5*u + 94*u + 127*u**2 + u**4 - 144*u - 66*u + 13*u**3 - 42*u**3.
(u - 24)*(u - 3)*(u - 1)**2
What is r in 38/17*r**2 - 4*r + 0 - 2/17*r**3 = 0?
0, 2, 17
Let l be 0/15*(-4 - -5)*(-2)/4. Factor 1/3*g**4 + 0*g**3 + 0*g**2 + 0*g + l + 1/3*g**5.
g**4*(g + 1)/3
Let s(x) be the first derivative of x**6/2160 + x**5/90 + x**4/9 + 41*x**3/3 - 20. Let q(w) be the third derivative of s(w). Solve q(b) = 0.
-4
Let b(w) be the first derivative of -2*w**3/21 + 144*w**2/7 - 846*w/7 - 4860. Determine g so that b(g) = 0.
3, 141
Let o(b) = -26*b + 107. Let d be o(4). Factor -53*k**2 - 50*k**2 + 2*k + 102*k**2 - k**d.
-k*(k - 1)*(k + 2)
Let m be ((-6)/9)/(6/(-63)). Suppose 102 = m*i + 74. Factor 2/3 + 4*h**2 + 8/3*h + 8/3*h**3 + 2/3*h**i.
2*(h + 1)**4/3
Let i be 520/(-5280) + (-2)/(-11). Let w(q) be the first derivative of -i*q**3 + 0*q + 0*q**4 - 8 + 1/20*q**5 + 0*q**2. Solve w(g) = 0 for g.
-1, 0, 1
Let t(m) be the first derivative of m**7/147 + 23*m**6/420 - m**5/21 - 21*m**2/2 + m + 69. Let x(r) be the second derivative of t(r). Factor x(b).
2*b**2*(b + 5)*(5*b - 2)/7
Let p(h) = h**5 - h**3 - 3*h - 1. Let c(g) = -10*g**5 + 745*g**4 + 4595*g**3 + 9250*g**2 + 7750*g + 2330. Let x(y) = -c(y) - 5*p(y). Factor x(u).
5*(u - 155)*(u + 1)**3*(u + 3)
Let k(y) be the third derivative of y**7/315 - 49*y**6/180 + 103*y**5/15 - 8*y**4 - 384*y**3 - 13*y**2 + 59*y. Determine s so that k(s) = 0.
-2, 3, 24
Let r = -2 + -13. Let a be (-4 - (r - -7)) + 0 + -2. What is n in 0 + 1/7*n**5 + 1/7*n**4 - 2/7*n - 3/7*n**3 - 5/7*n**a = 0?
-1, 0, 2
Let s(v) = -v**3 - 150*v**2 - 466*v - 71. Let k be s(-3). Factor 342*g**2 - 55/3*g**3 + 1944 + 1/3*g**k - 2268*g.
(g - 18)**3*(g - 1)/3
Let t(z) be the second derivative of -z**6/10 + 3*z**5/20 + 2*z**4 - 6*z**3 - 1810*z. Factor t(k).
-3*k*(k - 2)**2*(k + 3)
Let a be (716/88 - 4) + 960/2640. Determine n, given that 39/4*n**2 - a*n**3 + 12*n - 9/4 = 0.
-1, 1/6, 3
Let 429*g**4 + 0*g - 1/3*g**5 - 138245*g**3 + 413449/3*g**2 + 0 = 0. What is g?
0, 1, 643
Let k = 114304175/3024 + -37799. Let p = k + 13441/3024. Find l such that -8/3 - 2/3*l**2 + p*l = 0.
2/3, 6
Factor 451*q**2 + 478*q**2 - 15*q**3 - q**4 + 147*q + 472*q**2 - 1268*q**2.
-q*(q - 7)*(q + 1)*(q + 21)
Let s(q) be the first derivative of 1/4*q**4 + 46 + 1/25*q**5 + 0*q + 7/15*q**3 + 3/10*q**2. Find p such that s(p) = 0.
-3, -1, 0
Suppose -22*b = -16*b - 4*b. Let n(j) be the second derivative of 49/3*j**3 - 7/6*j**4 - 343/3*j**2 + b + 1/30*j**5 + 26*j. Factor n(c).
2*(c - 7)**3/3
Factor -4/3*m**3 - 34454*m - 25921/3 + 429*m**2.
-(m - 161)**2*(4*m + 1)/3
Let f(p) = p - 4. Let h(k) = -4*k - 20. Let m be h(-7). Let b be f(m). Factor 9*q**b - 27*q - 3*q**5 + 48*q**2 + 13*q**3 + 14*q**4 - 55*q**3 - 5*q**4 + 6.
