3
Factor -12/7*p**5 - 21*p**2 + 0 - 78*p**3 + 0*p + 165/7*p**4.
-3*p**2*(p - 7)**2*(4*p + 1)/7
Suppose -30*r = -650*r + 10285 - 2845. Factor r - 26/5*k - 2/5*k**2.
-2*(k - 2)*(k + 15)/5
Suppose 0 = -4272*b + 747*b + 84600. Factor -36 + b*k**2 + 0*k + 4/3*k**4 + 32/3*k**3.
4*(k - 1)*(k + 3)**3/3
Let z = -134 + 137. Let -4*h**5 - 6*h**z - 15*h**2 + 3*h**2 + 2*h**3 + 8*h + 12*h**4 = 0. What is h?
-1, 0, 1, 2
Let p = 21540 + -21540. Let b(w) be the third derivative of 0 + 1/44*w**4 - 1/330*w**5 - 2/33*w**3 - 44*w**2 + p*w. Suppose b(y) = 0. What is y?
1, 2
Let d be (275502/442)/(1/(-2)). Let o = d + 1248. Factor -14/13*z**2 - 4/13 + o*z.
-2*(z - 1)*(7*z - 2)/13
Let c(p) = 4*p + 27. Let k be c(-6). Suppose -2*t = -3*t + 2. Find f such that -3*f**5 - f + 9*f**4 - k*f**3 - 9*f**t + 6*f + f = 0.
-1, 0, 1, 2
Let r = 895405 + -6267831/7. Factor r*m**4 - 16/7*m + 32/7*m**2 + 0 - 20/7*m**3.
4*m*(m - 2)**2*(m - 1)/7
Suppose -1625*f = -1649*f + 144. Let y(o) be the third derivative of -20*o**2 + 0*o + 0 + 1/30*o**f - 4/3*o**3 - 1/2*o**4 + 0*o**5. Factor y(u).
4*(u - 2)*(u + 1)**2
Let u = 289775024/354595 + 2/70919. Let o = 818 - u. Factor o + 2/5*g**2 - 6/5*g.
2*(g - 2)*(g - 1)/5
Let i be ((-56)/(-35))/(((-5)/(-10))/1). Let s(f) be the first derivative of -28 - 4/5*f**2 + 4/5*f**3 - i*f + 2/25*f**5 + 1/2*f**4. Let s(k) = 0. Calculate k.
-2, 1
Suppose 3*m + 354 = 420. Factor 5*z - m*z**2 + 27*z**2 - 5*z + 5*z + 15*z.
5*z*(z + 4)
Let f(a) = -7*a + 85. Let m be f(5). Suppose -42*i + m*i = 32. Suppose 0 + 2/11*b**i + 2/11*b**5 - 2/11*b**3 + 0*b - 2/11*b**2 = 0. What is b?
-1, 0, 1
Let s = -21474 + 21489. Let b(y) be the first derivative of s*y**3 - 5/12*y**4 + 1215*y - 405/2*y**2 - 22. Factor b(l).
-5*(l - 9)**3/3
Let i(w) be the third derivative of -8*w**2 - 1/210*w**7 + 0*w + 0*w**3 - 1 + 0*w**4 - 1/15*w**5 + 1/30*w**6. What is t in i(t) = 0?
0, 2
Find g, given that -189*g - 45*g**4 + 186*g**3 - 17487 - 102*g**2 + 8788 + 3*g**5 + 8846 = 0.
-1, 1, 7
Suppose -x - 5 = 0, -41 = 5*d + 4*x + 109. Let y = -18 - d. Solve -52*g**2 + 14*g**3 + 8 + 9*g + 31*g + 0 + y = 0.
-2/7, 2
Suppose -14 = -2*p - 5*n, 2*p - 3*n + 4 = n. Suppose -2*z + 3 = -3*c, -p*z - 17*c = -19*c - 2. Factor -3/2*o + z - 21/4*o**2.
-3*o*(7*o + 2)/4
Let p(i) = -4*i**2 - 116*i + 120. Let u be 1 + 1 - (-28)/2. Let q be 15 + -30 + (18 - 8). Let d(o) = -o**2 - 39*o + 40. Let s(v) = q*p(v) + u*d(v). Factor s(z).
4*(z - 10)*(z - 1)
Let l be (16/12)/((-96)/(-18) - 5). Suppose b = -l*k + 9, 22*k + 3 = 21*k + 5*b. Factor k + 0*s - 1/2*s**2.
-(s - 2)*(s + 2)/2
Determine c, given that 1819/2*c - 13/3*c**4 + 1/6*c**5 + 808/3*c**2 + 867 + 19/3*c**3 = 0.
