- 2/3*p**4. Let g(l) = 0. Calculate l.
-10, -1/2
Let f(u) be the second derivative of u**5/60 + u**4/40 - u**3/15 + 13*u**2/2 - 32*u. Let y(v) be the first derivative of f(v). Determine x so that y(x) = 0.
-1, 2/5
Let m = 168/5 - 321/10. Let j(z) be the first derivative of -4 + m*z**4 - 3*z**2 + 0*z**3 + 3/5*z**5 - 3*z. Let j(r) = 0. What is r?
-1, 1
Let i(o) be the second derivative of 2*o**5/15 + 7*o**4/4 - 40*o**3/9 + 3*o**2/2 - 2*o - 505. Factor i(t).
(t - 1)*(t + 9)*(8*t - 1)/3
Let u(h) be the third derivative of -h**5/100 + 43*h**4/20 + 87*h**3/10 - 962*h**2. Determine w, given that u(w) = 0.
-1, 87
Let f = 3604 - 3609. Let r(t) be the first derivative of t**2/2 - t - 2. Let y(z) = 2*z**2 + 8*z - 4. Let i(g) = f*r(g) + y(g). Factor i(d).
(d + 1)*(2*d + 1)
Factor -3/2*i**2 - 153/2*i - 660.
-3*(i + 11)*(i + 40)/2
Let f(t) = t**4 + 10*t**3 - 3*t**2 - 7*t + 5. Let i(d) = -5*d**3 + d - 15*d - 5*d**2 - d + 10 + 25*d**3. Let n(a) = 5*f(a) - 3*i(a). Find m such that n(m) = 0.
-1, 1
Let n(w) be the third derivative of w**8/140 + 17*w**7/350 - 17*w**5/100 - w**4/10 + 1010*w**2. Determine z, given that n(z) = 0.
-4, -1, -1/4, 0, 1
Let z(x) be the first derivative of -x**6/30 - 21*x**5/10 - 147*x**4/4 + 291*x + 24. Let h(p) be the first derivative of z(p). Factor h(v).
-v**2*(v + 21)**2
Factor 44*h - 24*h**2 + 92*h + 3*h**3 - 91*h.
3*h*(h - 5)*(h - 3)
Suppose -6*d + 3*d + 9 = 0, 5*d = -4*f + 815. Determine v, given that -5234*v**2 + 5237*v**2 + f + 72*v + 232 = 0.
-12
Let b be (-403062)/465 + (-8)/(-10). Let s = b + 2606/3. Factor -4/3*j**2 + s + 4/3*j.
-4*(j - 2)*(j + 1)/3
Suppose 5*z - 2*y - 29 = -5*y, -3*y = 6. Factor z*s**2 - 20*s**2 + 45*s**3 - 25*s**4 + 4*s - 11*s**2.
-s*(s - 1)*(5*s - 2)**2
Let w(n) be the first derivative of 2*n**5/85 + 137*n**4/34 + 16*n**3/3 - 1235. Find y, given that w(y) = 0.
-136, -1, 0
Let f(k) be the third derivative of -61*k + 2*k**2 + 1/40*k**6 + 25/8*k**4 + 0 - 1/2*k**5 + 0*k**3. Factor f(q).
3*q*(q - 5)**2
Let t(y) be the first derivative of 1/20*y**5 - 67 + 55/2*y**2 + 121/4*y - 5/4*y**4 + 13/2*y**3. Factor t(j).
(j - 11)**2*(j + 1)**2/4
Suppose -4*s + 22 = 2*y, 31 = 5*y - 58*s + 62*s. Suppose -41*x**y + 180 - 485*x**2 - 700*x - 81*x**3 - 86*x**3 + 163*x**3 = 0. Calculate x.
-9, -2, 2/9
Factor 671*c**2 + 47775744 + 1538*c**2 + 29*c**3 - 481*c**2 - 497664*c + 13*c**3 - 44*c**3.
-2*(c - 288)**3
Let v = -4091/6 + 682. Let w(t) be the first derivative of v*t**6 + 0*t**2 - t**3 + 3/5*t**5 + 0*t + 4 - 1/4*t**4. Suppose w(s) = 0. What is s?
-3, -1, 0, 1
Suppose -2*l + 56*z + 5 = 55*z, -3*z + 3 = 0. Factor 3/4*o**3 - 6 + 3/2*o**2 - l*o.
3*(o - 2)*(o + 2)**2/4
Let d = -44 + 49. Factor -10*k - d*k - 6*k - 11*k - 4*k**2.
-4*k*(k + 8)
Suppose 2*k - 16 = 6 - 0. Let q(v) be the first derivative of -k - 10*v**2 - 5/6*v**6 - 20*v**3 - 6*v**5 + 0*v - 65/4*v**4. Factor q(m).
