 0
Suppose -3*t - 4*t = -7. Let p be -18 + 17 + t*3. Factor -8/13*m + 2/13*m**p + 8/13.
2*(m - 2)**2/13
Let c be (-434 - -1) + (-8)/(4 + 0). Let h = c - -7403/17. Factor 2/17 + 6/17*b**2 - h*b.
2*(b - 1)*(3*b - 1)/17
Suppose -3*s = -5*s - 10. Let r(l) = 3*l**2 + 2. Let c(t) = -7*t**2 - t - 5. Let o(j) = s*r(j) - 2*c(j). Factor o(q).
-q*(q - 2)
Suppose -49*w + 45*w - k = -21, 5 = -5*w + 5*k. Solve -2/3*l**w + 8/3*l**3 - 8/3*l**5 + 0*l + 0 + 2/3*l**2 = 0 for l.
-1, -1/4, 0, 1
Let f(z) be the second derivative of z**5/20 - 2*z**4/3 + z**3 + 6*z**2 + 2*z + 18. Let h be f(7). Factor -8/3*q + 0 - 2/3*q**h + 4*q**4 - 26/3*q**3 + 8*q**2.
-2*q*(q - 2)**2*(q - 1)**2/3
Suppose 2*i - 441 = -3*n + 193, -3*i + 950 = 5*n. Suppose -26*j**3 - 153*j - i + 21*j**3 - 60*j**2 - 87*j = 0. What is j?
-4
Let c(l) be the second derivative of l**9/3024 + l**8/1344 - l**4 - 18*l. Let u(b) be the third derivative of c(b). Factor u(p).
5*p**3*(p + 1)
Factor 2/3*s**2 + 2/3*s**4 + s**3 + 1/6*s**5 + 1/6*s + 0.
s*(s + 1)**4/6
Suppose -130*n + 135*n = 0. Let r = 25/2 - 11. Determine l, given that 3*l**4 + 3/2*l - 3*l**2 + n - r*l**5 + 0*l**3 = 0.
-1, 0, 1
Let n(y) = 7*y**3 - 104*y**2 - 668*y - 712. Let s(v) = 2*v**3 - 34*v**2 - 223*v - 237. Let i(u) = 3*n(u) - 8*s(u). Factor i(q).
5*(q - 12)*(q + 2)**2
Let s be 1/(-2)*5/(-10). Let r(d) be the second derivative of 0*d**2 + 0 - 1/2*d**3 - s*d**4 - 2*d. Let r(k) = 0. What is k?
-1, 0
Let k(l) = l**3 + 8*l**5 - l**3 + 2*l**3 + l**2 + 4*l**2 - 10*l**4. Let g(j) = 0 - j**4 + 0 + j**2 + j**5. Let v(c) = -5*g(c) + k(c). Factor v(s).
s**3*(s - 1)*(3*s - 2)
Let u(s) = 2*s**3 - 14*s**2 + 9*s - 4. Let v be u(6). Let i be (16/v)/((-11)/11). Let 10/11*q + 2/11*q**3 + i*q**2 + 4/11 = 0. Calculate q.
-2, -1
Let i(d) be the second derivative of 38*d - 1/54*d**4 + 0 + 2/9*d**3 + 0*d**2. Factor i(q).
-2*q*(q - 6)/9
Factor 103*n**3 - 624*n + 88*n**2 - 221*n**3 + 1440 + 114*n**3.
-4*(n - 10)*(n - 6)**2
Let h(m) be the second derivative of -12*m - 5/3*m**3 - 1/6*m**6 + 0 - m**5 + 0*m**2 - 25/12*m**4. Find b, given that h(b) = 0.
-2, -1, 0
Let a(v) = -v + 7. Let s be a(5). Suppose -8*p = -3*p - y - 14, 0 = 3*p - s*y - 7. Let 3/4*z**p - z - z**4 + 0 + z**2 + 1/4*z**5 = 0. Calculate z.
-1, 0, 1, 2
Let y(n) be the first derivative of 0*n + 8 + 4/3*n**3 - 6*n**2. Factor y(w).
4*w*(w - 3)
Factor -2*i**3 + 2204*i + 31944 + 14*i**3 + 2152*i + 198*i**2 - 9*i**3.
3*(i + 22)**3
Let s be (-1 - 28/(-16))*-12. Let a = s + 17. Suppose -a*x**2 + 0 + 0*x**3 + x - 3*x**3 - 4*x + 2 = 0. What is x?
-2, -1, 1/3
Factor -9/8*h + 3/8*h**3 + 3/2*h**2 - 27/4.
3*(h - 2)*(h + 3)**2/8
Let a = 394 - 142. Let v be (0 + 6)/1*56/a. Suppose -8/3*k - v*k**3 + 0 + 4*k**2 = 0. Calculate k.