-3, -2, 17
Let f be (2/(-21))/(14*15/(-147)). Let o(p) be the third derivative of 0 - 32/3*p**3 - p + 3*p**2 - 4/3*p**4 - f*p**5. Factor o(w).
-4*(w + 4)**2
Let c be (-42)/24 + (-213)/(-12). Suppose -36*x + 14063*x**3 - c - 14072*x**3 - 5*x**4 - 28*x**2 + 4*x**4 = 0. Calculate x.
-4, -2, -1
Let r(d) = -d**2 - 12*d - 32. Suppose -504*b = -499*b + 20. Let o be r(b). Factor 1/4*j**3 - 1/4*j + 0*j**2 + o.
j*(j - 1)*(j + 1)/4
Factor -40/7 - 1048*s + 734/7*s**2.
2*(s - 10)*(367*s + 2)/7
Let n = -1261 + 1252. Let l be n/(324/(-138)) + 25/(-30). Determine g, given that -16/9*g**4 - 10/9*g**5 + 2*g**l + 0 - 8/9*g + 16/9*g**2 = 0.
-2, -1, 0, 2/5, 1
Let k(m) = -m**2 - m + 4. Let b(g) = 15*g**2 + 309*g + 222. Let z(f) = b(f) + 18*k(f). Factor z(t).
-3*(t - 98)*(t + 1)
Let h = 246 - 244. Factor -53*k**2 + 417*k**4 + 51*k**2 + 100*k - 412*k**4 - 103*k**h.
5*k*(k - 4)*(k - 1)*(k + 5)
Suppose -12319 - 9005 = -1777*g. Factor -15/2*d - 3/4*d**2 - g.
-3*(d + 2)*(d + 8)/4
Suppose -21*t = -22*t + a + 19, 3*t - 50 = -4*a. What is j in t*j**2 - 3/2*j**3 + 81/2*j + 21 = 0?
-1, 14
Let v(j) be the second derivative of 1/2*j**2 + 1/12*j**4 - 1/3*j**3 + 49*j + 0. Find m, given that v(m) = 0.
1
Let z(x) be the third derivative of x**5/330 - 243*x**4/22 + 177147*x**3/11 - 7069*x**2. Let z(m) = 0. What is m?
729
Let r(h) be the first derivative of 3*h**5/100 - h**4/10 + 37*h + 26. Let l(w) be the first derivative of r(w). Suppose l(s) = 0. What is s?
0, 2
Let g(l) be the first derivative of 2*l**5/15 - 2*l**4/3 + 8*l**3/9 + 1406. Factor g(w).
2*w**2*(w - 2)**2/3
Let p be 19 + 123/(-7) + 453/378*4. Factor 2/9*c**2 + p*c + 392/9.
2*(c + 14)**2/9
Let t be (-43)/129 + (7 - 4)/((-15)/(-5)). Factor 2/3*g**2 + 4*g**3 + 0 - 4*g - t*g**4.
-2*g*(g - 6)*(g - 1)*(g + 1)/3
Factor 60552/7 + 696/7*a + 2/7*a**2.
2*(a + 174)**2/7
Let i be 2856/13328 - 3/14. Suppose i + 8/5*h**2 - 7/5*h - 1/5*h**3 = 0. What is h?
0, 1, 7
Factor -2/11*u**2 + 4*u + 0.
-2*u*(u - 22)/11
Let o = -1311581/165 + 7949. Let s = o - -106/165. Suppose -32/3*u**5 + 80/3*u**4 - 50/3*u**3 - 10/3*u**2 + s + 10/3*u = 0. Calculate u.
-1/4, 1
Let i be -12 + 2 + 299/23. Factor n**i + 0*n + 1/2*n**5 + 3/2*n**4 + 0 + 0*n**2.
n**3*(n + 1)*(n + 2)/2
Let s(r) be the first derivative of 14/5*r**2 + 234 - 4/15*r**3 + 72/5*r. Factor s(h).
-4*(h - 9)*(h + 2)/5
Let z(d) be the first derivative of 12*d**2 + 0*d - 24/5*d**5 + 9*d**4 - 7/4*d**6 + 32*d**3 - 315. Let z(o) = 0. What is o?
-2, -2/7, 0, 2
Let h(t) be the first derivative of -t**5/30 + 89*t**4/12 + 30*t**3 + 271*t**2/6 + 181*t/6 + 2771. Determine v, given that h(v) = 0.
-1, 181
Let f(b) = 17*b**3 + 127*b**2 + 178*b - 28. Let h(u) = 52*u**3 + 382*u**2 + 534*u - 84. Let w(j) = 10*f(j) - 3*h(j). Find c, given that w(c) = 0.
-7, -2, 1/7
Let u = 99305 + -99305. Factor u + 2*l**3 + 0*l**2 + 0*l + 2/3*l**4.
