 2)*(h + 4)*(h + 5)
Let d(s) be the third derivative of -2*s**5/75 + 107*s**4/20 - 16*s**3/3 - 195*s**2 + 2. Factor d(i).
-2*(i - 80)*(4*i - 1)/5
Let a = 145 + -128. Factor -g**4 + 24*g**2 + 7*g**4 + 3*g**3 - 2*g + a*g - 12*g**4.
-3*g*(g + 1)**2*(2*g - 5)
Let b be ((-8 + 2)/3)/((-320)/60). Let k(w) be the third derivative of 1/10*w**5 + 2/3*w**3 + 26*w**2 + 0*w + 0 + b*w**4 + 1/120*w**6. Factor k(q).
(q + 1)**2*(q + 4)
Let c be 8 + (-4 - (-8 + -2)). Let v(y) = -y**3 + 13*y**2 + 22*y - 112. Let s be v(c). Find i such that s - 2/3*i**4 - 1/3*i**5 + 0*i**3 + 2/3*i**2 + 1/3*i = 0.
-1, 0, 1
Let i(v) be the first derivative of v**6/66 - 12*v**5/55 - 115*v**4/44 - 322*v**3/33 - 186*v**2/11 - 152*v/11 + 3987. Factor i(w).
(w - 19)*(w + 1)*(w + 2)**3/11
Let k(c) be the third derivative of c**6/600 + 79*c**5/300 - 27*c**4/20 - 66*c**2 - 6*c + 6. What is a in k(a) = 0?
-81, 0, 2
Let p be (-3)/(((-15)/(-4))/5). Let r be p/(-6)*198/12. Solve -2*v + r*v**3 + 3*v**2 + v**2 - 13*v**3 = 0.
0, 1
Let p(x) = x**3 - 50*x**2 + 51*x - 109. Let l be p(49). Let f be (21 + l)*11/22. Determine r so that -4/3*r**4 + 1/3*r**f + 5/3*r**3 + 0*r + 0 - 2/3*r**2 = 0.
0, 1, 2
Suppose 4*j - 4 = 4*a, 8*a - 6 = 5*a. Solve -12*y**3 + 13*y**j + 10 + y**2 - 10 = 0.
-1, 0
Factor -88*c**2 + 283*c**2 - 105*c**2 - 87*c**2 + 576*c.
3*c*(c + 192)
Determine p so that -81/2 + 163/4*p - 1/4*p**2 = 0.
1, 162
Suppose -33 = -92*m + 81*m. Let k = -3 - -5. Suppose -o**4 - 9 - 4*o**m + 51*o - 39*o + 4*o**k - 2*o**2 = 0. What is o?
-3, 1
Let j(p) be the third derivative of p**7/280 - 19*p**6/480 - 29*p**5/240 + 215*p**4/96 + 25*p**3/4 - 2*p**2 - 90. Solve j(m) = 0.
-3, -2/3, 5
Determine d, given that 2696*d - 1182 - 402 - 52*d**4 - 1189*d**2 + 462*d**3 + 2*d**5 - 495*d**2 = 0.
2, 9, 11
Let j(d) be the first derivative of -d**6/24 + d**5/6 + 5*d**4/24 - 5*d**3/3 - 9*d**2/2 + d + 46. Let t(g) be the second derivative of j(g). Factor t(a).
-5*(a - 2)*(a - 1)*(a + 1)
Let r(a) be the second derivative of 8*a**4 + 0 + 52/3*a**3 + 6/5*a**5 + 111*a - 2/15*a**6 + 18*a**2. What is i in r(i) = 0?
-1, 9
What is q in 377*q**2 - 113*q**2 - 115*q**2 + 515 - 147*q**2 + 1311 - 188*q = 0?
11, 83
Let u(s) be the third derivative of 1/30*s**5 - 82*s**2 - 2*s + 5/24*s**4 + 0 + 1/2*s**3. Determine a, given that u(a) = 0.
-3/2, -1
Factor 394299 + 3*k**2 + 12*k**2 - 788601 + 394302 + 50*k.
5*k*(3*k + 10)
Let x(l) be the third derivative of -l**6/12 + 33*l**5/4 + 775*l**4/24 - 85*l**3 - 4*l**2 + 46*l. Factor x(r).
-5*(r - 51)*(r + 2)*(2*r - 1)
Let j(b) be the first derivative of b**4/30 + 18*b**3/5 + 729*b**2/5 - 21*b - 169. Let a(k) be the first derivative of j(k). Factor a(c).
2*(c + 27)**2/5
Let p(a) be the first derivative of 0*a + 0*a**4 + 1/12*a**5 - 5 + 5*a**2 - 5/6*a**3. Let w(r) be the second derivative of p(r). Factor w(f).
