*m. Let s(p) be the first derivative of n(p). Factor s(l).
4*(l + 1)*(l + 2)**2
Factor 0 + 0*z + 4/3*z**2 - 2/3*z**5 + 0*z**4 + 2*z**3.
-2*z**2*(z - 2)*(z + 1)**2/3
Let x = 161 + -159. Factor 7*u + 33*u + 5*u**x + 3*u + 12*u.
5*u*(u + 11)
Let u(l) be the first derivative of -4*l**5/5 - 2*l**4 + 44*l**3/3 + 24*l**2 - 402. Factor u(q).
-4*q*(q - 3)*(q + 1)*(q + 4)
Factor 2/7*u**3 - 14 + 10*u + 26/7*u**2.
2*(u - 1)*(u + 7)**2/7
Let -165*d**3 + d + 63*d**4 - 3*d - 13*d + 83*d**2 - 23*d**4 + 57*d**2 = 0. What is d?
0, 1/8, 1, 3
Let v be (-31 - 1)/((-2)/(-13)). Let s = v - -1046/5. What is g in 0*g**3 + s*g**5 - 4/5*g**4 + 0*g + 0 + 0*g**2 = 0?
0, 2/3
Let p(k) be the second derivative of k**4/90 + k**3/15 + 2*k**2/15 - 25*k - 1. Determine r, given that p(r) = 0.
-2, -1
Let d(h) be the first derivative of h**6/8 - 9*h**5/10 + 3*h**4/16 + 6*h**3 + 6*h**2 - 156. Factor d(l).
3*l*(l - 4)**2*(l + 1)**2/4
Suppose -13 = 2*v + 37. Let h be ((-78)/45 - -2)/((-10)/v). Factor 20/3*l**2 - 8/3*l**5 - h + 0*l + 10*l**4 - 40/3*l**3.
-2*(l - 1)**4*(4*l + 1)/3
Let v(m) = -26*m + 368. Let o be v(14). Let t(j) be the third derivative of 0 + 1/9*j**3 - 1/24*j**4 - o*j**2 + 1/180*j**5 + 0*j. Solve t(l) = 0.
1, 2
Suppose -2*u + 7 = -1. Determine h so that -16 - 7*h**u + 34*h**2 + h**4 - 14*h**2 + 2*h**4 = 0.
-2, -1, 1, 2
Suppose 4*q = -0*p - 2*p + 14, -4*p = q - 14. Let r be ((-24)/20)/((-8)/10). Let r*c**p + 0 + 9/2*c**2 + 3*c = 0. What is c?
-2, -1, 0
Let p be 1/((324/(-4752))/(2/(-11))). Factor p*x**2 + 0 + 2/3*x**3 + 8/3*x.
2*x*(x + 2)**2/3
Let n(w) = 2*w**2 - 82*w + 98. Let u(m) be the second derivative of m**4/12 - 9*m**3/2 + 33*m**2/2 + 11*m. Let v(s) = 3*n(s) - 10*u(s). Factor v(k).
-4*(k - 3)**2
Let w be ((-222)/1110)/(1 + (-2 - 0)). Suppose 2/5 - w*l**3 + 1/5*l - 2/5*l**2 = 0. What is l?
-2, -1, 1
Suppose -y = 5*z + 1, -3*y + 5*y + 5*z - 3 = 0. Factor 0*w + 8/5*w**3 + 4/5*w**y + 0 + 4/5*w**2.
4*w**2*(w + 1)**2/5
Factor 0*y + 0 - 2/5*y**3 - 66/5*y**2.
-2*y**2*(y + 33)/5
Let t(a) = -a**3 - a. Let p(h) = 9*h**3 + 3*h**2 + 12*h. Suppose m + 0 = -b + 2, -5*m + 15 = 0. Let u(j) = b*p(j) - 12*t(j). Factor u(y).
3*y**2*(y - 1)
Let m(d) = -9*d**3 + 40*d**2 + 11*d + 11. Let n(t) = 2*t**3 - 8*t**2 - 2*t - 2. Let y(j) = -2*m(j) - 11*n(j). Factor y(i).
-4*i**2*(i - 2)
Let c(v) = v**3 - 10*v**2 - 9*v + 2. Let l be c(11). Factor -l*b**2 + b + 8*b + 32*b**3 - 5*b.
4*b*(2*b - 1)*(4*b - 1)
Let r(a) be the first derivative of a**5/5 + 3*a**4/2 - 5*a**3 + 4*a**2 - 172. Factor r(y).
y*(y - 1)**2*(y + 8)
Let a be (-11 - (-246)/22)/(2/22). Let w be (7/3 - a) + (-24)/(-72). Factor -w*h**2 + 8/3*h + 0.
-2*h*(h - 4)/3
Let w = 6 - 4. Let u = -21 - -24. Factor 0*m**2 + w*m**4 - 8 + 5*m**u + 3*m**3 + 6*m**2 - 8*m.