-3*(q - 2)*(q - 1)**4
Let 98*h - 141 + 3*h**2 + 2*h**2 - h**2 - 7*h**2 + 46*h = 0. Calculate h.
1, 47
Let i be 7 - (-1)/((-80)/(-90)) - (-4)/(-32). Determine m, given that i*m**5 + 537/2*m**3 + 1111/6*m**2 + 260/3*m**4 + 95/2*m + 25/6 = 0.
-5, -1/3, -1/4
Let n(d) be the first derivative of -2*d**3/3 - 117*d**2/5 - 92*d/5 + 1035. Determine x so that n(x) = 0.
-23, -2/5
Factor 0 + 85*p**2 - 85*p + 5*p**4 - 6 + 6 - 35*p**3 + 30.
5*(p - 3)*(p - 2)*(p - 1)**2
Let k(f) be the first derivative of 0*f**2 - f**4 + 4/3*f**3 + 13 + 0*f. Suppose k(l) = 0. What is l?
0, 1
Suppose -4 = -0*u - 2*u. Factor -5318*a**2 + 5420*a**u + 3*a**5 - 23*a**3 - 120 - 34*a**3 + 36*a.
3*(a - 2)**3*(a + 1)*(a + 5)
Suppose 195*y = 187*y + 1 - 1. Let o(l) be the third derivative of 1/16*l**4 + y + 0*l + 1/120*l**5 - 1/3*l**3 - 11*l**2. Factor o(x).
(x - 1)*(x + 4)/2
Let k(j) be the first derivative of 76 - 2*j**2 + j**4 + 0*j + 4/3*j**3 - 4/5*j**5. Factor k(w).
-4*w*(w - 1)**2*(w + 1)
Let c(j) be the third derivative of j**7/84 + 7*j**6/6 + 467*j**5/12 + 875*j**4/2 + 9375*j**3/4 + 33*j**2 + 3*j + 17. Let c(k) = 0. What is k?
-25, -3
Let h(z) be the second derivative of z**5/100 - z**4/10 - 7*z**3/30 + z - 1290. Factor h(d).
d*(d - 7)*(d + 1)/5
Let g(m) = 45*m**3 + 70*m. Let z(r) = -5*r**3 - 8*r. Let u = -394 + 390. Let w(d) = u*g(d) - 35*z(d). Let w(x) = 0. What is x?
0
Let n(p) be the third derivative of -2*p**6/15 + 147*p**5/5 - 91*p**4 + 218*p**3/3 - 1746*p**2. Factor n(z).
-4*(z - 109)*(z - 1)*(4*z - 1)
Factor u**2 + 156 - 4*u - 3*u**2 - 8*u - 142*u.
-2*(u - 1)*(u + 78)
Solve -809*c**2 + 416*c**2 + 395*c**2 - 324 + 322*c = 0 for c.
-162, 1
Let r(c) = c**2 - 26210*c + 104826. Let s be r(4). Factor -1/2*a**4 + 1/4*a**3 + 1/4*a**5 + 0*a**s + 0*a + 0.
a**3*(a - 1)**2/4
Let k(g) be the first derivative of 0*g + 14/3*g**3 + 18/25*g**5 - 9 - 6/5*g**2 - 19/5*g**4. Suppose k(h) = 0. Calculate h.
0, 2/9, 1, 3
Let x = 24 + 359. Suppose 0 = -19*u - 345 + x. What is p in -73/8*p**2 - 21/4*p - 7*p**3 - u*p**4 - 9/8 = 0?
-1, -3/4
Let l(z) = -62*z + 2. Let y be l(1). Let h be (y/(-16) + (-2)/(-8))/1. Solve 4*b + h*b**3 - b**3 + 6*b**2 + 2*b**3 - 3*b**3 = 0 for b.
-2, -1, 0
Let c(t) = -111*t + 13. Let w be c(-10). Factor 3*j - 1124*j**2 + w*j**2 + 3 - j.
-(j - 3)*(j + 1)
Factor 29*d**4 + 48*d**2 - 166*d - 28*d**4 + 95 + 346*d**3 - 324*d**3.
(d - 1)**2*(d + 5)*(d + 19)
Let u(r) = 29*r**2 - 66*r + 7. Let w be (10 - 7)*-16*(-3)/18. Let z(a) = 87*a**2 - 196*a + 20. Let f(h) = w*u(h) - 3*z(h). Find y, given that f(y) = 0.
2/29, 2
Let q(u) be the first derivative of -u**3 + 48*u**2 - 768*u - 940. Determine j, given that q(j) = 0.
16
Let i(p) be the second derivative of p**7/840 - p**6/240 - p**5/20 - p**4/6 + 32*p**2 + p + 11. Let f(n) be the third derivative of i(n). Factor f(s).