2*l**3*(l + 3)/3
Let h(x) be the first derivative of x**6/9 + 22*x**5/15 - 12*x**4 + 248*x**3/9 - 64*x**2/3 + 1075. Determine z, given that h(z) = 0.
-16, 0, 1, 2
Let u be (4092/(-19096))/((-2)/12). Suppose u*a**2 + 30/7 + 51/7*a = 0. Calculate a.
-5, -2/3
Let 3*s + 71*s + 10*s + 0*s**2 - s**2 - 490 - s**2 = 0. Calculate s.
7, 35
Let b(x) be the first derivative of -x**6/540 - x**5/20 - 5*x**4/9 + 47*x**3/3 + 78. Let i(v) be the third derivative of b(v). Factor i(f).
-2*(f + 4)*(f + 5)/3
Let v = -4 - -15. Let g be (1 - 3)*11/v. Let z(d) = -4*d**2 + 24*d - 74. Let u(m) = 5*m**2 - 24*m + 75. Let c(l) = g*u(l) - 3*z(l). Factor c(h).
2*(h - 6)**2
Let g be 16 + (2 + -2 - 5). Let i be (-6)/(-15) - (-144)/15. Factor -i - r**2 + 12*r - g*r + 12.
-(r - 2)*(r + 1)
Let t = 685 + -559. Let x be 6/(-8)*(-48)/t. Let -4/7*r**4 - x*r**5 + 0 - 2/7*r**3 + 0*r**2 + 0*r = 0. Calculate r.
-1, 0
Suppose 43 = -3*n + 58. Suppose -3*d + 22 = n*w, 125*w - 127*w + 4 = 0. Solve -5/2*s**d + 40*s + 20*s**3 - 45*s**2 - 25/2 = 0.
1, 5
Let f(n) be the third derivative of -1 - 4/3*n**4 + 0*n - 1/3*n**5 - 8/3*n**3 - 1/30*n**6 - 7*n**2. Determine s, given that f(s) = 0.
-2, -1
Solve 1048 - 103*z**4 - 1108*z + 396*z**2 - 440 + 56*z**4 + 51*z**4 + 100*z**3 = 0.
-19, -8, 1
Let y(x) be the second derivative of -55*x**7/42 - 19*x**6/2 - 109*x**5/4 - 475*x**4/12 - 30*x**3 - 10*x**2 + 274*x - 2. Find m such that y(m) = 0.
-2, -1, -2/11
Let f(j) be the second derivative of -135*j**7/77 - 523*j**6/55 - 33*j**5/2 - 177*j**4/22 + 4*j**3 + 12*j**2/11 + 2*j + 2562. Let f(y) = 0. What is y?
-2, -1, -2/27, 1/5
Let q be (-231084)/(-23520) + 15/(-24). Determine z, given that -46/5*z**2 + q - 2/5*z + 2/5*z**3 = 0.
-1, 1, 23
Suppose -90*r + 91*r - 22 = 0. Suppose -5*b = r - 32. Factor y**3 - 11*y**3 + 5*y**2 + y**3 - 3*y**b.
-y**2*(9*y - 2)
Let d(a) be the third derivative of 0*a + 1/6*a**6 + 0*a**4 + 0*a**3 + 0 - 4/15*a**5 + 34*a**2 - 2/105*a**7. Factor d(c).
-4*c**2*(c - 4)*(c - 1)
Suppose 1 = -m, 0 = -4*r + 4*m + 285 + 131. Solve -372*l**2 + 21*l**4 - 112*l**3 + r*l**3 - 258*l**3 - 84*l = 0 for l.
-1, -2/7, 0, 14
Suppose -2*a = -5*t - 18, 4*t + 2*a + 18 = -0*t. Let k be (1 - -8) + t/2. Determine r so that k*r**4 - 9*r - r - 5*r**5 - 11*r**2 + 13*r**3 + 4 + 2*r = 0.
-1, 2/5, 1, 2
Let o(a) be the second derivative of -1875/2*a**2 - 1/4*a**4 + 25*a**3 + 17 + 2*a. Factor o(v).
-3*(v - 25)**2
Let f(n) be the second derivative of n**5/45 - 40*n**4/27 + 74*n**3/27 + 52*n**2/3 + 320*n. Factor f(s).
4*(s - 39)*(s - 2)*(s + 1)/9
Suppose -71 = -5*b + 3*u, 0 = 10*u - 9*u - 3. Let q be b/(-4) + (12 - (2 - -4)). Determine d so that -14/9*d**3 + 0 + 4/9*d**q + 2/9*d + 8/9*d**4 = 0.
-1/4, 0, 1
Let j = 89388 - 89386. Factor 8/5 - c**j + 18/5*c.
-(c - 4)*(5*c + 2)/5