2*(m - 1)*(m + 1)*(m + 2)**2
Factor -144/11*u**2 - 2/11*u**4 + 0 + 864/11*u - 42/11*u**3.
-2*u*(u - 3)*(u + 12)**2/11
Factor 2/5*n**2 + 4/5*n + 0.
2*n*(n + 2)/5
Let o(c) be the third derivative of c**7/420 + 7*c**6/40 + 41*c**5/120 + 438*c**2. Suppose o(l) = 0. What is l?
-41, -1, 0
Let q be 4/(-6)*6/(-4). Suppose 0 = 2*h - 3 - q. Solve -6*k - 6*k**2 + h*k + 2*k**3 - 4*k**3 = 0.
-2, -1, 0
Factor 170/3 + 175/3*t + 5/3*t**2.
5*(t + 1)*(t + 34)/3
Let a(l) be the second derivative of -l**4/27 + 5*l**3/27 + l**2/3 + l - 28. Suppose a(v) = 0. What is v?
-1/2, 3
Let i(z) be the first derivative of -z**5/180 - z**4/18 - 2*z**3/9 + 21*z**2/2 + 23. Let n(r) be the second derivative of i(r). Solve n(p) = 0.
-2
Let b(x) = 15*x**3 + 210*x**2 - 740*x + 240. Let p(y) = y**3 + 15*y**2 - 53*y + 17. Let d(v) = -4*b(v) + 55*p(v). Find f such that d(f) = 0.
-5, 1
Let p(h) = 24*h**4 - 54*h**3 + 36*h**2 + 7*h - 13. Let d(i) = -12*i**4 + 27*i**3 - 18*i**2 - 3*i + 6. Let c(k) = 13*d(k) + 6*p(k). Find s such that c(s) = 0.
0, 1/4, 1
Let r(y) be the first derivative of y**7/105 - y**6/30 - 5*y**2 + 2. Let l(v) be the second derivative of r(v). Find c such that l(c) = 0.
0, 2
Let j be (-5 + 3 + -22)/(-2). Determine b so that 14*b**4 + j*b**3 - 20*b**4 + 9*b**4 = 0.
-4, 0
Let q be 7/(8 - 15) - -4. Solve 1/3*d**4 + 2/3 + 7/3*d + 3*d**2 + 5/3*d**q = 0 for d.
-2, -1
Let a(w) be the second derivative of 0 + 0*w**2 - 1/20*w**5 + 1/12*w**4 + 0*w**3 - 6*w. Let a(m) = 0. What is m?
0, 1
Let d(m) be the second derivative of m**4/9 + 10*m**3/9 + 8*m**2/3 + 39*m. Factor d(c).
4*(c + 1)*(c + 4)/3
Let f(i) = i**2 - 1. Let g(l) = 6*l**2 - 6*l - 4. Let d(v) = v**2 - 3*v - 14. Suppose -2*t = -10 - 0. Let y be d(t). Let k(c) = y*f(c) + g(c). Factor k(u).
2*u*(u - 3)
Let m = -118 + 126. Factor 8*r**2 - 5*r**2 + 40 + 68*r + m*r**2 + r**2.
4*(r + 5)*(3*r + 2)
Let u be (2/8)/(-1) + (-105)/(-20). Factor -u*g**2 + 0*g**2 + 8*g**2 + 24 + 18*g.
3*(g + 2)*(g + 4)
Let i be 3 + (-3 + 2)*(252/52 - 2). Factor 0 + 2/13*p + i*p**2.
2*p*(p + 1)/13
Suppose 0*q = -3*q + 9. Let f be q/(-2) + (-27)/(-6). Factor 2*a**3 + 3*a + 6*a**2 - a**f + a**4 - 3 - 7*a**3 + 3*a**5 - 4*a**4.
3*(a - 1)**3*(a + 1)**2
Let s = 269089/56 + -4805. Let c = s - -1/8. Factor 6/7*d + 0*d**2 - 4/7 - c*d**3.
-2*(d - 1)**2*(d + 2)/7
Let b be -2 - 137/(-56) - (-117)/(-1638). Suppose -2*c + 0*c = 0. Let 0 - b*q**4 - 3/4*q + c*q**3 + 9/8*q**2 = 0. What is q?
-2, 0, 1
Let b(m) be the third derivative of 5/24*m**4 - 1/6*m**5 - 7*m**2 - 1/6*m**3 + 1/12*m**6 + 0 + 1/336*m**8 - 1/42*m**7 + 0*m. Solve b(h) = 0.
1
Let c(t) = -t**3 + 2*t**2 - 2*t. Let k(z) = 15*z**3 + 1962*z**2 + 69162*z + 19600. Let i(n) = 2*c(n) + 2*k(n). Factor i(w).
