
-1, 3
Let q = 103 + -66. Factor 50*j**2 + 20*j - q - 5*j**4 - 3 - j**4 - 14*j**4 - 5*j**3 - 5*j**5.
-5*(j - 1)**2*(j + 2)**3
Let 132651/5 + 7803/5*y + 1/5*y**3 + 153/5*y**2 = 0. Calculate y.
-51
Let t = 20/23 - 877/1035. Let s(v) be the second derivative of 0*v**2 + t*v**6 + 0*v**3 + 0*v**5 + 0 + 1/63*v**7 - 4*v + 0*v**4. Let s(u) = 0. What is u?
-1, 0
Let 462*c - 35*c**2 + 12*c**2 + 19*c**2 - 62*c - 10000 = 0. What is c?
50
Factor 11*x**2 + x**2 + 77*x - 10*x**3 - 18*x + 85*x - 24 - 26*x.
-2*(x - 4)*(x + 3)*(5*x - 1)
Suppose 3*k + 2*s - 24 = 0, 33 = 4*k - s + 4*s. Factor -3 - k*i**2 + 8 + i**2.
-5*(i - 1)*(i + 1)
Let o(g) be the third derivative of -g**3/6 + g**2. Let p be (5/(-15))/((-12)/180). Let c(w) = w**2 - 8*w + 11. Let u(y) = p*o(y) - c(y). What is m in u(m) = 0?
4
Let d(o) = 2*o + 18. Let v be d(-8). Determine z so that 2*z**v - 20*z + 0*z**2 - 148 + 198 = 0.
5
Let i(t) = -t + 1. Let y(p) be the second derivative of p**4/12 + p**3 - p**2/2 + p. Suppose -9*k - 7 + 16 = 0. Let m(a) = k*y(a) + 3*i(a). Factor m(h).
(h + 1)*(h + 2)
Let j(r) = -40*r**2 + 1385*r - 11510. Let i(w) = -5*w**2 + 173*w - 1439. Let t(g) = 25*i(g) - 3*j(g). Factor t(p).
-5*(p - 17)**2
Let q be 4*5/15 - (-2280)/450. Suppose 16/5*w + 4/5 - q*w**3 + 16/5*w**5 - 8/5*w**2 + 4/5*w**4 = 0. What is w?
-1, -1/4, 1
Suppose y + 38 = -0. Let n = y + 40. Suppose 7*z**n - z + 0 - 49/4*z**3 = 0. Calculate z.
0, 2/7
Let x(v) be the second derivative of v**7/504 - v**6/120 - v**5/40 + 7*v**4/36 - v**3/3 - 106*v. Suppose x(d) = 0. What is d?
-3, 0, 2
Let v(j) be the first derivative of -8*j - 8*j**2 - 1/2*j**4 - 7 - 10/3*j**3. Factor v(r).
-2*(r + 1)*(r + 2)**2
Suppose 21*k - 20 = 22. Let z(v) be the third derivative of -1/15*v**5 + 0*v - 1/30*v**6 + 0*v**4 + 0*v**3 + 7*v**k + 0. Let z(p) = 0. What is p?
-1, 0
Let k(p) be the first derivative of 4*p**5 + 32*p**4 + 76*p**3 + 76*p**2 + 32*p - 166. Determine q, given that k(q) = 0.
-4, -1, -2/5
Suppose 6*g = -1 - 17. Let b(o) = o**2 - o + 3. Let c(z) = 2*z**2 - z + 5. Let k(y) = g*c(y) + 5*b(y). What is d in k(d) = 0?
-2, 0
Suppose 12/7 + 15/7*g + 3/7*g**2 = 0. What is g?
-4, -1
Let g be 2*-1*(-24)/16. Let c be (g/(-3) - -5) + 1. Determine q so that 1/3*q**3 + 0 + 2/3*q**4 + 0*q**2 + 1/3*q**c + 0*q = 0.
-1, 0
Let f = 2452 + -12259/5. Solve -3/5*g**4 - 8/5*g**3 + 8/5*g - f*g**2 + 4/5 = 0 for g.
-2, -1, -2/3, 1
Let r(m) = 2*m**2 - 14*m - 11. Let o be r(8). Let p(c) be the third derivative of 1/80*c**6 + 1/4*c**3 + 0*c - 8*c**2 + 3/40*c**o + 3/16*c**4 + 0. Factor p(i).
3*(i + 1)**3/2
Factor 0 + 1/3*w**2 + 1/3*w - 1/3*w**4 - 1/3*w**3.
-w*(w - 1)*(w + 1)**2/3
Let h(j) be the first derivative of -j**7/1260 + j**5/360 + 7*j**2/2 + 3. Let m(u) be the second derivative of h(u). Let m(f) = 0. What is f?