3*(s - 2)*(s + 1)
Let o(m) be the second derivative of m**5/20 + 31*m**4/3 + 122*m**3/3 - 257*m. Factor o(a).
a*(a + 2)*(a + 122)
Suppose -4137 = -12*s + 2727. Suppose -156*o**3 - s*o + 53*o**3 + 11*o**4 - 117*o**3 + 7*o**4 + 96 + 678*o**2 = 0. What is o?
2/9, 1, 3, 8
Let p(d) be the third derivative of 1/60*d**5 + 5/12*d**4 + 0 - 11/6*d**3 + d**2 + 5*d. Factor p(m).
(m - 1)*(m + 11)
Let s(v) = v**3 - v**2 + v - 1. Let q(y) = -9*y**3 + 3*y**2 + 186*y + 198. Let w(o) = q(o) + 6*s(o). Solve w(h) = 0 for h.
-8, -1, 8
Let x(d) be the second derivative of d**6/225 - d**5/6 - 113*d**4/90 - 29*d**3/15 - 949*d. Suppose x(v) = 0. What is v?
-3, -1, 0, 29
Let g = 29710/3 + -9895. Factor -4*i**2 - 2 - g*i + 7/3*i**3.
(i - 3)*(i + 1)*(7*i + 2)/3
Let h(o) be the first derivative of -648/19*o - 36 - 2/57*o**3 + 36/19*o**2. Let h(j) = 0. Calculate j.
18
Let g be (14*14/2352*106 - 9)/(4/(-8)). Factor -12*n + 2*n**2 + g*n**3 + 40/3.
(n - 2)**2*(n + 10)/3
Suppose -137 = -4*i + 147. Let s = i - 67. Suppose -92*v**4 + 181*v**s - 90*v**4 + v**2 = 0. What is v?
-1, 0, 1
Factor 272*s + 2/3*s**2 + 27744.
2*(s + 204)**2/3
Let s be (-600)/(-125)*(-9 - -10). Find q such that 32/5*q + s - 18/5*q**3 + 4/5*q**4 - 42/5*q**2 = 0.
-2, -1/2, 1, 6
Let h be (240/54 - 4)*(-4)/(96/(-108)). Suppose -1/2*l**h + 0 - 2*l = 0. What is l?
-4, 0
Factor 2*w**4 - 6412*w**2 + 7110*w**2 + 330*w + 102*w**3 - 4300 + 0*w**4.
2*(w - 2)*(w + 5)**2*(w + 43)
Suppose 4*o = 14*o - 30. Factor -2*g**5 - 6*g - 1 + 0*g**2 - 3 - 42*g**3 + 92*g**3 + 4*g**2 - 42*g**o.
-2*(g - 2)*(g - 1)*(g + 1)**3
Let -2 + 2 - 8*x + 88691*x**3 - 94*x**2 - 88714*x**3 = 0. Calculate x.
-4, -2/23, 0
Factor 2/5*t**2 + 11110898/5 + 9428/5*t.
2*(t + 2357)**2/5
Let x(p) be the first derivative of 3*p**4/16 + 9*p**3/2 - 72*p**2 + 312*p - 618. Solve x(y) = 0.
-26, 4
Let u = 472890 - 472886. Factor 0 - 7/2*h + 1/2*h**u - 9/2*h**3 + 15/2*h**2.
h*(h - 7)*(h - 1)**2/2
Suppose -200 = 6*l - 812. Let b be 2/4*-1 - (-1275)/l. Factor 39*q**2 - 2 + 42*q**3 + b*q - 10 - 27*q**3.
3*(q + 1)*(q + 2)*(5*q - 2)
Let d = -1343493 - -1343495. Suppose 972 + 1/3*u**d - 36*u = 0. Calculate u.
54
Let s be (2 - 208/65)/(0 - 96/60). Factor 1/8*d**2 - 5 + s*d.
(d - 4)*(d + 10)/8
Determine t, given that 0 - 1/4*t**2 - 5/4*t = 0.
-5, 0
Let f = -2676231 - -34842402/13. Let g = f + -3951. Determine b so that 14/13*b**4 - g*b**3 - 2*b + 6/13 + 44/13*b**2 - 2/13*b**5 = 0.
1, 3
Suppose 286*y - 816*y - 7 + 5715*y**2 - 570*y + 67 + 1445*y**4 - 6120*y**3 = 0. What is y?
2/17, 1, 3
Let b(u) be the third derivative of 0*u - 1 + 4/25*u**5 - 1/300*u**6 + 1/60*u**4 + 52*u**2 - 8/5*u**3. Factor b(m).
-2*(m - 24)*(m - 1)*(m + 1)/5
Let z(g) = -3*g**3 - g**2 - g - 2. Let t(a) = 2*a**4 - 71*