- 20 = -11*h. Suppose 5*z + 3 = -t + 59, h = -t. Factor o**2 + 13*o + 2*o**2 + o - 2*o + z.
3*(o + 2)**2
Let j = 27 - 20. Suppose -j*y + 20 = -2*y. Factor 0*h**3 - 4*h**3 + 4*h + 6*h**y - 10*h**2 + 4*h**4.
2*h*(h - 1)*(h + 1)*(5*h - 2)
Determine j so that -76/3*j - 12*j**2 + 76/3*j**3 + 20/3*j**4 + 16/3 = 0.
-4, -1, 1/5, 1
Let w(p) be the third derivative of p**7/525 - 3*p**5/50 - p**4/15 + 4*p**3/5 + 124*p**2. Determine i, given that w(i) = 0.
-2, 1, 3
Let h = -98 - -101. Determine q, given that -2*q**h + 14*q + 4*q**5 - 20*q + 7*q - 3*q**5 = 0.
-1, 0, 1
Let f(y) = 10*y**2 + 9*y - 10. Suppose 5*p + 15 = 3*r - 22, 3 = 2*r + p. Let z(b) = b + 4 + b**2 - 3 - 2. Let n(k) = r*f(k) - 36*z(k). Factor n(c).
4*(c - 1)*(c + 1)
Suppose -76 = 4*n + 2*r - 324, 3*r - 12 = 0. Let y = n - 58. Find l, given that 6/5*l**y + 2/5*l**3 + 2/5 + 6/5*l = 0.
-1
Factor -35/4*w**2 - 3/4*w**3 - 13/4 + 51/4*w.
-(w - 1)*(w + 13)*(3*w - 1)/4
Let p be (-321)/(-21) + (-6)/21. Suppose 8 = 21*f - 17*f. Factor 3*l**4 + p*l**f - 6*l - 19*l**3 - 5*l**4 + 31*l**3 - 7*l**4.
-3*l*(l - 2)*(l + 1)*(3*l - 1)
Suppose 26*p + 12*p - 16*p = 0. Factor p + 2/7*r**5 - 2/7*r + 4/7*r**4 + 0*r**3 - 4/7*r**2.
2*r*(r - 1)*(r + 1)**3/7
Factor 8*k**4 - 7*k**3 + 4*k**5 - 4 - 4*k**2 - 6*k**5 + 30*k - k**3 - 10*k - 10*k.
-2*(k - 2)*(k - 1)**3*(k + 1)
Let r(z) be the first derivative of 4/3*z**2 - 16*z - 1/27*z**3 + 31. Factor r(v).
-(v - 12)**2/9
Let x(f) be the third derivative of f**7/350 - f**6/25 + 23*f**5/100 - 7*f**4/10 + 6*f**3/5 + 159*f**2. Factor x(m).
3*(m - 3)*(m - 2)**2*(m - 1)/5
Let d(f) be the third derivative of -f**6/360 - f**5/60 - f**4/24 - f**3/18 - 2*f**2 + 42*f. Factor d(y).
-(y + 1)**3/3
Let g be 3/6*(4 + 4). Factor -20*j + 6*j**4 + 0*j + 9*j**g + 35*j**3.
5*j*(j + 1)*(j + 2)*(3*j - 2)
Suppose 4/5*g**3 + 126/5*g**2 - 18/5*g**4 + 24/5 - 136/5*g = 0. What is g?
-3, 2/9, 1, 2
Suppose 0 = 2*m - 4*m + 60. Determine w so that m*w**3 + 7*w - 44*w**4 + 10*w**5 + 2*w**5 + 30*w**3 - 36*w**2 + w = 0.
0, 2/3, 1
Let y(p) = 2*p**2 + 4*p + 1. Let v be y(-3). Factor -7*g + 2*g + v*g - 2*g**3.
-2*g*(g - 1)*(g + 1)
Suppose 0 = -14*f + 4*f - 35*f + 90. Find y such that -2/5*y**f + 2/5*y + 4/5 = 0.
-1, 2
Let p(o) be the first derivative of 6 + 2/7*o + 3/14*o**2 + 1/21*o**3. Factor p(s).
(s + 1)*(s + 2)/7
Suppose 2*u = 4*x - u - 5, -x + 1 = -u. Determine v so that 4*v - 4*v + 75*v**x + 6*v - 24*v**2 = 0.
-2/17, 0
Let l(f) be the first derivative of -2*f**5/45 + 5*f**4/9 - 22*f**3/9 + 40*f**2/9 - 32*f/9 + 95. Find j, given that l(j) = 0.
1, 4
Let g = 2/1419 + 157/473. Let v(z) be the second derivative of 5/6*z**3 - 5/6*z**4 + 0*z**5 + 2*z + g*z**6 + 0 - 5/42*z**7 + 0*z**2. Solve v(d) = 0 for d.