0, 1, 2
Let s(m) = -5*m**2 + 27*m - 7. Let f be s(5). Let n be -1*(0 + f)*39/(-351). Factor t**3 + 0 - t**2 - 1/3*t**4 + n*t.
-t*(t - 1)**3/3
Let v(s) be the first derivative of -s**4/36 + s**3/9 - 11*s - 4. Let t(g) be the first derivative of v(g). What is d in t(d) = 0?
0, 2
Let o = 274 + -3560/13. Let i(q) = -2*q + 20. Let v be i(9). Factor 0*w + 0 - o*w**v.
-2*w**2/13
Let m(f) = 5*f**3 - 9*f + 4. Let b(c) = 29*c**3 - 53*c + 24. Let a(t) = 6*b(t) - 34*m(t). Solve a(p) = 0.
-2, 1
Let l(a) be the first derivative of 0*a**3 + 0*a**2 + 0*a + 1/25*a**5 + 3/10*a**4 - 13. Determine v so that l(v) = 0.
-6, 0
Let b(h) be the first derivative of 3 - 5/6*h**2 + 4/9*h**3 - 1/12*h**4 + 2/3*h. Let b(d) = 0. Calculate d.
1, 2
Suppose -v + 19 = d, -2*v + 41 = -5*d + 164. Factor -48 + d - 9*x - x - x**2.
-(x + 5)**2
Let r(n) be the second derivative of n**9/1512 - n**7/210 + n**5/60 + 5*n**3/2 + 18*n. Let i(p) be the second derivative of r(p). Factor i(d).
2*d*(d - 1)**2*(d + 1)**2
Let n(x) be the first derivative of 8*x**2 + 64*x - 2 + 1/3*x**3. What is a in n(a) = 0?
-8
Let a(b) be the first derivative of -b**5/30 + b**2/2 - 2. Let t(d) be the second derivative of a(d). Solve t(j) = 0 for j.
0
Let r(n) be the first derivative of -81/4*n**4 - 3*n**2 - 7/2*n**6 + 10 - 69/5*n**5 + 0*n - 13*n**3. Let r(v) = 0. Calculate v.
-1, -2/7, 0
Let g(y) = 17*y + 136. Let w be g(-8). Factor 2/5*a + 1/5*a**4 - 1/5*a**2 + 1/5*a**5 + w - 3/5*a**3.
a*(a - 1)**2*(a + 1)*(a + 2)/5
Suppose 2 = -4*q - p, -4 = -4*q + 3*p + 2. Suppose 0 = -t + 10 - q. Suppose -t*k + 27 + 3*k**2 + 10*k - 18*k = 0. Calculate k.
3
Suppose -78 = -5*s + 17. Let c = s + -15. Suppose 4*v + 1 - 2*v - 2*v**2 + c*v - 5 = 0. What is v?
1, 2
Let x = 49/17 - 407/153. Factor 0 + 2/9*k**3 + 0*k + x*k**2.
2*k**2*(k + 1)/9
Let s(a) be the second derivative of -a**6/50 + 27*a**5/100 + 33*a**4/20 + 7*a**3/2 + 18*a**2/5 + 4*a + 125. Factor s(j).
-3*(j - 12)*(j + 1)**3/5
Let y(j) be the first derivative of 0*j + 8/9*j**3 - 1/2*j**4 - 1/3*j**2 - 1. Let y(r) = 0. What is r?
0, 1/3, 1
Factor 110/17*j - 56/17 - 2/17*j**3 - 52/17*j**2.
-2*(j - 1)**2*(j + 28)/17
Let k(i) be the third derivative of -i**6/60 - 8*i**5/15 - 16*i**4/3 + 165*i**2. Find h, given that k(h) = 0.
-8, 0
Let r(w) be the second derivative of w**6/10 + 33*w**5/5 + 157*w**4 + 1584*w**3 + 7776*w**2 - 286*w. Solve r(g) = 0.
-18, -4
Let f(c) = c**3 - 2*c**2 + 7*c - 4. Let y(b) = -4*b**2 + 5 - 3*b**3 + 3 + 5 - 22*b + 9*b**2. Let o(k) = -7*f(k) - 2*y(k). Factor o(x).
-(x - 2)*(x - 1)**2
Let n(x) be the first derivative of -7*x**6/18 + 16*x**5/15 + 31*x**4/12 - 52*x**3/9 + 2*x**2 + 767. Determine b so that n(b) = 0.
-2, 0, 2/7, 1, 3
Let b(l) = 2*l**3 + 21*l**2 + 120*l + 155. Let s(a) = 2*a**3 + 20*a**2 + 122*a + 156. Let r(d) = 6*b(d) - 5*s(d). Factor r(z).