-1, 0, 1
Let t(b) be the third derivative of b**5/5 + 49*b**4/12 + 8*b**3/3 + 52*b**2 + 2*b. Find n, given that t(n) = 0.
-8, -1/6
Suppose -3*i = -2*i. Suppose a - 3 = -i*a. Factor -s**5 - s**2 + s**a + 2*s**4 + 0*s**5 - s**4.
-s**2*(s - 1)**2*(s + 1)
Suppose 0 = -3*d - 2 + 23. Let m be (-2)/1*(-7)/d. Factor -3 + 3 + 8*f**3 - 2*f**m - 3*f**4 - 4*f**2 + 1.
-(f - 1)**3*(3*f + 1)
Let f be 98/84*(-24)/(-56). Factor -1/2*n + 0 + f*n**2.
n*(n - 1)/2
Find y, given that -4/7*y**2 + 116/7*y + 384/7 = 0.
-3, 32
Let q(l) = -8*l**4 - 7*l**3 + 65*l**2 - 50*l. Let z(u) = -15*u**4 - 15*u**3 + 130*u**2 - 100*u. Let h(m) = -5*q(m) + 3*z(m). Solve h(g) = 0.
-5, 0, 1, 2
Let g be (4 - -1)*(2 - 136/70). Let z(s) be the first derivative of -g*s**2 + 0*s**3 + 2/35*s**5 + 5 + 1/7*s**4 - 2/7*s. Factor z(v).
2*(v - 1)*(v + 1)**3/7
Suppose -10 + 58 = 3*o. Determine s, given that 2*s**3 + 30 + 10*s**3 - 35*s + o*s**3 - 45*s**2 + 7*s**3 + 15*s**4 = 0.
-3, -1, 2/3, 1
Let p(o) be the second derivative of -9*o - 5/12*o**4 + 5/2*o**2 + 0 + 0*o**3. Determine n, given that p(n) = 0.
-1, 1
Let n(a) be the second derivative of a**6/200 + 3*a**5/50 + 11*a**4/40 + 3*a**3/5 + 7*a**2/2 - 40*a. Let t(r) be the first derivative of n(r). Factor t(m).
3*(m + 1)*(m + 2)*(m + 3)/5
Factor -55*z**4 + 74*z**4 - 49*z**4 + 120*z**2 + 0*z**3 - 80*z - 5*z**3 - 5*z**5.
-5*z*(z - 1)**2*(z + 4)**2
Solve 86*c**2 - 40*c + 24 + 4*c**4 - 24*c**3 - 38*c**2 - 1 - 11 = 0 for c.
1, 3
Let d(y) be the first derivative of y**4/4 - 14*y**3/15 + 7*y**2/10 + 2*y/5 + 152. Factor d(j).
(j - 2)*(j - 1)*(5*j + 1)/5
Let q(b) be the second derivative of -7/54*b**4 + 0*b**2 + 8/27*b**3 - 28*b + 0 - 1/90*b**5. Factor q(d).
-2*d*(d - 1)*(d + 8)/9
Let i(p) = 4*p - 9. Let z be i(3). Let b be z*((-88)/(-42) + -2). Factor 2/7*d**4 - 8/7*d**3 - 8/7*d + 12/7*d**2 + b.
2*(d - 1)**4/7
Suppose -4*y - s = -15, y - s - 17 = -3*y. Find w such that 1/2*w**3 + 1/2*w**y - 1/4*w - w**2 - 1/4*w**5 + 1/2 = 0.
-1, 1, 2
Let a(d) be the third derivative of d**6/300 - d**5/30 + d**4/15 - 19*d**2 + 3. Factor a(i).
2*i*(i - 4)*(i - 1)/5
Let n(r) be the first derivative of -r**9/10584 + r**7/588 - r**5/105 + 2*r**3 + 26. Let s(k) be the third derivative of n(k). Solve s(p) = 0 for p.
-2, -1, 0, 1, 2
Let a(p) be the third derivative of -1/44*p**4 + 0*p - 1/330*p**5 + 0 - 6*p**2 - 2/33*p**3. Factor a(i).
-2*(i + 1)*(i + 2)/11
Let g(a) be the first derivative of 1/9*a**3 + 4*a**2 - 10 + 48*a. What is m in g(m) = 0?
-12
Let y(x) = 4*x**3 - 5*x**2 + 10*x. Let d(r) be the first derivative of 7*r**4/4 - 10*r**3/3 + 19*r**2/2 - r + 10. Let h(v) = 3*d(v) - 5*y(v). Factor h(g).
(g - 3)*(g - 1)**2
Let h(n) be the second derivative of -1/4*n**5 + 5/12*n**4 + 10/3*n**3 + 2*n + 0 - 10*n**2. Find f such that h(f) = 0.
