Factor n(w).
4*(w - 22)*(w + 2)
Find g, given that -13974*g + 66*g**3 - 7550*g - 76*g - 810*g**2 - 51840 + 129*g**3 - 5*g**4 = 0.
-6, -3, 24
Suppose 62*g 