5*(f - 1)*(f + 1)
Suppose 14*g - 104 - 232 = 0. Suppose 0 = 5*h - 14 - 1. Factor g*s**3 - 6*s**2 - 4*s**h - 9*s**2 + 7*s**2 - 16*s**4 + 4*s**5.
4*s**2*(s - 2)*(s - 1)**2
Let p(v) be the first derivative of -v**5/120 - v**4/6 - 7*v**3/12 + 87*v**2/2 - 12. Let h(f) be the second derivative of p(f). Determine m so that h(m) = 0.
-7, -1
Let q(s) = s**3 + 3*s**2 - 53*s + 11. Let w be q(-9). Factor -968*m + 305*m + 4 + 16 - 717*m + 23805*m**w.
5*(69*m - 2)**2
Factor -658*n + 131*n - 4*n**2 - 2280 - 32 + 323*n.
-4*(n + 17)*(n + 34)
Let f(b) be the second derivative of -2 - 16/9*b**3 - 1/9*b**4 - 37*b + 17/6*b**2. Factor f(j).
-(2*j - 1)*(2*j + 17)/3
Let u be ((12/8)/(-3))/((-3)/24). Let r(p) = -4*p**2 - 80*p + 88. Let k(i) = i. Let s(t) = u*k(t) - r(t). Find n such that s(n) = 0.
-22, 1
Let m(o) = o + 8. Let v be m(-6). Let s(t) = -t**3 - 5*t**2 - 9*t - 2. Let j be s(-7). Factor -139*p - 15 + 4*p**v + j*p - 9*p**2.
-5*(p - 3)*(p - 1)
Let y(v) be the first derivative of v**4/24 + 50*v**3/9 + 91*v**2 + 528*v - 5621. Suppose y(n) = 0. What is n?
-88, -6
Let g(t) = -2*t**3 - 2*t - 1. Let s(m) = -5*m**3 + 2*m**2 - 3*m - 4. Let d(w) = 6*g(w) - 3*s(w). Solve d(h) = 0.
-1, 1, 2
Let k(t) be the first derivative of t**6/7 + 306*t**5/35 + 1080*t**4/7 + 3448*t**3/7 - 576*t**2/7 - 13824*t/7 + 113. Determine d so that k(d) = 0.
-24, -2, 1
Let q(g) be the first derivative of -31*g**5/220 - 95*g**4/264 - g**3/33 + g**2/2 + 5*g - 115. Let m(a) be the second derivative of q(a). Solve m(o) = 0 for o.
-1, -2/93
Let l = -215703/5 - -43141. Factor 1/5*g + 0 + 1/5*g**3 - l*g**2.
g*(g - 1)**2/5
Let n be (130/3)/(26/(-117)). Let h be ((-12)/(-8))/(n/(-20)). Let h*c + 4/13 - 4/13*c**2 - 2/13*c**3 = 0. Calculate c.
-2, -1, 1
Let y(n) = 1. Let o(b) = 4*b - 5. Let d(m) = o(m) + 4*y(m). Let v be d(1). Factor -3*w**2 + 4 + w + w + w**4 - 2*w**v + 4*w - 2*w.
(w - 2)**2*(w + 1)**2
Let t(o) = -6*o - 3 + 3 + 2 + 5*o. Let h(p) = -p**2 + 29*p + 14. Let g(a) = -5*h(a) + 35*t(a). Factor g(u).
5*u*(u - 36)
Let o(s) be the third derivative of 0 + 2209/18*s**3 + 9*s - 5*s**2 + 1/180*s**5 + 47/36*s**4. Determine w so that o(w) = 0.
-47
Let x(u) be the third derivative of -25/3*u**3 + 0 - 1/48*u**5 + 0*u - 65/96*u**4 - 103*u**2. Factor x(b).
-5*(b + 5)*(b + 8)/4
Let l(b) = -21*b + 2*b**2 - 11*b - 4*b - 3*b**2 + 7*b - 180. Let s be l(-20). Factor 0*c + 0*c**2 - 2/9*c**4 + 4/9*c**3 + s - 2/9*c**5.
-2*c**3*(c - 1)*(c + 2)/9
Let i(s) be the third derivative of s**6/40 + 23*s**5/32 - 39*s**4/32 - 45*s**3/16 - 8393*s**2. Factor i(j).
3*(j - 1)*(j + 15)*(8*j + 3)/8
Let m = -1/4190 - -211/6285. Let f(w) be the second derivative of 5*w - 1/20*w**5 + 1/42*w**7 + 0*w**2 + 0*w**3 - m*w**6 + 1/12*w**4 + 0. Factor f(a).
a**2*(a - 1)**2*(a + 1)
Find i, given that 453*i**4 + 20*i - 132*i**5 - 12*i**3 + 321*i**5 - 581*i**2 + 209*i**2 - 23*i - 93*i = 0.
