*q + 13*q + 9 - 1. Let k be p(-5). Let 2*b**2 - 4*b**2 + 4*b**k + 2*b = 0. Calculate b.
-1, 0
Let n be (-41)/(-8) - 83/664. Let t(h) be the second derivative of 1/60*h**6 - 2*h**3 + 0 + 11/12*h**4 + 2*h - 1/5*h**n + 9/4*h**2. Factor t(d).
(d - 3)**2*(d - 1)**2/2
Let z be 1/((-30)/8 - -4). Let n be 3/((-3)/2) - -4. Suppose 2*l**3 - 10 + 2*l**2 - 2*l**z - n*l + 10 = 0. What is l?
-1, 0, 1
Let r(b) be the first derivative of -4*b**2 - 8*b**3 - 13/2*b**4 + 0*b - 1/3*b**6 + 14 - 12/5*b**5. Find s such that r(s) = 0.
-2, -1, 0
Solve -2*b - 42*b**3 - 388*b + 3*b**4 - 882*b**2 + 225 + 1086*b**2 = 0.
1, 3, 5
Let h = 2063 + -2063. Suppose -1/3*x + h - 1/6*x**2 + 1/6*x**3 = 0. What is x?
-1, 0, 2
Let k = 2 - -2. Let x(o) be the first derivative of 0*o**3 - o**2 + 0*o + 1/2*o**4 - k. What is t in x(t) = 0?
-1, 0, 1
Factor 1/5*b**2 + 0*b + 0 + 8/5*b**4 - 11/10*b**3 - 7/10*b**5.
-b**2*(b - 1)**2*(7*b - 2)/10
Let d = 2 - -3. Suppose 3*g - d*g = -120. Factor j - 2*j**2 - j + g*j**3 - 6*j**2.
4*j**2*(15*j - 2)
Let p(d) be the second derivative of -d**5/330 + 13*d**4/132 - 4*d**3/11 + 17*d**2 + 33*d. Let z(t) be the first derivative of p(t). Factor z(c).
-2*(c - 12)*(c - 1)/11
Let f(r) be the third derivative of -r**8/30240 - r**7/1260 + 7*r**6/1080 + 29*r**5/60 + 42*r**2. Let w(k) be the third derivative of f(k). Factor w(l).
-2*(l - 1)*(l + 7)/3
Let a be 999/3330*(-5)/(-3). Factor a*j + 1/4*j**2 + 0.
j*(j + 2)/4
Let q = -39/4 + 175/18. Let k = q + 13/36. Find t, given that -2/3*t**2 - 1/3*t**5 - k - 2/3*t**3 + t**4 + t = 0.
-1, 1
Determine l so that 51/2 - 3/2*l**3 + 3/2*l - 51/2*l**2 = 0.
-17, -1, 1
Let z be 94/6 + 5/15. Let y(c) = c. Let x be y(5). Factor -13 + x + 21*v**2 + 14*v**3 + z*v - 3*v**2 + 20*v**2.
2*(v + 1)*(v + 2)*(7*v - 2)
Let j(x) be the third derivative of -1/480*x**6 + 2*x**2 - 5/32*x**4 + 0 + 3*x - 3/8*x**3 - 7/240*x**5. Factor j(k).
-(k + 1)*(k + 3)**2/4
Let b(a) be the first derivative of 41 + 11/7*a**2 + 12/7*a + 2/7*a**3. Let b(f) = 0. What is f?
-3, -2/3
Suppose -o + 6 = -5*y - 5*o, 5*y + 3*o + 2 = 0. Suppose -3*x**2 + x**2 + 2*x**3 - y*x - 21*x**4 + 23*x**4 = 0. What is x?
-1, 0, 1
Determine i, given that -27/7 + 6/7*i**2 - 9/7*i = 0.
-3/2, 3
Factor -n**2 + 5/3*n - 5/3*n**3 + 1.
-(n - 1)*(n + 1)*(5*n + 3)/3
Factor 0 + 19/2*x**2 + 23/8*x**3 - 3/4*x**4 + 3/2*x.
-x*(x - 6)*(x + 2)*(6*x + 1)/8
Let i(q) be the third derivative of 0*q**3 - 9*q**2 + 1/420*q**5 + 0*q + 0*q**4 + 0 + 1/840*q**6. Factor i(c).
c**2*(c + 1)/7
Factor 3*v - 3/2*v**4 + 3/2 - 3*v**3 + 0*v**2.
-3*(v - 1)*(v + 1)**3/2
Let h be (-25)/(-9) - 34/(-153). What is v in 0 + 2/11*v**2 + 0*v - 2/11*v**h = 0?
0, 1
Factor 169/3*x + 0 + 143/3*x**2 + 1/3*x**4 - 25/3*x**3.
x*(x - 13)**2*(x + 1)/3
Let n be (-2)/21 - (-3231)/189. Suppose 9*z = -n*z + 4*z. What is a in 0*a + 0*a**2 + 5/3*a**4 + z - 5/3*a**3 = 0?