-2, 1, 2
Let w(v) = -7*v**3 - v + 12. Let h(y) = 6*y**3 - y**2 + 2*y - 11. Let g(i) = 6*h(i) + 5*w(i). Let z be g(5). Factor -4*l**4 + 37*l - 8*l**3 + z*l**3 - 37*l.
-4*l**3*(l + 1)
Factor -167/6*v + 13/3 - 13/6*v**2.
-(v + 13)*(13*v - 2)/6
Suppose -g + 15 = 5*h, 4*h + 4*g = h - 8. Determine a, given that 5*a**h + 99*a**2 + 9*a**5 - 22*a**4 - 7*a**3 - 22*a**4 + 4*a**3 + 54*a = 0.
-1, -2/3, 0, 3
Let w(f) be the second derivative of 2/9*f**3 - 5/54*f**4 + 0*f**2 + 0 + 1/90*f**5 + 8*f. Factor w(t).
2*t*(t - 3)*(t - 2)/9
Suppose 5*p + 5 = -20. Let y be (-6 - -1)/(p/5). Factor -25*v**3 + 55*v**4 + 9*v**3 + 21*v**y + 7*v**5 - 7*v**4.
4*v**3*(v + 2)*(7*v - 2)
Factor 409*k - 175 + 0*k**2 + 3*k**2 + 3*k**2 - 269 + 476*k.
3*(k + 148)*(2*k - 1)
Let s(o) be the first derivative of -25*o**6/3 + 122*o**5 - 319*o**4/2 - 266*o**3/3 + 128*o**2 + 88*o + 256. Let s(g) = 0. What is g?
-2/5, 1, 11
Let z(n) = -7 + 4*n**2 - n**3 + n + 4*n**2 + 4*n**2 - 3*n**2. Let d be z(9). Factor 5*o**2 + 4*o**2 + 2 - 13*o**d + 7*o + 0.
-(o - 2)*(4*o + 1)
Let h(g) = -g. Let p(v) = -v**2. Let n(r) = -h(r) - p(r). Suppose 5*a - 6 + 1 = 0. Let q(o) = 3*o**2 - 5*o. Let w(x) = a*n(x) + q(x). Let w(z) = 0. What is z?
0, 1
Let q be 36 + -27 - (-177)/(-21). Let 2/7*y**4 + 0 + 2/7*y**3 + 0*y - q*y**2 = 0. What is y?
-2, 0, 1
Let m(t) = 6*t**4 + 11*t**3 - 7*t**2 + 7*t + 7. Let i(n) = 2*n**4 + 4*n**3 - 2*n**2 + 2*n + 2. Let j(l) = -14*i(l) + 4*m(l). Suppose j(a) = 0. Calculate a.
-3, 0
Let i = 119 - 473/4. Let s = -2653 - -2653. Find d, given that -d**5 + 5/4*d**3 + 3/4*d**4 - i*d**2 + s - 1/4*d = 0.
-1, -1/4, 0, 1
Let 36/5*l**2 + 2/5*l**3 + 88/5*l - 1/5*l**4 + 64/5 = 0. What is l?
-2, 8
Let t(j) be the second derivative of 2*j**3/3 - j**2 - 3*j. Let l be t(6). Find q such that -4*q - 2*q**2 + l*q**3 - 24*q**3 - 4*q**2 = 0.
-2, -1, 0
Let o(w) be the third derivative of 0*w**4 + 0*w**3 + 1/20*w**5 + 0 + 5*w**2 + 0*w. Determine p so that o(p) = 0.
0
Let j = 1/994 - -461211/4970. Suppose 2*h + h - 1474 = -k, 3*h = -5*k + 1490. Let 1088/5*n**3 - j*n**2 - h*n**5 + 32/5 + 378*n**4 - 96/5*n = 0. Calculate n.
-2/5, 2/7, 1
Let 0*i**4 + 33/2*i - 1/2*i**5 + 8*i**3 + 19*i**2 + 5 = 0. What is i?
-2, -1, 5
Let y(c) = -c**3 + 5*c**2 + c - 16. Let m be y(4). Let n(p) be the first derivative of 0*p - 3/14*p**2 + 3/28*p**m - 1 + 0*p**3. Factor n(i).
3*i*(i - 1)*(i + 1)/7
Let j(u) be the second derivative of 13*u + 2/3*u**4 - 1/5*u**5 + 0 + 0*u**2 + 0*u**3. Find v, given that j(v) = 0.
0, 2
Factor 208/5*m + 26*m**2 + 8 + 18/5*m**3.
2*(m + 2)*(m + 5)*(9*m + 2)/5
Factor 4/3*b**2 - 1/3*b**4 + 0*b + 0 + 0*b**3.
-b**2*(b - 2)*(b + 2)/3
Suppose 76 = -10*d - 104. Let a be (-38)/342 + (-38)/d. Solve -6/7*j + 4/7 + 8/7