-5*m*(m + 1)**2*(m + 2)**2
Let l(n) = n**3 + 4*n**2 + 6*n + 11. Let c be l(-3). Find j, given that -11*j**4 + c*j**2 + 16*j**3 + 8*j**4 + 2*j**4 + 15*j**2 = 0.
-1, 0, 17
Let i(b) = -36*b**2 + 13248*b + 13284. Let q(d) = 7*d**2 - 2650*d - 2657. Let g(x) = 3*i(x) + 16*q(x). Factor g(s).
4*(s - 665)*(s + 1)
Factor 32/5*t**2 - 57/5*t - 1/5*t**3 - 18.
-(t - 30)*(t - 3)*(t + 1)/5
Let n be (4/(-6) - 112/48) + 5. Factor -3*c**5 + 4*c**5 + 0*c**5 - 3*c**3 + 7*c + 5*c**2 + 0*c**n - c**4 - 9*c.
c*(c - 1)**3*(c + 2)
Let r(u) = -u**3 + u**2 - u. Let v(a) = -12*a**3 + 11*a**2 - 8*a - 2. Let l = 183 + -185. Let q(s) = l*v(s) + 22*r(s). Solve q(x) = 0.
-2, 1
Suppose -4*v - 101 = -d - 61, 3*d + 3*v - 90 = 0. Let t be (d/(-28))/(-2) + (-75)/315. Determine g so that t*g**2 - 4/3 + 0*g = 0.
-2, 2
Let m(w) be the third derivative of 1/720*w**6 - 1/24*w**5 + 0 - 1/144*w**4 + 0*w + 73*w**2 + 5/12*w**3. Factor m(d).
(d - 15)*(d - 1)*(d + 1)/6
Suppose -27 = 20*o - 29*o. Suppose -19*u - o + 41 = 0. Factor -1/12*h - 1/3*h**u + 0.
-h*(4*h + 1)/12
Let d(s) be the third derivative of -s**5/90 - 301*s**4/9 - 362404*s**3/9 + 1797*s**2. Factor d(r).
-2*(r + 602)**2/3
Let d = 330 - 72. Let v be (1 + d/(-96))*2/(-3). Factor 3/4*o**3 + v*o**2 - 3/8 + 0*o.
3*(o + 1)**2*(2*o - 1)/8
Suppose 18 = 3*y + 3*i, 2*y - 15 = -12*i + 9*i. Let -1 - n**4 - 7*n**y + 7/2*n + 7/2*n**5 + 2*n**2 = 0. What is n?
-1, 2/7, 1
Let s(r) be the second derivative of 256/15*r**6 - 3 + 576*r**4 - 2/3*r**7 - 288*r**3 - 8*r + 0*r**2 - 792/5*r**5. Let s(x) = 0. Calculate x.
0, 2/7, 6
Let k(v) be the second derivative of 27*v**5/20 + 41*v**4/4 + 47*v**3/2 + 45*v**2/2 + 603*v - 2. Solve k(n) = 0.
-3, -1, -5/9
Let j(n) = 11*n**2 + 96*n - 621. Let r(k) = 12*k**2 + 84*k - 620. Let q(z) = 10*j(z) - 9*r(z). Suppose q(g) = 0. Calculate g.
-105, 3
Let w(f) be the second derivative of f**7/42 - 2*f**6 + 117*f**5/20 - 29*f**4/6 + 676*f + 7. Solve w(i) = 0.
0, 1, 58
Let s be (-2688)/16478 - 4/(-22). Let n = s + 414/749. Find a such that 0 + 8/7*a + 12/7*a**2 - 4/7*a**3 - n*a**5 - 12/7*a**4 = 0.
-2, -1, 0, 1
Let r(s) be the first derivative of -s**5/5 + 5*s**4/4 + 10*s**3/3 - 40*s**2 + 96*s + 6980. Determine x so that r(x) = 0.
-4, 2, 3, 4
Solve -2545*u**2 - 52*u + 2440*u**2 + 156 - 51*u**4 + 11*u + 165*u**3 + 3*u**5 - 127*u = 0 for u.
-1, 1, 2, 13
Let n = 5333/3574 + 14/1787. Factor -729/2*o**2 + 81/2*o - n + 2187/2*o**3.
3*(9*o - 1)**3/2
Determine n, given that 254/5*n + 2/5*n**3 - 46/5*n**2 - 42 = 0.
1, 7, 15
Suppose 22*s - v + 6 = 25*s, -5*v - 15 = 0. Let h(l) be the first derivative of 2*l**2 - 35 - 19/6*l**s + 7/8*l**4 + 2*l. Factor h(m).