0, 1
Factor -4*c**3 + 3*c**2 - 5*c**3 + 23 + 0*c - 31 + 6*c + 8*c**3.
-(c - 4)*(c - 1)*(c + 2)
Let v(z) be the second derivative of -5*z**5/22 - 65*z**4/33 + 116*z**3/33 - 24*z**2/11 - 175*z + 2. Factor v(t).
-2*(t + 6)*(5*t - 2)**2/11
Let w be (2 + -7)*432/(-45). Factor 48*p**3 + 4*p**4 + w*p**3 - 92*p**3.
4*p**3*(p + 1)
Let r(a) be the first derivative of -a**4/4 + 2*a**3 - 4*a**2 - 189. Find g such that r(g) = 0.
0, 2, 4
Let s = 692 + -687. Let y(k) be the third derivative of -1/50*k**s + 0*k - 1/15*k**3 + 0 - 1/300*k**6 + 5*k**2 - 1/20*k**4. Factor y(l).
-2*(l + 1)**3/5
Suppose 25 = 3*s - 2*s. Let w = s - 25. Find k such that -1/5*k**2 + 0*k + 1/5*k**3 + w = 0.
0, 1
Let r(k) be the first derivative of -2*k**3/3 - 16*k**2/5 - 6*k/5 + 47. Factor r(f).
-2*(f + 3)*(5*f + 1)/5
Suppose -15/2 - 5/4*p + 5/4*p**2 = 0. What is p?
-2, 3
Let o be 10 - -104*6/(-64). Factor o*y**2 + 3/4*y - 1.
(y - 1)*(y + 4)/4
Suppose -6*p + 3*p - 189 = 0. Let o be (-7)/(p/12)*1/8. Factor 0*v**2 + 0 - 1/6*v**3 + o*v.
-v*(v - 1)*(v + 1)/6
Let y(z) be the second derivative of -z**7/168 + 11*z**6/120 - 2*z**5/5 + z**4/12 + 2*z**3 - 9*z + 16. Suppose y(j) = 0. Calculate j.
-1, 0, 2, 4, 6
Let j(z) be the third derivative of -z**5/105 + 5*z**4/42 - 5*z**2 + 16*z. Factor j(s).
-4*s*(s - 5)/7
Suppose 12*t - 17*t - 10 = -5*s, -2*t = -2. What is i in 2/7*i**s - 18/7*i**2 - 54/7 + 54/7*i = 0?
3
Factor -106*w**2 - 100*w**2 - 279*w + 306*w**2 - 103*w**2.
-3*w*(w + 93)
Factor -43*t**2 + 75*t**2 + 19*t - 36*t**2 + 45*t.
-4*t*(t - 16)
Let s = -190 - -194. Suppose 4*b - 12 = s. Factor 0 - 9/4*w**2 - 3/4*w**b + 9/4*w**3 + 3/4*w.
-3*w*(w - 1)**3/4
Let p be (-2)/8 + (509395/(-95620) - -1). Let v = -4/683 - p. Find m, given that -v - 216/7*m**3 - 160/7*m - 288/7*m**2 - 54/7*m**4 = 0.
-2, -2/3
Let m be (-12)/(-36)*(8 + 1). Let x(r) be the third derivative of 0*r**m + 0*r**4 + 1/20*r**5 + 0*r**6 + 3*r**2 - 1/70*r**7 + 0*r + 0. Let x(i) = 0. What is i?
-1, 0, 1
Suppose -5*c - 30 = -2*q - 5, 4*c - 4*q + 20 = 0. Let b be (-3)/c*(5 - 4)/3. Determine i, given that 0 + 0*i + b*i**4 - 2/5*i**3 + 1/5*i**2 = 0.
0, 1
Let v(i) = -3*i**3 + 104*i**2 + 222*i - 2. Let t(r) = -20*r**3 + 730*r**2 + 1555*r - 15. Let a(y) = -2*t(y) + 15*v(y). Factor a(p).
-5*p*(p - 22)*(p + 2)
Let c(k) = -k**2 - k + 7. Let v(b) = 3*b**2 + 3*b - 20. Let z(x) = 17*c(x) + 6*v(x). Let s(y) = 2*y**2 - 3*y - 12. Let d(q) = -4*s(q) + 12*z(q). Factor d(p).
4*(p + 3)**2
Factor -43 + 687*i**2 - 96*i + 19 + 1617*i**2 + 11 + 14.
(48*i - 1)**2
Solve -5/2*j**2 + 0 - 1/2*j**4 + 4*j**3 - 25*j = 0 for j.
-2, 0, 5
Let m(g) be the second derivative of -g**4/42 - 2*g**3/21 - 10*g - 5. Suppose m(c) = 0. Calculate c.