-1, 0, 1
Let 0 + 0*n**3 + 0*n + 0*n**2 - 34/9*n**4 - 2/9*n**5 = 0. Calculate n.
-17, 0
Let b(c) be the first derivative of -c**3 - 3/2*c + 6 - 15/8*c**2 - 3/16*c**4. Factor b(p).
-3*(p + 1)**2*(p + 2)/4
Let g(c) = -15*c**3 + 19*c**2 - 11*c - 6. Let q(r) = -7*r**3 + 9*r**2 - 5*r - 3. Let b = -57 - -44. Let t(o) = b*q(o) + 6*g(o). Factor t(m).
(m - 3)*(m - 1)*(m + 1)
Suppose -9*b + 85 - 216 + 21*b**2 + 101 = 0. Calculate b.
-1, 10/7
Suppose 2*h - 4*l = -l + 23, -10 = 2*l. Suppose -4*s = -h - 4. Factor 4*c + 16*c**s - 3 - 13*c**3 - c**3 + 2*c**3 - 5.
-4*(c - 1)**2*(3*c + 2)
What is i in 14/9 - 16/9*i**3 - 4/3*i**2 - 2/9*i**4 + 16/9*i = 0?
-7, -1, 1
Let q(c) be the third derivative of c**5/3 + 5*c**4/6 + 5*c**3/6 - 60*c**2. Factor q(i).
5*(2*i + 1)**2
Let d(a) = -4*a**2 - a - 2. Let s(v) = 1. Let u(l) = -d(l) - 2*s(l). Factor u(x).
x*(4*x + 1)
Let s(f) be the second derivative of -f**5/40 + 11*f**4/8 - 10*f**3 + 29*f**2 + 14*f. Suppose s(j) = 0. Calculate j.
2, 29
Let b = -13 + 16. Let n = 7 - b. Solve 5*k**3 + k**3 - 2*k**5 + 0*k**3 - n*k**2 = 0 for k.
-2, 0, 1
Let o(l) = 2*l**2 - 129*l - 1404. Let u be o(74). Let 5/3*q**3 - 1/3*q**4 - 7/3*q**u + 0 + q = 0. What is q?
0, 1, 3
Let d(j) be the first derivative of -j**7/28 - j**6/10 + 9*j**5/40 + j**4/2 - j**3 - 53*j + 5. Let c(h) be the first derivative of d(h). Factor c(v).
-3*v*(v - 1)**2*(v + 2)**2/2
Let z(j) = j**3 - 3*j**2 + j - 5. Let a(k) be the first derivative of 2/3*k**3 - 1 + 2*k + 0*k**2. Let n(t) = -5*a(t) - 2*z(t). Factor n(q).
-2*q*(q + 1)**2
Factor -1/2*d + 1/2*d**3 + 11/2 - 11/2*d**2.
(d - 11)*(d - 1)*(d + 1)/2
Let r = -304 - -306. Let z(l) be the first derivative of 0*l - 3 + 0*l**3 + 0*l**r + 3/8*l**4 - 3/5*l**5 + 1/4*l**6. Factor z(g).
3*g**3*(g - 1)**2/2
Let l = 13 - 10. Let k = -2 + l. Find w such that 36*w**4 + 15*w**3 - k - 76*w**2 - 17*w**2 + 3*w**2 - 5 + 45*w = 0.
-2, 1/4, 1/3, 1
Suppose -9 + 1/2*d**4 - 15/2*d**3 - 51/2*d**2 - 53/2*d = 0. Calculate d.
-1, 18
Let p(q) = 206*q - 1028. Let r be p(5). Let l = -161/2 + 82. Solve 3*d**r + 0*d - l*d**3 + 0 = 0 for d.
0, 2
What is p in 12*p**3 + 83 + 12*p**4 - 83 + 3*p**5 = 0?
-2, 0
Suppose 4*w + 0 = -5*r - 6, -2*w = -r + 10. Let u(h) be the second derivative of 0*h**r + 1/5*h**5 + 0 - 5*h + 0*h**3 - 1/3*h**4. Factor u(n).
4*n**2*(n - 1)
Let m(a) = 0*a**2 - 9*a**2 - 8*a**2 - 19*a - 13*a + 17 + 32*a**3. Let v(h) = 11*h**3 - 6*h**2 - 11*h + 6. Let o(k) = 6*m(k) - 17*v(k). Factor o(c).
5*c*(c - 1)*(c + 1)
Let n(x) be the first derivative of -x**6/45 + 2*x**5/15 - x**4/5 - 231. Factor n(i).