2*(z + 3)*(z + 5)**2
Suppose 2408 = 5*f - 4*b, 0 = -8*f + 3*f - 2*b + 2396. Factor 5 + 10*j**3 - 10*j**2 + 475*j**5 - f*j**5 + 2*j**4 - 5*j + 3*j**4.
-5*(j - 1)**3*(j + 1)**2
Let v(w) be the first derivative of 2*w**5/25 - 13*w**4/10 + 34*w**3/5 - 63*w**2/5 - 377. Determine o, given that v(o) = 0.
0, 3, 7
Let j(d) = 20*d - 54. Let y be j(4). Suppose n - y = -23. Factor -2/9*v**n + 0 - 8/9*v**2 - 2/3*v.
-2*v*(v + 1)*(v + 3)/9
Let s(f) be the first derivative of 1/8*f**4 + 0*f + f**3 - 7 + 7/2*f**2 - 1/20*f**5. Let k(n) be the second derivative of s(n). Factor k(m).
-3*(m - 2)*(m + 1)
Let x = -482/7 + 1558/21. What is z in 4/3*z**4 + 0 + 8*z**3 + x*z + 12*z**2 = 0?
-4, -1, 0
Let l = 587/66 - 96/11. Let p(h) be the second derivative of 0 + 0*h**2 - h**3 + l*h**4 + 3*h. Factor p(s).
2*s*(s - 3)
Let v = -11 + 19. Suppose -2*j - v + 14 = 0. Let -b - 5/3*b**2 + 1/3 + b**j + 4/3*b**4 = 0. Calculate b.
-1, 1/4, 1
Let f = 202 + -457. Let i = 255 + f. Factor -8/3*x**3 - x**4 + i*x - 2*x**2 + 1/3.
-(x + 1)**3*(3*x - 1)/3
Let b = -3 + 7. Suppose 3*l = 0, -b*v + 2*v + 4 = -3*l. Factor 0*t - 2/7*t**v + 0.
-2*t**2/7
Determine c, given that 1/4*c**4 + 1/4 - 1/2*c**2 - 1/4*c + 1/2*c**3 - 1/4*c**5 = 0.
-1, 1
Let f(y) = y**3 + 4*y**2. Let c be f(-4). Suppose 8*g = 6*g + 38. Factor 16 + 3*r**2 - g + c*r**2.
3*(r - 1)*(r + 1)
Let a = 11503/14 + -827. Let q = a + 48/7. What is l in -1/2*l**5 - q*l**3 + 0*l - 3/2*l**4 - 1/2*l**2 + 0 = 0?
-1, 0
Let t(a) be the first derivative of 0*a**2 - 2*a - 1/5*a**3 + 2 + 1/20*a**4. Let k(w) be the first derivative of t(w). Factor k(i).
3*i*(i - 2)/5
Suppose -66*h**3 - 264*h - 3/4*h**5 + 189*h**2 + 45/4*h**4 + 144 = 0. What is h?
2, 3, 4
Let d(o) be the second derivative of -o**4/12 + 4*o**3/3 - 6*o**2 + 5*o - 12. Factor d(u).
-(u - 6)*(u - 2)
Let f be 186 + (-8)/(48/30). Let m = 907/5 - f. Solve -m - 4/5*p - 2/5*p**2 = 0.
-1
Factor 0 - 3/5*m**5 - 18/5*m**4 + 0*m + 0*m**2 + 21/5*m**3.
-3*m**3*(m - 1)*(m + 7)/5
Let d(j) be the first derivative of j**8/1176 - 4*j**7/735 - 5*j**2 + 14. Let m(w) be the second derivative of d(w). Solve m(n) = 0 for n.
0, 4
Let -7977*d + 23*d**2 + 112 + 8025*d - 27*d**2 = 0. What is d?
-2, 14
Let v = 15287 - 108190/7. Let a = 169 + v. Solve a*w - 2/7*w**2 + 0 = 0 for w.
0, 1
Find b such that -4*b**4 - 92*b**2 + 5*b**4 + 2*b**4 - 21*b**3 + 110*b**2 = 0.
0, 1, 6
Let x = -718 + 723. Solve 0 + 4/9*i**x + 0*i - 4/9*i**3 - 4/9*i**4 + 4/9*i**2 = 0.
-1, 0, 1
Factor -1/5*t**2 + 1/5*t + 56/5.
-(t - 8)*(t + 7)/5
Suppose 403*j = 22*j. Factor j*q - 1/6*q**2 + 2/3.
-(q - 2)*(q + 2)/6
Let z = -19 + 24. Let x be 1*(z - 2/2). Determine g so that -4*g**2 - 20 + 20 - x*g = 0.
-1, 0
Let d(a) = a**2. Let j(h) = 32*h**2 + 3*h + 3. Let o(b)