-2, 0
Factor 3/5*a**2 - 18/5*a + 3.
3*(a - 5)*(a - 1)/5
Let v(a) be the first derivative of -a**6/180 - a**5/90 + a**4/36 + a**3/9 + 10*a**2 - 22. Let c(x) be the second derivative of v(x). Factor c(n).
-2*(n - 1)*(n + 1)**2/3
Suppose 0 = 32*n - 16*n - 80. Suppose -n*p + p = p. Let -8/7*s - 20/7*s**4 + p - 4*s**2 - 36/7*s**3 - 4/7*s**5 = 0. What is s?
-2, -1, 0
Let r(a) = a**3 + 3*a**2 + 3*a + 5. Let x be r(-2). Let w be x - (40/15 - 1/(-3)). Solve 0*z - 4/7*z**2 + w = 0.
0
Let u be (-1)/2*(24/(-3) + 0). Factor 0*r**2 - 249*r + 261*r + 40 - u*r**2.
-4*(r - 5)*(r + 2)
Let c(m) = -18*m + 43. Let u be c(-7). Let f = -165 + u. Factor -10/11*d**2 - 2/11*d**f + 4/11*d + 0 + 8/11*d**3.
-2*d*(d - 2)*(d - 1)**2/11
Determine d so that 453*d + 3*d**3 + 55 - 123*d**2 - 187 - 201 = 0.
1, 3, 37
Suppose -3*w = -3*u - 57, -14 = -2*w - 4*u - 0*u. What is c in 44*c**2 - w*c**3 - 20*c - 18*c**2 - c**3 - 8 + 18*c**2 = 0?
-1/4, 1, 2
Find f such that 260/3*f - 33800/3 - 1/6*f**2 = 0.
260
Let v(q) be the first derivative of -12*q + 12*q**3 - 14 - 2*q**2 + 8/5*q**5 + 9*q**4. Solve v(m) = 0.
-3, -1, 1/2
Factor 3/4*z**5 - 15*z**2 + 48 + 75/4*z**3 - 60*z + 15/2*z**4.
3*(z - 1)**2*(z + 4)**3/4
Let t be 36/48 - (-221)/(-476). Suppose -8/7 + 50/7*y**5 + 32/7*y - t*y**2 - 82/7*y**3 + 10/7*y**4 = 0. Calculate y.
-1, 2/5, 1
Suppose 0*i = 4*i - 5*t - 139, 4*i + 4*t = 148. Let s be ((-21)/10)/((-81)/i). Factor -s*b + 4/15 + 2/3*b**2.
2*(b - 1)*(5*b - 2)/15
Factor 0*l + 0*l**2 - 1/3*l**5 + 0 + 2/3*l**4 + 0*l**3.
-l**4*(l - 2)/3
Let b(x) = -2*x**3 - x**2 + x - 1. Let n(k) = 4*k**5 - 155*k**4 + 1409*k**3 + 1964*k**2 + 396*k + 4. Let t(i) = 20*b(i) + 5*n(i). Find f such that t(f) = 0.
-1, -1/4, 0, 20
Let d(s) be the first derivative of -5*s**4/4 + 95*s**3/3 - 200*s**2 - 500*s + 419. Factor d(k).
-5*(k - 10)**2*(k + 1)
Let d be -3 + 2/6*0. Let c be (-6)/(-2) + (-3 - d). Factor 10*u**4 + 2*u - 5*u**4 - 3*u**4 + 2*u**3 - 2*u**2 - 4*u**c.
2*u*(u - 1)**2*(u + 1)
Factor 7/3 + 8/3*t + 1/3*t**2.
(t + 1)*(t + 7)/3
Let x(w) = 12*w**3 - 32*w**2 + 265*w - 486. Let q(v) = 19*v**3 - 47*v**2 + 397*v - 729. Let h(s) = 5*q(s) - 8*x(s). Factor h(c).
-(c - 9)**2*(c - 3)
Let v(y) be the second derivative of 0*y**2 + 0*y**3 + 0 + 1/60*y**6 - 1/252*y**7 + 1/72*y**4 - 1/40*y**5 + 3*y. Determine w so that v(w) = 0.
0, 1
Determine d, given that 26/9 - 2/9*d**2 + 8/3*d = 0.
-1, 13
Let f(t) be the second derivative of 0*t**2 + 2/25*t**5 + 8*t + 2/15*t**6 + 0*t**3 - 1/5*t**4 + 1. Let f(x) = 0. Calculate x.
-1, 0, 3/5
Let n be (273/(-6) + 0)/(2/(-4)). Let j = n + -89. Let 2/5*y**j + 0*y + 0 = 0. Calculate y.
0
Let z(o) = 4*o**2 + o - 5. Let q(y) be the third derivative of -7*y**5/20 - y**4/4 + 4*y**3 + 16*y**2. Let d(l) = -5*q(l) - 