4*(w + 70)**2*(7*w + 2)
Let b(t) = 20*t**2 - 356*t - 696. Let o(v) = 2*v**2 + v + 2. Let j(i) = -b(i) + 12*o(i). Suppose j(y) = 0. What is y?
-90, -2
Factor 810*l - 388 + 764 - 36312*l**2 - 392 - 26188*l**2 + 1190*l.
-4*(125*l - 2)**2
Let g(y) be the second derivative of 36*y - 10*y**2 + 0 - 1/4*y**5 - 25/12*y**4 - 20/3*y**3. Find q such that g(q) = 0.
-2, -1
Suppose -140 = 2*h - 6*h. Solve -4*d**3 + 3*d**3 + 36*d - h*d = 0 for d.
-1, 0, 1
Let j be (185/74)/((-6)/(-14)). Let p = -10/3 + j. What is b in 1 - 3/2*b**2 - p*b = 0?
-2, 1/3
Let u be (-3)/7*497/(-284). Factor -15/2*f - 75/4 - u*f**2.
-3*(f + 5)**2/4
Suppose -8*k - 20 = -12*k. Factor -6*g**3 + g**5 + 148*g**2 + g**k - 288*g**2 + 144*g**2.
2*g**2*(g - 1)**2*(g + 2)
Let f = -811 - -815. Let u(o) be the second derivative of 8/3*o**3 - 16*o**2 - 1/6*o**f + 0 + o. Suppose u(g) = 0. Calculate g.
4
Let u(w) be the second derivative of w**6/60 + 3*w**5/40 + w**4/24 - w**3/4 - w**2/2 + 48*w. Factor u(r).
(r - 1)*(r + 1)**2*(r + 2)/2
Let v(f) be the third derivative of -f**7/280 + 11*f**6/160 + 13*f**5/80 - 11*f**4/32 - 3*f**3/2 + 173*f**2. Suppose v(z) = 0. What is z?
-1, 1, 12
Let s(g) = -g + 3. Let r(l) = -l - 12. Let b be r(-12). Let i be s(b). Suppose -3 + q**2 - q + q**3 - q**4 + i = 0. What is q?
-1, 0, 1
Suppose 48 = -6*x + 22*x. Let c(q) be the first derivative of 1/12*q**2 + 1/9*q**x - 1 + 1/24*q**4 + 0*q. Factor c(r).
r*(r + 1)**2/6
Factor 0*z - 3/7 + 3/7*z**2.
3*(z - 1)*(z + 1)/7
Let m(g) be the second derivative of -g**8/5880 + g**7/1470 + g**6/420 - g**3/6 + 2*g. Let f(o) be the second derivative of m(o). Factor f(w).
-2*w**2*(w - 3)*(w + 1)/7
Factor 110/3 + 1/3*l**2 + 37*l.
(l + 1)*(l + 110)/3
Suppose 3*c + 5472 = 5481. Solve 7/2*l**c - 4 - 1/2*l**4 - 9*l**2 + 10*l = 0 for l.
1, 2
Let z be -10*(0 - 2)/4. Factor -9*h**3 - 3*h**2 - z*h**2 + 3*h**3 + 2*h**3.
-4*h**2*(h + 2)
Suppose 0 = -135*z + 94*z + 205. Factor 1/3*p + 2/3*p**4 - 2/3*p**2 + 0*p**3 - 1/3*p**z + 0.
-p*(p - 1)**3*(p + 1)/3
Determine j so that 436*j**3 - 6691*j - 4*j**4 + 6691*j - 432*j**2 = 0.
0, 1, 108
Let f(m) be the third derivative of m**7/210 - m**6/6 - 7*m**5/20 - 147*m**2. Factor f(p).
p**2*(p - 21)*(p + 1)
Let a(w) be the third derivative of -w**6/40 - 8*w**5/5 - 285*w**4/8 - 225*w**3 + 119*w**2 - 2. Factor a(i).
-3*(i + 2)*(i + 15)**2
Let t(v) = -v + 9 - 5*v**2 + v**2 + 5*v**2. Let u be t(0). Factor 5*m + 5*m**3 - m - u*m**2 + 1 - m.
(m - 1)**2*(5*m + 1)
Suppose 2/17*m**2 + 12/17 - 14/17*m = 0. Calculate m.
1, 6
Let r = 223/2 + -109. Let b = r + -2. Solve 0 - 1/2*t**4 + b*t**2 - 1/4*t + 0*t**3 + 1/4*t**5 = 0.
-1, 0, 1
Let -36/7 + 33/7*k + 6/7*k**2 - 3/7*k**3 = 0. What is k?
-3, 1, 4
Let i(w) be the third derivative of -17*w**5/30 + 4*w**4 - 179*w**2 - 2*w. Determine m, given that i(m) = 0.
0, 48/17
Let i(k) =