-2*i**3*(i - 3)*(i - 2)/15
Let w(d) be the first derivative of -d**6/1980 + 7*d**5/660 - d**4/11 - 25*d**3/3 - 19. Let g(t) be the third derivative of w(t). Suppose g(m) = 0. What is m?
3, 4
Suppose 0 = 2*k - 2*n + 6, 2*k + 2*n + 1 = 15. Determine r so that -8*r + r - 2*r + 3*r**3 - 12*r**k + 54 = 0.
-2, 3
Let f(w) = 2*w**2 + 11*w + 11. Let k be f(-5). Suppose 5*j + 6 = 21. Determine h so that -3*h**2 + j*h**3 + 27 + k*h**2 - 15*h - 18 = 0.
-3, 1
Let v(w) be the second derivative of -w**7/336 + w**5/12 - 14*w**3/3 + 22*w. Let s(d) be the second derivative of v(d). Factor s(t).
-5*t*(t - 2)*(t + 2)/2
Factor 0 + 14/9*b**2 - 20/9*b - 2/9*b**3.
-2*b*(b - 5)*(b - 2)/9
Let u = 33 - 30. Let c(k) be the first derivative of 1/3*k**6 - 8*k + 2/5*k**5 + 8*k**2 + 4 - 2/3*k**u - 5/2*k**4. Determine p, given that c(p) = 0.
-2, 1
Let h = -194 - -587/3. Factor f**2 + h*f + 2/3.
(f + 1)*(3*f + 2)/3
Let l be (-20)/(-25) - 101/(-5). Determine h, given that -l*h**3 + 5*h**5 + 9*h - 132 + 135 + 7*h**5 - 3*h**2 = 0.
-1, -1/2, 1
Let l(z) be the second derivative of -1/150*z**6 + 0*z**2 + 0*z**3 + 3*z + 0 - 1/30*z**4 - 3/100*z**5. Factor l(j).
-j**2*(j + 1)*(j + 2)/5
Let s(n) = 4*n**2 + 31*n + 59. Let z(j) = j**2 + 8*j + 15. Let d(y) = 6*s(y) - 26*z(y). Factor d(u).
-2*(u + 2)*(u + 9)
Let y(x) be the first derivative of 4*x**3/15 - 8*x**2/5 + 134. Determine z so that y(z) = 0.
0, 4
Let q be (-130)/(-104) + (-87)/204. Factor -4/17 - q*o**2 - 18/17*o.
-2*(o + 1)*(7*o + 2)/17
Let c(f) be the first derivative of 39 - 3/2*f**4 + 3*f**5 + 9*f - 8*f**3 + 3*f**2. Solve c(a) = 0 for a.
-1, -3/5, 1
Let n(b) be the first derivative of b**7/1260 + b**6/90 + b**5/20 + 8*b**3/3 + 28. Let f(u) be the third derivative of n(u). Factor f(t).
2*t*(t + 3)**2/3
Let q(z) be the third derivative of z**8/3360 + z**7/1680 - z**6/720 - z**5/240 + 2*z**3/3 + 8*z**2. Let n(d) be the first derivative of q(d). Solve n(s) = 0.
-1, 0, 1
Let f(x) be the third derivative of -x**8/8960 - x**7/560 - x**6/192 + 5*x**4/8 - 14*x**2. Let b(t) be the second derivative of f(t). Factor b(d).
-3*d*(d + 1)*(d + 5)/4
Let o(m) be the first derivative of 0*m**3 + 8 + 1/135*m**5 - 1/108*m**4 - 1/540*m**6 + 0*m - 5*m**2. Let z(u) be the second derivative of o(u). Factor z(s).
-2*s*(s - 1)**2/9
Let h(d) = 6*d**5 + 2*d**4 - 10*d**3 + 6*d**2 - 4*d - 4. Let g(v) = -2*v**5 + v**4 + v**3 - v**2 + v + 1. Let b(a) = 4*g(a) + h(a). Find p such that b(p) = 0.
0, 1
Suppose -105 = -5*c - 0*c. Let b = -11 + c. Suppose -21*r**3 + 4*r**4 - b*r**3 + 35*r**3 = 0. What is r?
-1, 0
Suppose -6 = -3*w + 5*l, 4*w - 36 = 2*w - 2*l. Factor -21/2 - w*o - 3/2*o**2.
-3*(o + 1)*(o + 7)/2
Let d = 45 + -40. Let q(i) be the third derivative of 1/144*i**4 - 1/720*i**6 - 1/18*i**3 + 0*i - 3*i**2 + 1/180*i**d + 0. Factor q(j).
-(j - 2)*(j - 1)*(j + 1)/6
Let r(j) be the third derivative of -j**5/140 + 3*j**4/28 - 9*j**3/14 + 21*j**2 + 2. Let r(d) = 0. What is d?
3
Let l = 997 + -989. Let r(q) be the first derivative of