-2, -1, -2/7, 0, 8/9
What is i in -108 - 40*i**4 - 632*i**2 + 540*i + 32*i**3 + 51*i**3 + 140*i**3 - 52*i**2 + 69*i**3 = 0?
3/10, 1, 3
Let a = 1456 + -1182. Let r = 278 - a. Factor 4/5*o - 4/5 + 3/5*o**2 - 2/5*o**3 - 1/5*o**r.
-(o - 1)**2*(o + 2)**2/5
Suppose 31*c - 255 = 303. Let i be ((-140)/c)/(14/(-21)). Let -25/3 - i*g - 1/3*g**3 - 11/3*g**2 = 0. Calculate g.
-5, -1
Let c = 326461 - 326459. Factor 4/11*l**c + 0 + 2/11*l**3 + 0*l.
2*l**2*(l + 2)/11
Factor -2/9*j**3 - 52*j**2 + 0 + 2390/9*j.
-2*j*(j - 5)*(j + 239)/9
Let a(t) be the third derivative of -t**7/1470 + t**6/168 + 37*t**5/140 + 29*t**4/24 + 7*t**3/3 - 9462*t**2. Factor a(r).
-(r - 14)*(r + 1)**2*(r + 7)/7
Let g(u) be the second derivative of u**7/294 + 17*u**6/70 - 16*u**5/5 + 346*u**4/21 - 312*u**3/7 + 472*u**2/7 - 560*u. Find i, given that g(i) = 0.
-59, 2
Suppose h - 4 = -3*o, -2*h + 4*o - o - 1 = 0. Let c be h + (-100)/(-36) - (-4)/18. Solve 35*r**3 + c*r**2 - 12*r**3 + 4*r**4 - 15*r**3 = 0 for r.
-1, 0
Let q(o) be the first derivative of -o**5/45 + 137*o**4/36 - 4891*o**3/27 + 4489*o**2/6 - 8912. Find b, given that q(b) = 0.
0, 3, 67
Let m = -745 - -733. Let f be (2/14)/((-4)/m) - 0. Factor -3/7*r**4 + 9/7*r**3 - 9/7*r**2 + 0 + f*r.
-3*r*(r - 1)**3/7
Let d(q) = -12*q**3 + q**2 - q - 1. Let o(m) = 236*m**3 + 2368*m**2 - 475192*m + 31522416. Let t(f) = -20*d(f) - o(f). Factor t(p).
4*(p - 199)**3
Let c be (-1430)/121 - 6/33. Let o be 13/(78/c)*6/(-15). Determine x so that o*x**3 - 36/5*x**2 + 96/5*x - 64/5 = 0.
1, 4
Let h(a) be the second derivative of -a**4/24 + 295*a**3/6 + 591*a**2/4 + 150*a + 5. Factor h(d).
-(d - 591)*(d + 1)/2
Let d(r) be the first derivative of 19 + r**3 + 0*r - 21/2*r**2. Factor d(s).
3*s*(s - 7)
Let w = 221/447 + 5/894. Factor -1/2*z**2 + w + 0*z.
-(z - 1)*(z + 1)/2
Let 891/4 - 3/8*i**2 - 171/8*i = 0. What is i?
-66, 9
Let i be 39425/57 + (-1 - -1) + 1. Let r = 693 - i. Factor 1/3*b**3 - 1/3*b + 0 + 1/3*b**4 - r*b**2.
b*(b - 1)*(b + 1)**2/3
Let t(m) = 4*m**2 - 120*m + 308. Let z(v) = 43 - 4*v + v**2 - 36*v + 60. Suppose -4*x + 31 = g, 9*x - 7*x + 2*g = 14. Let n(s) = x*z(s) - 3*t(s). Factor n(b).
-4*(b - 5)**2
Let b(y) be the third derivative of 0 + 1/120*y**6 + 18*y**2 + 32*y**4 + 0*y + 2048/3*y**3 + 4/5*y**5. Factor b(o).
(o + 16)**3
Let g(l) be the third derivative of 121/6*l**4 - 22/15*l**5 + 1/30*l**6 + 0 + 3*l + 0*l**3 - l**2. Let g(q) = 0. What is q?
0, 11
Let y = -21131/3 - -42271/6. Factor -21/4*u - 3 - y*u**2 + 3/4*u**3.
3*(u - 4)*(u + 1)**2/4
Let -99/4*v + 189/4 + 3/4*v**2 + 3/4*v**3 = 0. Calculate v.
-7,