(m - 2)*(m - 1)*(7*m + 2)/2
Suppose -25*i + 19*i - 2400 = 0. Let j = -400 - i. Factor -3/7 + j*c + 3/7*c**2.
3*(c - 1)*(c + 1)/7
Suppose 63*y**2 - 8*y + 19*y + 0*y**4 - y**4 + 3*y**3 - 60 - 14*y - 2*y**4 = 0. Calculate y.
-4, -1, 1, 5
Let u(o) be the first derivative of 7/60*o**5 + 4*o**3 - 20 + 0*o + 49/24*o**4 + 1/360*o**6 + 0*o**2. Let h(t) be the third derivative of u(t). Factor h(m).
(m + 7)**2
Suppose 5*s = -4*z + 616, 2*s + 0*s - 2*z - 250 = 0. Factor 28 + 108*j**2 - 20*j - 36 - 7*j + 44*j**4 + 7*j - s*j**3.
4*(j - 1)**3*(11*j + 2)
Let d(q) = 19*q**2 - 1. Let n be d(1). Let x be (0 - n/(-15))/((-42)/(-28)). Solve 6/5*i - 2*i**2 + x = 0 for i.
-2/5, 1
Find m, given that -2*m + 1/4*m**2 + 0 = 0.
0, 8
Let q(r) = -14 - 1 + 10*r**2 - 3*r**3 - 11*r + 2*r**3 - 21. Let h be q(8). Factor -1/2*c**3 + 2/3*c**h - 1/6*c**2 + 0 + 0*c.
c**2*(c - 1)*(4*c + 1)/6
Let m be (2/(-22))/(6/11*330/(-396)). Let -m*q**3 - 7/5*q - 3/5 - q**2 = 0. Calculate q.
-3, -1
Let z be (1 + -1)/((5 - -1)/6). Let z*h**2 - 2*h + 5*h**5 + 7*h**4 - 5*h**2 - 4*h**3 - 2*h**2 + h**3 = 0. What is h?
-1, -2/5, 0, 1
Let d = 1109 + -1104. Let l(f) be the first derivative of 117*f**d + 845/6*f**6 + 0*f + 20/3*f**3 - 6 + 0*f**2 - 60*f**4. Determine j so that l(j) = 0.
-1, 0, 2/13
Suppose 0 = -4871*f + 4832*f + 117. Let n(m) be the second derivative of -12*m + 0*m**2 + 2/3*m**f + 0 - 1/12*m**4. Find z, given that n(z) = 0.
0, 4
Suppose 4*u + 5 = 5*u. Suppose -u*t + 2*a + 14 = -0*a, -a = -t + 1. Factor -17 - 8 + 30*x - 30*x**3 + 5*x**t - 63*x**2 + 83*x**2.
5*(x - 5)*(x - 1)**2*(x + 1)
Let l(g) be the first derivative of -4*g**3/3 - 868*g**2 - 188356*g + 566. Factor l(v).
-4*(v + 217)**2
Factor -301088/3 - 2/3*l**2 - 1552/3*l.
-2*(l + 388)**2/3
Suppose -5*u - 4*d + 18 = 0, 5*u + 0*d = 2*d + 6. Suppose -1056*a = -1049*a - 133. Solve 6*j + u*j**2 - 21*j**3 + a*j**2 - 6*j**2 = 0 for j.
-2/7, 0, 1
Let v = 56/85 - -16/17. Let w = 210194/19 - 1050932/95. Factor -4/5*m**2 + w*m**4 - v*m**3 + 18/5 + 24/5*m.
2*(m - 3)**2*(m + 1)**2/5
Suppose 54*o + 141*o = 0. Let g(d) be the third derivative of o*d + 1/30*d**6 + 1/3*d**4 + 0*d**3 + 0 - 1/5*d**5 + 12*d**2. Factor g(j).
4*j*(j - 2)*(j - 1)
Let p = 254 + -243. Factor 5*h**2 + 17*h - 11*h - 10*h + 6 + 4 - p*h.
5*(h - 2)*(h - 1)
Let l(r) = 15*r**3 - 160*r**2 - 280*r + 115. Let q(p) = -4*p**2 + p + 1. Let d(n) = l(n) - 5*q(n). Suppose d(v) = 0. What is v?
-2, 1/3, 11
Let k(r) be the first derivative of r**6/15 - 28*r**5/25 + 29*r**4/10 + 352*r**3/15 - 192*r**2/5 - 26. Find x, given that k(x) = 0.
-3, 0, 1, 8
Let s(y) be the second derivative of y**8/5880 - y**7/588 - 31*y**3/3 - 71*y. Let m(b) be the second derivative of s(b). Factor m(w).
2*w**3*(w - 5)/7
Let p(b) = -896*b**2 + 891*b + 27. Let f(w) = -67